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Dimension

Authors:
(1) Todd K. Moon, Electrical and Computer Engineering Department, Utah State University, Logan, Utah;
(2) Jacob H. Gunther, Electrical and Computer Engineering Department, Utah State University, Logan, Utah. Table of Links Abstract and 1 Introduction and Background 2 Statistical Parsing and Extracted Features 3 Parse Tree Features 4 Classifier 5 Dimension Reduction 6 The Federalist Papers 6.1 Sanditon 7 Conclusions, Discussion, and Future Work A. A Brief Introduction to Statistical Parsing B. Dimension Reduction: Some Mathematical Details References B Dimension Reduction: Some Mathematical Details This material is drawn from [27]. The trace of Sw provides a measure of the clustering of the feature for each class around their respective centroids, Note that Sw, being the sum of the outer product of n terms, generically has rank min(n, m). In the work here, the dimension of the feature vectors m is very large, so that rank(Sw) = n; Sw is singular. Similarly, tr(Sb) measures the total distance between cluster centroids and the overall centroid, A measure of cluster quality which measures the degree to which tr(Sw) is small and tr(Sb) is large is To express the algorithm, the following matrices are defined. The scatter matrices Sw, Sb and Sm can be expressed in terms of the matrices That is, Hm, Hb and Hm form factors of the respective scatter matrices. The algorithm for computing G is shown below. (adapted from Algorithm 1 of [27]). References [1] R. Lord, “de Morgan and the Statistical Study of Literary Style,” Biometrica, vol. 3, p. 282, 1958. [2] A. Morton, Literary Detection. New York: Charles Scribner’s Sons, 1978. [3] T. Mendenhall, “A Mechanical Solution of a Literary Problem,” Popular Science Monthly, 1901. [4] C. D. Chretien, “A Statistical Method for Determining Authorship: The Junius Letters,” Languages, vol. 40, pp. 95–90, 1964. [5] D. Wishart and S. V. Leach, “A Multivariate Analysis of Platonic Prose Rhythm,” Computer Studies in the Humanities and Verbal Behavior, vol. 3, no. 2, pp. 109–125, 1972. [6] C. S. Brinegar, “Mark Twain and the Quintis Curtis Snodgrass Letters: A Statistical Test of Authorship,” Journal of the Americal Statistical Association, vol. 53, p. 85, 1963. [7] F. Mosteller and D. Wallace, Inference and Disputed Authorship: The Federalist. Reading, MA: Addison Wesley, 1964. [8] P. Hanus and J. Hagenauer, “Information Theory Helps Historians,” IEEE Information Theory Society Newsletter, vol. 55, p. 8, Sept. 2005. [9] D. Holmes, “The analysis of literary style — a review,” J. Royal Statistical Society, Series A, vol. 148, no. 4, pp. 328–341, 1985. [10] J. L. Hilton, “On Verifying Wordprint Studies: Book of Mormon Authorship,” Brigham Young University Studies, 1990. [11] D. Holmes, “A Stylometric Analysis of Mormon Scriptures and Related Texts,” Journal of the Royal Statistical Society, A, vol. 155, pp. 91–120, 1992. [12] K. Luyckx and W. Daelemans, “Shallow text analysis and machine learning for authorship attribution,” in Proceedings of the Fifteenth Meeting of Computational Linguistics in the Netherlands, pp. 149–160, 2005. [13] J. Grieve, “Quantitative authorship attribution: an evaluation of techniques,” Liter. Linguist. Comput., vol. 22, no. 3, pp. 251–270, 2007. [14] F. Iqbal, H. Binsalleeh, B. Fung, and M. Debbabi, “A unified data mining solution for authorship analysis in anonymous textual communication,” Inform. Sci, vol. 231, pp. 98–112, 2007. [15] E. Stamatos, “A survey of modern authorship attribution methods,” J. Am. Soc. Inform. Sci. Technol., vol. 60, no. 3, pp. 538–556, 2009. [16] C. Zhang, X. Wu, Z. Niu, and W. Ding, “Authorship identification from unstructured texts,” Knowledge-Based Systems, vol. 66, pp. 99–111, 2014. [17] I. Jolliffe, Principal Component Analysis. New York: Springer-Verlag, 1986. [18] S. Corbara, B. Chulvi, and A. Moreo, Experimental IR meets multilingality, multimodality, and interaction, vol. 13390 of Lecture Notes in Computer Science, ch. Rythmic and Psycholinguistic Features for Authorship Tasks in the Spanish Parliament: Evaluation and Analysis. Springer, 2022. [19] S. Corbara, C. C. Ferriols, P. Rosso, and A. Moreo, Natural Language Processing and Information Systems, vol. 13286 of Lecture Notes in Computer Science, ch. Investigating Topic-Agnostic Features for Authorship Tasks in Spanish Political Speeches. Springer, 2022. [20] M. Sanchez-Perez, I. Markov, H. Gomez-Adorno, and G. Sidorov, ´ Experimental IR Meets Multilinguality, Multimodality, and Interaction, vol. 10456 of Lecture Notes in Computer Science, ch. Comparison of Character n-grams and Lexical Features on Author, Gender, and Language Variety Identification on the Same Spanish News Corpus. Springer, 2017. [21] D. Klein and C. D. Manning, “Accurate unlexicalized parsing,” in Proceedings of the 41st Annual Meeting on Association for Computational Linguistics, vol. 1, pp. 423–430, 2003. https://doi.org/10.3115/1075096.1075150. [22] M. P. Marcus, B. Santorini, and M. A. Marcinkiewicz, “Building a Large Annotated Corpus of English: The Penn Treebank,” Computational Linguisistics, vol. 19, no. 2, pp. 313–330, 1993. [23] A. Taylor, M. Marcus, and B. Santorini, “The Penn Treebank: An Overview.” https://www. researchgate.net/publication/2873803_The_Penn_Treebank_An_overview, 2003. [24] D. Klein and C. D. Mannning, “Accurate unlexicalized parsing,” in Proceedings of the 41st Meeting of the Association for Computational Linguisistics, pp. 423–430, 2003. [25] T. S. N. L. Group, “Software: Stanford parser.” https://nlp.stanford.edu/software/ lex-parser.html, 2020. [26] D. Juraksky and J. H. Martin, Speech and Language Processing: An introduction to natural language processing, computational linguistics, and speech recognition. Upper Saddle River, NJ: Prentice-Hall, 2009. [27] P. Howland, M. Jeon, and H. Park, “Structure preserving dimension reduction for clustered text data based on the generalized singular value decomposition,” SIAM J. Matrix Anal. Appl., vol. 25, no. 1, pp. 165–179, 2003. [28] T. K. Moon, P. Howland, and J. H. Gunther, “Document author classification using generalized discriminant analysis,” in SIAM Conference on Text Mining, (Baltimore, MD), May 23–25 2006. [29] P. Howland, J. Wang, and H. Park, “Solving the small sample size problem in face recognition using generalized discriminant analysis,” Pattern Recognition, vol. 39, pp. 277–287, 2006. [30] A. Hamilton, J. Madison, and J. Jay, “The Federalist,” in American State Papers (R. M. Hutchins, ed.), vol. 43 of Great Books of the Western World, pp. 29–266, Encyclopedia Britannica, Chicago ed., 1952. [31] A. Hamilton, J. Madison, and J. Jay, “The Federalist (machine readable).” http://www.gutenberg.org /etext/18. [32] P. Poplawski, A Jane Austen Encyclopedia. London: Aldwych Press, 1998. [33] J. Austen and A. Lady, Sanditon. London: Peter Davies, 1975. [34] D. Hopkinson, “Completions,” in The Jane Austen Companion (J. D. Grey, ed.), Macmillan, 1986. [35] “Sanditon (machine readable).” http://etext.lib.virginia.edu/toc/modeng/public/ AusSndt.html. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Todd K. Moon, Electrical and Computer Engineering Department, Utah State University, Logan, Utah; (2) Jacob H. Gunther, Electrical and Computer Engineering Department, Utah State University, Logan, Utah. Authors: Authors: (1) Todd K. Moon, Electrical and Computer Engineering Department, Utah State University, Logan, Utah; (2) Jacob H. Gunther, Electrical and Computer Engineering Department, Utah State University, Logan, Utah. Table of Links Abstract and 1 Introduction and Background Abstract and 1 Introduction and Background 2 Statistical Parsing and Extracted Features 2 Statistical Parsing and Extracted Features 3 Parse Tree Features 3 Parse Tree Features 4 Classifier 4 Classifier 5 Dimension Reduction 5 Dimension Reduction 6 The Federalist Papers 6 The Federalist Papers 6.1 Sanditon 6.1 Sanditon 7 Conclusions, Discussion, and Future Work 7 Conclusions, Discussion, and Future Work A. A Brief Introduction to Statistical Parsing A. A Brief Introduction to Statistical Parsing B. Dimension Reduction: Some Mathematical Details B. Dimension Reduction: Some Mathematical Details References References B Dimension Reduction: Some Mathematical Details This material is drawn from [27]. The trace of Sw provides a measure of the clustering of the feature for each class around their respective centroids, Note that Sw, being the sum of the outer product of n terms, generically has rank min(n, m). In the work here, the dimension of the feature vectors m is very large, so that rank(Sw) = n; Sw is singular. Similarly, tr(Sb) measures the total distance between cluster centroids and the overall centroid, A measure of cluster quality which measures the degree to which tr(Sw) is small and tr(Sb) is large is To express the algorithm, the following matrices are defined. The scatter matrices Sw, Sb and Sm can be expressed in terms of the matrices That is, Hm, Hb and Hm form factors of the respective scatter matrices. The algorithm for computing G is shown below. (adapted from Algorithm 1 of [27]). References [1] R. Lord, “de Morgan and the Statistical Study of Literary Style,” Biometrica, vol. 3, p. 282, 1958. [2] A. Morton, Literary Detection. New York: Charles Scribner’s Sons, 1978. [3] T. Mendenhall, “A Mechanical Solution of a Literary Problem,” Popular Science Monthly, 1901. [4] C. D. Chretien, “A Statistical Method for Determining Authorship: The Junius Letters,” Languages, vol. 40, pp. 95–90, 1964. [5] D. Wishart and S. V. Leach, “A Multivariate Analysis of Platonic Prose Rhythm,” Computer Studies in the Humanities and Verbal Behavior, vol. 3, no. 2, pp. 109–125, 1972. [6] C. S. Brinegar, “Mark Twain and the Quintis Curtis Snodgrass Letters: A Statistical Test of Authorship,” Journal of the Americal Statistical Association, vol. 53, p. 85, 1963. [7] F. Mosteller and D. Wallace, Inference and Disputed Authorship: The Federalist. Reading, MA: Addison Wesley, 1964. [8] P. Hanus and J. Hagenauer, “Information Theory Helps Historians,” IEEE Information Theory Society Newsletter, vol. 55, p. 8, Sept. 2005. [9] D. Holmes, “The analysis of literary style — a review,” J. Royal Statistical Society, Series A, vol. 148, no. 4, pp. 328–341, 1985. [10] J. L. Hilton, “On Verifying Wordprint Studies: Book of Mormon Authorship,” Brigham Young University Studies, 1990. [11] D. Holmes, “A Stylometric Analysis of Mormon Scriptures and Related Texts,” Journal of the Royal Statistical Society, A, vol. 155, pp. 91–120, 1992. [12] K. Luyckx and W. Daelemans, “Shallow text analysis and machine learning for authorship attribution,” in Proceedings of the Fifteenth Meeting of Computational Linguistics in the Netherlands, pp. 149–160, 2005. [13] J. Grieve, “Quantitative authorship attribution: an evaluation of techniques,” Liter. Linguist. Comput., vol. 22, no. 3, pp. 251–270, 2007. [14] F. Iqbal, H. Binsalleeh, B. Fung, and M. Debbabi, “A unified data mining solution for authorship analysis in anonymous textual communication,” Inform. Sci, vol. 231, pp. 98–112, 2007. [15] E. Stamatos, “A survey of modern authorship attribution methods,” J. Am. Soc. Inform. Sci. Technol., vol. 60, no. 3, pp. 538–556, 2009. [16] C. Zhang, X. Wu, Z. Niu, and W. Ding, “Authorship identification from unstructured texts,” Knowledge-Based Systems, vol. 66, pp. 99–111, 2014. [17] I. Jolliffe, Principal Component Analysis. New York: Springer-Verlag, 1986. [18] S. Corbara, B. Chulvi, and A. Moreo, Experimental IR meets multilingality, multimodality, and interaction, vol. 13390 of Lecture Notes in Computer Science, ch. Rythmic and Psycholinguistic Features for Authorship Tasks in the Spanish Parliament: Evaluation and Analysis. Springer, 2022. [19] S. Corbara, C. C. Ferriols, P. Rosso, and A. Moreo, Natural Language Processing and Information Systems, vol. 13286 of Lecture Notes in Computer Science, ch. Investigating Topic-Agnostic Features for Authorship Tasks in Spanish Political Speeches. Springer, 2022. [20] M. Sanchez-Perez, I. Markov, H. Gomez-Adorno, and G. Sidorov, ´ Experimental IR Meets Multilinguality, Multimodality, and Interaction, vol. 10456 of Lecture Notes in Computer Science, ch. Comparison of Character n-grams and Lexical Features on Author, Gender, and Language Variety Identification on the Same Spanish News Corpus. Springer, 2017. [21] D. Klein and C. D. Manning, “Accurate unlexicalized parsing,” in Proceedings of the 41st Annual Meeting on Association for Computational Linguistics, vol. 1, pp. 423–430, 2003. https://doi.org/10.3115/1075096.1075150. [22] M. P. Marcus, B. Santorini, and M. A. Marcinkiewicz, “Building a Large Annotated Corpus of English: The Penn Treebank,” Computational Linguisistics, vol. 19, no. 2, pp. 313–330, 1993. [23] A. Taylor, M. Marcus, and B. Santorini, “The Penn Treebank: An Overview.” https://www. researchgate.net/publication/2873803_The_Penn_Treebank_An_overview, 2003. [24] D. Klein and C. D. Mannning, “Accurate unlexicalized parsing,” in Proceedings of the 41st Meeting of the Association for Computational Linguisistics, pp. 423–430, 2003. [25] T. S. N. L. Group, “Software: Stanford parser.” https://nlp.stanford.edu/software/ lex-parser.html, 2020. [26] D. Juraksky and J. H. Martin, Speech and Language Processing: An introduction to natural language processing, computational linguistics, and speech recognition. Upper Saddle River, NJ: Prentice-Hall, 2009. [27] P. Howland, M. Jeon, and H. Park, “Structure preserving dimension reduction for clustered text data based on the generalized singular value decomposition,” SIAM J. Matrix Anal. Appl., vol. 25, no. 1, pp. 165–179, 2003. [28] T. K. Moon, P. Howland, and J. H. Gunther, “Document author classification using generalized discriminant analysis,” in SIAM Conference on Text Mining, (Baltimore, MD), May 23–25 2006. [29] P. Howland, J. Wang, and H. Park, “Solving the small sample size problem in face recognition using generalized discriminant analysis,” Pattern Recognition, vol. 39, pp. 277–287, 2006. [30] A. Hamilton, J. Madison, and J. Jay, “The Federalist,” in American State Papers (R. M. Hutchins, ed.), vol. 43 of Great Books of the Western World, pp. 29–266, Encyclopedia Britannica, Chicago ed., 1952. [31] A. Hamilton, J. Madison, and J. Jay, “The Federalist (machine readable).” http://www.gutenberg.org /etext/18. [32] P. Poplawski, A Jane Austen Encyclopedia. London: Aldwych Press, 1998. [33] J. Austen and A. Lady, Sanditon. London: Peter Davies, 1975. [34] D. Hopkinson, “Completions,” in The Jane Austen Companion (J. D. Grey, ed.), Macmillan, 1986. [35] “Sanditon (machine readable).” http://etext.lib.virginia.edu/toc/modeng/public/ AusSndt.html. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

A Mathematical Overview of Dimension Reduction in Text Classification

Authors:
(1) Tony Lee, Stanford with Equal contribution;
(2) Michihiro Yasunaga, Stanford with Equal contribution;
(3) Chenlin Meng, Stanford with Equal contribution;
(4) Yifan Mai, Stanford;
(5) Joon Sung Park, Stanford;
(6) Agrim Gupta, Stanford;
(7) Yunzhi Zhang, Stanford;
(8) Deepak Narayanan, Microsoft;
(9) Hannah Benita Teufel, Aleph Alpha;
(10) Marco Bellagente, Aleph Alpha;
(11) Minguk Kang, POSTECH;
(12) Taesung Park, Adobe;
(13) Jure Leskovec, Stanford;
(14) Jun-Yan Zhu, CMU;
(15) Li Fei-Fei, Stanford;
(16) Jiajun Wu, Stanford;
(17) Stefano Ermon, Stanford;
(18) Percy Liang, Stanford. Table of Links Abstract and 1 Introduction 2 Core framework 3 Aspects 4 Scenarios 5 Metrics 6 Models 7 Experiments and results 8 Related work 9 Conclusion 10 Limitations Author contributions, Acknowledgments and References A Datasheet B Scenario details C Metric details D Model details E Human evaluation procedure 8 Related work Holistic benchmarking. Benchmarks drive the advancements of AI by orienting the directions for the community to improve upon [20, 56, 57, 58]. In particular, in natural language processing (NLP), the adoption of meta-benchmarks [59, 60, 61, 62] and holistic evaluation [1] across multiple scenarios or tasks has allowed for comprehensive assessments of models and accelerated model improvements. However, despite the growing popularity of image generation and the increasing number of models being developed, a holistic evaluation of these models has been lacking. Furthermore, image generation encompasses various technological and societal impacts, including alignment, quality, originality, toxicity, bias, and fairness, which necessitate comprehensive evaluation. Our work fills this gap by conducting a holistic evaluation of image generation models across 12 important aspects. Benchmarks for image generation. Existing benchmarks primarily focus on assessing image quality and alignment, using automated metrics [23, 36, 24, 63, 64, 65]. Widely used benchmarks such as MS-COCO [21] and ImageNet [20] have been employed to evaluate the quality and alignment of generated images. Metrics like Fréchet Inception Distance (FID) [23, 66], Inception Score [36], and CLIPScore [24] are commonly used for quantitative assessment of image quality and alignment. To better capture human perception in image evaluation, crowdsourced human evaluation has been explored in recent years [25, 6, 35, 67]. However, these evaluations have been limited to assessing aspects such as alignment and quality. Building upon these crowdsourcing techniques, we extend the evaluation to include additional aspects such as aesthetics, originality, reasoning, and fairness. As the ethical and societal impacts of image generation models gain prominence [19], researchers have also started evaluating these aspects [33, 29, 8]. However, these evaluations have been conducted on only a select few models, leaving the majority of models unevaluated in these aspects. Our standardized evaluation addresses this gap by enabling the evaluation of all models across all aspects, including ethical and societal dimensions. Art and design. Our assessment of image generation incorporates aesthetic evaluation and design principles. Aesthetic evaluation considers factors like composition, color harmony, balance, and visual complexity [68, 69]. Design principles, such as clarity, legibility, hierarchy, and consistency in design elements, also influence our evaluation [70]. Combining these insights, we aim to determine whether generated images are visually pleasing, with thoughtful compositions, harmonious colors, balanced elements, and an appropriate level of visual complexity. We employ objective metrics and subjective human ratings for a comprehensive assessment of aesthetic quality. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Tony Lee, Stanford with Equal contribution; (2) Michihiro Yasunaga, Stanford with Equal contribution; (3) Chenlin Meng, Stanford with Equal contribution; (4) Yifan Mai, Stanford; (5) Joon Sung Park, Stanford; (6) Agrim Gupta, Stanford; (7) Yunzhi Zhang, Stanford; (8) Deepak Narayanan, Microsoft; (9) Hannah Benita Teufel, Aleph Alpha; (10) Marco Bellagente, Aleph Alpha; (11) Minguk Kang, POSTECH; (12) Taesung Park, Adobe; (13) Jure Leskovec, Stanford; (14) Jun-Yan Zhu, CMU; (15) Li Fei-Fei, Stanford; (16) Jiajun Wu, Stanford; (17) Stefano Ermon, Stanford; (18) Percy Liang, Stanford. Authors: Authors: (1) Tony Lee, Stanford with Equal contribution; (2) Michihiro Yasunaga, Stanford with Equal contribution; (3) Chenlin Meng, Stanford with Equal contribution; (4) Yifan Mai, Stanford; (5) Joon Sung Park, Stanford; (6) Agrim Gupta, Stanford; (7) Yunzhi Zhang, Stanford; (8) Deepak Narayanan, Microsoft; (9) Hannah Benita Teufel, Aleph Alpha; (10) Marco Bellagente, Aleph Alpha; (11) Minguk Kang, POSTECH; (12) Taesung Park, Adobe; (13) Jure Leskovec, Stanford; (14) Jun-Yan Zhu, CMU; (15) Li Fei-Fei, Stanford; (16) Jiajun Wu, Stanford; (17) Stefano Ermon, Stanford; (18) Percy Liang, Stanford. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Core framework 2 Core framework 3 Aspects 3 Aspects 4 Scenarios 4 Scenarios 5 Metrics 5 Metrics 6 Models 6 Models 7 Experiments and results 7 Experiments and results 8 Related work 8 Related work 9 Conclusion 9 Conclusion 10 Limitations 10 Limitations Author contributions, Acknowledgments and References Author contributions, Acknowledgments and References A Datasheet A Datasheet B Scenario details B Scenario details C Metric details C Metric details D Model details D Model details E Human evaluation procedure E Human evaluation procedure 8 Related work Holistic benchmarking. Benchmarks drive the advancements of AI by orienting the directions for the community to improve upon [20, 56, 57, 58]. In particular, in natural language processing (NLP), the adoption of meta-benchmarks [59, 60, 61, 62] and holistic evaluation [1] across multiple scenarios or tasks has allowed for comprehensive assessments of models and accelerated model improvements. However, despite the growing popularity of image generation and the increasing number of models being developed, a holistic evaluation of these models has been lacking. Furthermore, image generation encompasses various technological and societal impacts, including alignment, quality, originality, toxicity, bias, and fairness, which necessitate comprehensive evaluation. Our work fills this gap by conducting a holistic evaluation of image generation models across 12 important aspects. Holistic benchmarking. Benchmarks for image generation. Existing benchmarks primarily focus on assessing image quality and alignment, using automated metrics [23, 36, 24, 63, 64, 65]. Widely used benchmarks such as MS-COCO [21] and ImageNet [20] have been employed to evaluate the quality and alignment of generated images. Metrics like Fréchet Inception Distance (FID) [23, 66], Inception Score [36], and CLIPScore [24] are commonly used for quantitative assessment of image quality and alignment. Benchmarks for image generation. To better capture human perception in image evaluation, crowdsourced human evaluation has been explored in recent years [25, 6, 35, 67]. However, these evaluations have been limited to assessing aspects such as alignment and quality. Building upon these crowdsourcing techniques, we extend the evaluation to include additional aspects such as aesthetics, originality, reasoning, and fairness. As the ethical and societal impacts of image generation models gain prominence [19], researchers have also started evaluating these aspects [33, 29, 8]. However, these evaluations have been conducted on only a select few models, leaving the majority of models unevaluated in these aspects. Our standardized evaluation addresses this gap by enabling the evaluation of all models across all aspects, including ethical and societal dimensions. Art and design. Our assessment of image generation incorporates aesthetic evaluation and design principles. Aesthetic evaluation considers factors like composition, color harmony, balance, and visual complexity [68, 69]. Design principles, such as clarity, legibility, hierarchy, and consistency in design elements, also influence our evaluation [70]. Combining these insights, we aim to determine whether generated images are visually pleasing, with thoughtful compositions, harmonious colors, balanced elements, and an appropriate level of visual complexity. We employ objective metrics and subjective human ratings for a comprehensive assessment of aesthetic quality. Art and design. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

New Dimensions in Text-to-Image Model Evaluation

Vector Databases: Unlocking New Dimensions in Similarity Search 

Authors:
(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);
(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions We have investigated whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field coupled to fermions in the RS warped spacetime or not. Imposing CBCs on fields involved in inflation, we have shown that the one-loop effective potential for a Wilson line phase obtained by quantum corrections can behave as an inflaton potential by finding parameter regions consistent with Planck 2018 results. Our model shares basic properties with higher-dimensional models on a flat spacetime, e.g., a potential is generated radiatively, and is robust owing to the gauge symmetry, and then a model has a predictability for physics on inflation. The remaining issues and future prospects are as follows. There is a fine-tuning problem that the (initial) vaules of φ and other parameters should be chosen in order to make φ as an inflaton work well. It would be better if they are determined from a fundamental theory. Or we would have to rely on the anthropic principle in the framework of multiverse. It is necessary to consider contributions of a radion and/or modulus in order to identify an inflaton. In concrete, it is essential to study their stabilization and how inflation can be realized in a system with such several scalar fields including a Wilson line phase on the RS warped background. It would be wonderful to construct a more realistic higher-dimensional gauge theory which solves riddles of particle physics and cosmology on a similar footing. More specifically, it would be fantastic that, in a system governed by the gauge principle, there are several Wilson line phases originated from extra components of gauge bosons, which behave as Higgs boson, an inflaton, a dark matter and so forth. A top-down approach would be useful to construct such a model in a more unified form. Superstring theory, for instance, provides many scalar and vector fields, and possesses many candidates of Higgs boson, an inflaton, a dark matter and so on. Hence, it is intriguing to investigate how a 5d effective theory on the warped geometry can be realized in such a top-down framework. Acknowledgements T.K. would like to thank Dr. O. Seto for the helpful discussions and advice. This work was supported in part by scientific grants from the Ministry of Education, Culture, Sports, Science and Technology under Grant No. 22K03632 (YK). References [1] D. H. Lyth and A. Riotto, “Particle physics models of inflation and the cosmological density perturbation”, Phys. Rept. 314 , 1 (1999), arXiv:hep-ph/9807278, and references therein. [2] Y. Hosotani, “Dynamical Mass Generation by Compact Extra Dimensions”, Phys. Lett. B126, 309 (1983). [3] Y. Hosotani, “Dynamics of Nonintegrable Phases and Gauge Symmetry Breaking”, Annals. Phys. 190, 233 (1989). [4] N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, “Extranatural Inflation”, Phys. Rev. Lett. 90, 221302 (2003), arXiv:hep-th/0301218. [5] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Radion stabilization in the presence of a Wilson line phase”, Prog. Theor. Exp. Phys. 2014, 073B04 (2014), arXiv:1404.5125 [hep-th]. [6] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Inflation from radion gauge-Higgs potential at Planck scale”, Prog. Theor. Exp. Phys. 2015, 093B03 (2015), arXiv:1504.06905 [hep-th]. [7] N. Aghanim et al. (Planck), “Planck 2018 results. VI. Cosmological parameters”, Astron. Astrophys. 641, [Erratum: Astron.Astrophys. 652, C4 (2021)], A6 (2020), arXiv:1807.06209 [astro-ph.CO]. [8] L. Randall and R. Sundrum, “A Large mass hierarchy from a small extra dimension”, Phys. Rev. Lett. 83, 3370-3373 (1999), arXiv:hep-ph/9905221. [9] L. Randall and R. Sundrum, “An Alternative to compactification”, Phys. Rev. Lett. 83, 4690-4693 (1999), arXiv:hep-ph/9906064. [10] A. D. Medina, N. R. Shah, and C. E. M. Wagner, “Gauge-Higgs Unification and Radiative Electroweak Symmetry Breaking in Warped Extra Dimensions”, Phys. Rev. D 76, 095010 (2007), arXiv:0706.1281 [hep-ph]. [11] Y. Hosotani, K. Oda, T. Ohnuma, and Y. Sakamura, “Dynamical Electroweak Symmetry Breaking in SO(5) × U(1) Gauge-Higgs Unification with Top and Bottom Quarks”, Phys. Rev. D 78, [Erratum: Phys. Rev.D 79, 079902 (2009)], 096002 (2008), arXiv:0806.0480[hep-ph]. [12] Y. Hosotani, “New dimensions from gauge-Higgs unification”, PoS CORFU2016, 026 (2017), arXiv:1702.08161 [hep-ph]. [13] S. Funatsu, H. Hatanaka, Y. Hosotani, Y. Orikasa, and N. Yamatsu, “CKM matrix and FCNC suppression in SO(5)×U(1)×SU(3) gauge-Higgs unification”, Phys. Rev. D 101, 055016 (2020), arXiv:1909.00190 [hep-ph]. [14] A. Hebecker and J. March-Russell, “The structure of GUT breaking by orbifolding”, Nucl. Phys. B 625, 128-150 (2002), arXiv:hep-ph/0107039. [15] N. Haba, Y. Kawamura, and K.-y. Oda, “Dynamical Rearrangement of Theta Parameter in Presence of Mixed Chern-Simons Term”, Phys. Rev. D 78, 085021 (2008), arXiv:0803.4380 [hep-ph]. [16] Y. Abe, Y. Goto, Y. Kawamura, and Y. Nishikawa, “Conjugate boundary condition, hidden particles, and gauge-Higgs inflation”, Mod. Phys. Lett. A 31, 1650208 (2016), arXiv:1608.06393 [hep-ph]. [17] K. Kojima and Y. Okubo, “Early dark energy from a higher-dimensional gauge theory”, Phys. Rev. D 106, 063540 (2022), arXiv:2205.13777 [astro-ph.CO]. [18] C. C´saki, S. Lombardo, and O. Telem, “TASI Lectures on Non-supersymmetric BSM Models”, Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics : Anticipating the Next Discoveries in Particle Physics (TASI 2016): Boulder, CO, USA, June 6-July 1, 2016 , edited by R. Essig and I. Low (WSP, 2018), 501-570, arXiv:1811.04279 [hep-ph]. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Authors: Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions We have investigated whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field coupled to fermions in the RS warped spacetime or not. Imposing CBCs on fields involved in inflation, we have shown that the one-loop effective potential for a Wilson line phase obtained by quantum corrections can behave as an inflaton potential by finding parameter regions consistent with Planck 2018 results. Our model shares basic properties with higher-dimensional models on a flat spacetime, e.g., a potential is generated radiatively, and is robust owing to the gauge symmetry, and then a model has a predictability for physics on inflation. The remaining issues and future prospects are as follows. There is a fine-tuning problem that the (initial) vaules of φ and other parameters should be chosen in order to make φ as an inflaton work well. It would be better if they are determined from a fundamental theory. Or we would have to rely on the anthropic principle in the framework of multiverse. It is necessary to consider contributions of a radion and/or modulus in order to identify an inflaton. In concrete, it is essential to study their stabilization and how inflation can be realized in a system with such several scalar fields including a Wilson line phase on the RS warped background. It would be wonderful to construct a more realistic higher-dimensional gauge theory which solves riddles of particle physics and cosmology on a similar footing. More specifically, it would be fantastic that, in a system governed by the gauge principle, there are several Wilson line phases originated from extra components of gauge bosons, which behave as Higgs boson, an inflaton, a dark matter and so forth. A top-down approach would be useful to construct such a model in a more unified form. Superstring theory, for instance, provides many scalar and vector fields, and possesses many candidates of Higgs boson, an inflaton, a dark matter and so on. Hence, it is intriguing to investigate how a 5d effective theory on the warped geometry can be realized in such a top-down framework. Acknowledgements T.K. would like to thank Dr. O. Seto for the helpful discussions and advice. This work was supported in part by scientific grants from the Ministry of Education, Culture, Sports, Science and Technology under Grant No. 22K03632 (YK). References [1] D. H. Lyth and A. Riotto, “Particle physics models of inflation and the cosmological density perturbation”, Phys. Rept. 314 , 1 (1999), arXiv:hep-ph/9807278, and references therein. [2] Y. Hosotani, “Dynamical Mass Generation by Compact Extra Dimensions”, Phys. Lett. B126, 309 (1983). [3] Y. Hosotani, “Dynamics of Nonintegrable Phases and Gauge Symmetry Breaking”, Annals. Phys. 190, 233 (1989). [4] N. Arkani-Hamed, H.-C. Cheng, P. Creminelli, and L. Randall, “Extranatural Inflation”, Phys. Rev. Lett. 90, 221302 (2003), arXiv:hep-th/0301218. [5] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Radion stabilization in the presence of a Wilson line phase”, Prog. Theor. Exp. Phys. 2014, 073B04 (2014), arXiv:1404.5125 [hep-th]. [6] Y. Abe, T. Inami, Y. Kawamura, and Y. Koyama, “Inflation from radion gauge-Higgs potential at Planck scale”, Prog. Theor. Exp. Phys. 2015, 093B03 (2015), arXiv:1504.06905 [hep-th]. [7] N. Aghanim et al. (Planck), “Planck 2018 results. VI. Cosmological parameters”, Astron. Astrophys. 641, [Erratum: Astron.Astrophys. 652, C4 (2021)], A6 (2020), arXiv:1807.06209 [astro-ph.CO]. [8] L. Randall and R. Sundrum, “A Large mass hierarchy from a small extra dimension”, Phys. Rev. Lett. 83, 3370-3373 (1999), arXiv:hep-ph/9905221. [9] L. Randall and R. Sundrum, “An Alternative to compactification”, Phys. Rev. Lett. 83, 4690-4693 (1999), arXiv:hep-ph/9906064. [10] A. D. Medina, N. R. Shah, and C. E. M. Wagner, “Gauge-Higgs Unification and Radiative Electroweak Symmetry Breaking in Warped Extra Dimensions”, Phys. Rev. D 76, 095010 (2007), arXiv:0706.1281 [hep-ph]. [11] Y. Hosotani, K. Oda, T. Ohnuma, and Y. Sakamura, “Dynamical Electroweak Symmetry Breaking in SO(5) × U(1) Gauge-Higgs Unification with Top and Bottom Quarks”, Phys. Rev. D 78, [Erratum: Phys. Rev.D 79, 079902 (2009)], 096002 (2008), arXiv:0806.0480[hep-ph]. [12] Y. Hosotani, “New dimensions from gauge-Higgs unification”, PoS CORFU2016, 026 (2017), arXiv:1702.08161 [hep-ph]. [13] S. Funatsu, H. Hatanaka, Y. Hosotani, Y. Orikasa, and N. Yamatsu, “CKM matrix and FCNC suppression in SO(5)×U(1)×SU(3) gauge-Higgs unification”, Phys. Rev. D 101, 055016 (2020), arXiv:1909.00190 [hep-ph]. [14] A. Hebecker and J. March-Russell, “The structure of GUT breaking by orbifolding”, Nucl. Phys. B 625, 128-150 (2002), arXiv:hep-ph/0107039. [15] N. Haba, Y. Kawamura, and K.-y. Oda, “Dynamical Rearrangement of Theta Parameter in Presence of Mixed Chern-Simons Term”, Phys. Rev. D 78, 085021 (2008), arXiv:0803.4380 [hep-ph]. [16] Y. Abe, Y. Goto, Y. Kawamura, and Y. Nishikawa, “Conjugate boundary condition, hidden particles, and gauge-Higgs inflation”, Mod. Phys. Lett. A 31, 1650208 (2016), arXiv:1608.06393 [hep-ph]. [17] K. Kojima and Y. Okubo, “Early dark energy from a higher-dimensional gauge theory”, Phys. Rev. D 106, 063540 (2022), arXiv:2205.13777 [astro-ph.CO]. [18] C. C´saki, S. Lombardo, and O. Telem, “TASI Lectures on Non-supersymmetric BSM Models”, Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics : Anticipating the Next Discoveries in Particle Physics (TASI 2016): Boulder, CO, USA, June 6-July 1, 2016 , edited by R. Essig and I. Low (WSP, 2018), 501-570, arXiv:1811.04279 [hep-ph]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Exploring Gauge-Higgs Inflation with Extra Dimensions: Conclusions, Acknowledgements, and References

Authors:
(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);
(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 3 Gauge-Higgs inflation on a warped background 3.2 Model with a single fermion A graph of V (φ) is depicted in Figure 1. Here, it is obtained by summing the function 3.3 Model with multiple fermions Next, let us consider a combination of these cos-type potentials. We have now two fermions ψ1 and ψ2. Each fermion has the values of α, β and qψ as shown in Table 2, and then the potential is written as This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Authors: Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions, Acknowledgements, and References 3 Gauge-Higgs inflation on a warped background 3.2 Model with a single fermion A graph of V (φ) is depicted in Figure 1. Here, it is obtained by summing the function 3.3 Model with multiple fermions Next, let us consider a combination of these cos-type potentials. We have now two fermions ψ1 and ψ2. Each fermion has the values of α, β and qψ as shown in Table 2, and then the potential is written as This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Exploring Gauge-Higgs Inflation with Extra Dimensions: On a Warped Background

Authors:
(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);
(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 2 U(1) gauge theory on a warped background 2.1 Randall-Sundrum metric and action integral The spacetime is assumed to be 5d one with the RS metric given by [8, 9] 2.2 Conjugate boundary conditions where β is a constant called a twisted phase, the superscript C denotes a 4d charge conjugation, θC is a real number, and the asterisk means the complex conjugation. Then, the covariant derivatives obey the relations: 2.3 Mass spectrum Then, the action integral is rewritten as 2.4 Effective potential Let us derive the effective potential for the Wilson line phase θ(= θ(x)). Taking the standard procedure, a d-dimensional effective potential involving one degree of freedom at the one-loop level is given b This paper is available on arxiv under CC BY 4.0 DEED license. [3] We introduce both Mψ and cσ′ (y) in a general standpoint, and we will see that cσ′ (y) is forbidden by imposing specific boundary conditions on fields in the next subsection. Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Authors: Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions, Acknowledgements, and References 2 U(1) gauge theory on a warped background 2.1 Randall-Sundrum metric and action integral The spacetime is assumed to be 5d one with the RS metric given by [8, 9] 2.2 Conjugate boundary conditions where β is a constant called a twisted phase, the superscript C denotes a 4d charge conjugation, θC is a real number, and the asterisk means the complex conjugation. Then, the covariant derivatives obey the relations: 2.3 Mass spectrum Then, the action integral is rewritten as 2.4 Effective potential Let us derive the effective potential for the Wilson line phase θ(= θ(x)). Taking the standard procedure, a d-dimensional effective potential involving one degree of freedom at the one-loop level is given b This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv [3] We introduce both Mψ and cσ′ (y) in a general standpoint, and we will see that cσ′ (y) is forbidden by imposing specific boundary conditions on fields in the next subsection.

Exploring Gauge-Higgs Inflation with Extra Dimensions: U(1) Gauge Theory on a Warped Background

Authors:
(1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp);
(2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References Abstract We investigate whether inflation in the early universe can be induced by an extra component of a five-dimensional U(1) gauge field in the Randall-Sundrum warped spacetime or not. We show that an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results. In our model, fields involved in inflation obey a different type of boundary condition from that of the visible particles, and a surviving Wilson line phase can play a specific role for physics beyond the standard model. 1 Introduction Inflation can solve both the flatness problem and the horizon problem at the same time and also explain temperature fluctuations of the cosmic microwave background (CMB) [1]. It is therefore almost certain that inflation occurred in the early universe. However, a specific mechanism or an origin of a quanta called “inflaton” is still a mystery. An inflaton is assumed to be a scalar field in typical models, but its potential is, in general, not stable against quantum (gravity) corrections and should be fine-tuned to satisfy constraints of cosmological observations. This problem stems from the fact that radiative corrections on scalar fields cannot be controlled without any assistance of a powerful symmetry. One way to solve this problem is to consider a higher-dimensional gauge theory, and then a Wilson line phase made of an extra component of a gauge field can become an inflaton whose potential can be determined by the gauge principle. In this scenario, a relevant part of potential is obtained as a function of the Wilson line phase radiatively, taking a finite value [2, 3]. Such an inflaton potential is robust owing to the gauge symmetry and its stability can be guaranteed. A famous five-dimensional (5d) model compactified on a circle S 1 has been proposed in the name of extranatural inflation [4]. In a similar setup, a model with both a radion and a Wilson line phase has been constructed, and it is shown that the radion is stabilized [5] and the Wilson line phase can be, in most cases, an inflaton [6]. Recently, constraints on cosmological parameters from various observations have become more stringent and inflation models can be selected more rigorously [7]. It is valuable to reexamine whether an extranatural inflation scenario is still valid today or not, in a wide variety of spacetime. It is known that the Randall-Sundrum (RS) warped spacetime can provide rich properties in phenomenological aspects of particle physics. For instance, RS1 model provides a solution of the hierarchy problem of the standard model [8], RS2 model explains the weakness of gravitational force on the TeV brane because the graviton localizes on the Planck brane [9], and gauge-Higgs unification (GHU) models in the warped spacetime can show promise as physics beyond the standard model (BSM) [10, 11, 12, 13]. Hence, it would be favorable if a riddle in cosmology such as inflation could be solved in the same background. In this paper, we investigate whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field in the warped background or not. In concrete, we examine whether an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results or not. The RS spacetime contains an orbifold S 1/Z2 and a different type of boundary condition called “conjugate boundary condition” can be imposed on fields to survive an extra component of a gauge boson in QED-like models and this enables fields involved in inflation to play a specific role for BSM. This paper is organized as follows. In the next section, we present a 5d U(1) gauge theory on the warped spacetime. In section 3, we study an extranatural inflation scenario on the warped spacetime based on our model. The last section is devoted to conclusions and discussions. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Authors: Authors: (1) Toshiki Kawai, Department of Physics, Hokkaido University, Sapporo 060-0810, Japan (E-mail: t-kawai@higgs3.sci.hokudai.ac.jp); (2) Yoshiharu Kawamura, Department of Physics, Shinshu University, Matsumoto 390-8621, Japan (E-mail: haru@azusa.shinshu-u.ac.jp). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 U(1) gauge theory on a warped background 2 U(1) gauge theory on a warped background 3 Gauge-Higgs inflation on a warped background 3 Gauge-Higgs inflation on a warped background 4 Conclusions and discussions, Acknowledgements, and References 4 Conclusions and discussions, Acknowledgements, and References Abstract We investigate whether inflation in the early universe can be induced by an extra component of a five-dimensional U(1) gauge field in the Randall-Sundrum warped spacetime or not. We show that an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results. In our model, fields involved in inflation obey a different type of boundary condition from that of the visible particles, and a surviving Wilson line phase can play a specific role for physics beyond the standard model. 1 Introduction Inflation can solve both the flatness problem and the horizon problem at the same time and also explain temperature fluctuations of the cosmic microwave background (CMB) [1]. It is therefore almost certain that inflation occurred in the early universe. However, a specific mechanism or an origin of a quanta called “inflaton” is still a mystery. An inflaton is assumed to be a scalar field in typical models, but its potential is, in general, not stable against quantum (gravity) corrections and should be fine-tuned to satisfy constraints of cosmological observations. This problem stems from the fact that radiative corrections on scalar fields cannot be controlled without any assistance of a powerful symmetry. One way to solve this problem is to consider a higher-dimensional gauge theory, and then a Wilson line phase made of an extra component of a gauge field can become an inflaton whose potential can be determined by the gauge principle. In this scenario, a relevant part of potential is obtained as a function of the Wilson line phase radiatively, taking a finite value [2, 3]. Such an inflaton potential is robust owing to the gauge symmetry and its stability can be guaranteed. A famous five-dimensional (5d) model compactified on a circle S 1 has been proposed in the name of extranatural inflation [4]. In a similar setup, a model with both a radion and a Wilson line phase has been constructed, and it is shown that the radion is stabilized [5] and the Wilson line phase can be, in most cases, an inflaton [6]. Recently, constraints on cosmological parameters from various observations have become more stringent and inflation models can be selected more rigorously [7]. It is valuable to reexamine whether an extranatural inflation scenario is still valid today or not, in a wide variety of spacetime. It is known that the Randall-Sundrum (RS) warped spacetime can provide rich properties in phenomenological aspects of particle physics. For instance, RS1 model provides a solution of the hierarchy problem of the standard model [8], RS2 model explains the weakness of gravitational force on the TeV brane because the graviton localizes on the Planck brane [9], and gauge-Higgs unification (GHU) models in the warped spacetime can show promise as physics beyond the standard model (BSM) [10, 11, 12, 13]. Hence, it would be favorable if a riddle in cosmology such as inflation could be solved in the same background. In this paper, we investigate whether inflation in the early universe can be induced by an extra component of a 5d U(1) gauge field in the warped background or not. In concrete, we examine whether an effective potential obtained by quantum corrections can act as an inflaton potential by finding parameter regions consistent with Planck 2018 results or not. The RS spacetime contains an orbifold S 1/Z2 and a different type of boundary condition called “conjugate boundary condition” can be imposed on fields to survive an extra component of a gauge boson in QED-like models and this enables fields involved in inflation to play a specific role for BSM. This paper is organized as follows. In the next section, we present a 5d U(1) gauge theory on the warped spacetime. In section 3, we study an extranatural inflation scenario on the warped spacetime based on our model. The last section is devoted to conclusions and discussions. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Exploring Gauge-Higgs Inflation with Extra Dimensions: Abstract and Introduction

Authors:
(1) Agustin Moreno;
(2) Francesco Ruscelli. Table of Links Abstract
Introduction
Preliminaries
The B-signature
GIT sequence: low dimensions
GIT sequence: arbitrary dimension
Appendix A. Stability, the Krein–Moser theorem, and refinements and References 4. GIT sequence: low dimensions We now discuss global topological methods in the study of periodic orbits, following the exposition in [AFKM]. These methods encode: bifurcations; stability; eigenvalue configurations; obstructions to existence of regular families; and B-signs, in a visual and resource-efficient way. The GIT sequence is the sequence of maps and spaces given by Then, by the above, the stability point is the result of applying the GIT sequence of maps to the given matrix. 4.1. GIT sequence: 2D. We start with the simplest case, i.e. the case of an autonomous Hamiltonian of two degrees of freedom, so that the reduced monodromy matrix is an element in Sp(2) = SL(2, R). The Broucke stability diagram is then simply the real line, split into three components; see Figure 1. If two orbits lie in different components of the diagram, then there are always bifurcations in any family joining them, as the topology of the diagram implies that any path between them has to cross the ±1 eigenvalues (corresponding respectively to bifurcation or period-doubling bifurcation). One can think that the stability index “collapses” the two elliptic branches in the middle layer of Figure 1 together. These two branches are distinguished by the B-signs, coinciding with the Krein signs [Kre2; Kre3]. There is an extra top layer for symmetric orbits, where now each hyperbolic branch separates into two, and there is a collapsing map from the top to middle layer. Note that to go from one branch to the other (say from the positive hyperbolic branch I to the positive hyperbolic branch II), the topology of the top layer implies that the eigenvalue 1 needs to be crossed. This means that one should expect bifurcations in any (symmetric) family joining them, even if they project to the same component of the Broucke diagram. In this way, the information given by the diagram is much more refined for the case of symmetric orbits. If we say that two orbits are qualitatively equivalent if they can be joined by a regular orbit cylinder, then the topology of the spaces in the GIT sequence give criteria to determine whenever two orbits are not qualitatively equivalent. To sum up: • B-signs “separate” hyperbolic branches, for symmetric orbits. • If two orbits lie in different components of the Broucke diagram, there are always bifurcations in any path joining them. • If two symmetric orbits lie in the same component of the Broucke diagram, but if B-signs differ, one should also expect bifurcation in any (symmetric) path joining them[1]. 4.2. GIT sequence: 3D. Now we apply the same idea, but for autonomous Hamiltonian systems with three degrees of freedom, for which reduced monodromy matrices are elements in Sp(4). The GIT sequence [FM] adds two layers to this diagram, as shown in Figure 3. The top layer has two extra branches than the middle one, for each hyperbolic eigenvalue. While the combinatorics and the global topology of the spaces involved is more complicated than the 2D case, the intuitive idea is still the same, i.e. that the amount of information for symmetric orbits is richer, and that we can distinguish more orbits up to qualitative equivalence. Note that as in this dimension we have two pairs of eigenvalues, the B-signature is a pair (±, ±) of signs, and therefore the top layer has 4 branches over each component of the Broucke diagram (except the nonreal component). This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. [1] We cautiosuly use the word “expect” rather than give a mathematical statement, as theoretically orbits could tangentially pass through the Maslov cycle without birfurcating. Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Authors: Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Table of Links Abstract Introduction Preliminaries The B-signature GIT sequence: low dimensions GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract Abstract Introduction Introduction Preliminaries Preliminaries The B-signature The B-signature GIT sequence: low dimensions GIT sequence: low dimensions GIT sequence: arbitrary dimension GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Appendix A. Stability, the Krein–Moser theorem, and refinements and References 4. GIT sequence: low dimensions We now discuss global topological methods in the study of periodic orbits, following the exposition in [AFKM]. These methods encode: bifurcations; stability; eigenvalue configurations; obstructions to existence of regular families; and B-signs, in a visual and resource-efficient way. The GIT sequence is the sequence of maps and spaces given by Then, by the above, the stability point is the result of applying the GIT sequence of maps to the given matrix. 4.1. GIT sequence: 2D. We start with the simplest case, i.e. the case of an autonomous Hamiltonian of two degrees of freedom, so that the reduced monodromy matrix is an element in Sp(2) = SL(2, R). GIT sequence: 2D. The Broucke stability diagram is then simply the real line, split into three components; see Figure 1. If two orbits lie in different components of the diagram, then there are always bifurcations in any family joining them, as the topology of the diagram implies that any path between them has to cross the ±1 eigenvalues (corresponding respectively to bifurcation or period-doubling bifurcation). One can think that the stability index “collapses” the two elliptic branches in the middle layer of Figure 1 together. These two branches are distinguished by the B-signs, coinciding with the Krein signs [Kre2; Kre3]. There is an extra top layer for symmetric orbits, where now each hyperbolic branch separates into two, and there is a collapsing map from the top to middle layer. Note that to go from one branch to the other (say from the positive hyperbolic branch I to the positive hyperbolic branch II), the topology of the top layer implies that the eigenvalue 1 needs to be crossed. This means that one should expect bifurcations in any (symmetric) family joining them, even if they project to the same component of the Broucke diagram. In this way, the information given by the diagram is much more refined for the case of symmetric orbits. If we say that two orbits are qualitatively equivalent if they can be joined by a regular orbit cylinder, then the topology of the spaces in the GIT sequence give criteria to determine whenever two orbits are not qualitatively equivalent. To sum up: • B-signs “separate” hyperbolic branches, for symmetric orbits. • If two orbits lie in different components of the Broucke diagram, there are always bifurcations in any path joining them. • If two symmetric orbits lie in the same component of the Broucke diagram, but if B-signs differ, one should also expect bifurcation in any (symmetric) path joining them[1]. 4.2. GIT sequence: 3D . Now we apply the same idea, but for autonomous Hamiltonian systems with three degrees of freedom, for which reduced monodromy matrices are elements in Sp(4). GIT sequence: 3D The GIT sequence [FM] adds two layers to this diagram, as shown in Figure 3. The top layer has two extra branches than the middle one, for each hyperbolic eigenvalue. While the combinatorics and the global topology of the spaces involved is more complicated than the 2D case, the intuitive idea is still the same, i.e. that the amount of information for symmetric orbits is richer, and that we can distinguish more orbits up to qualitative equivalence. Note that as in this dimension we have two pairs of eigenvalues, the B-signature is a pair (±, ±) of signs, and therefore the top layer has 4 branches over each component of the Broucke diagram (except the nonreal component). This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv [1] We cautiosuly use the word “expect” rather than give a mathematical statement, as theoretically orbits could tangentially pass through the Maslov cycle without birfurcating.

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