Anisotropic constant-roll \(k\)-inflation model

Duy H. Nguyen, Tuyen M. Pham, Thien D. Le, Tuan Q. Do
Author affiliations

Authors

  • Duy H. Nguyen Phenikaa Institute for Advanced Study, Phenikaa University, Hanoi 12116, Vietnam and Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Hanoi 11307, Vietnam
  • Tuyen M. Pham Phenikaa Institute for Advanced Study, Phenikaa University, Hanoi 12116, Vietnam and Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Hanoi 11307, Vietnam
  • Thien D. Le Department of Natural Science, Phu Cuong High School, Hoa Binh 36100, Vietnam
  • Tuan Q. Do Phenikaa Institute for Advanced Study, Phenikaa University, Hanoi 12116, Vietnam

DOI:

https://doi.org/10.15625/0868-3166/17360

Keywords:

Inflation, Bianchi type I metric, Cosmic no-hair conjecture, cosmology

Abstract

In this paper, we would like to figure out whether a {\it k}-inflation model admits the Bianchi type I metric as its inflationary solution under a constant-roll condition in the presence of the supergravity motivated coupling between scalar and vector fields, \(f^2(\phi)F_{\mu\nu}F^{\mu\nu}\). As a result, some novel anisotropic inflationary solutions are shown to appear along with a power-law one in this scenario. Furthermore, these solutions are numerically confirmed to be attractive, in contrast to the prediction of the Hawking's cosmic no-hair conjecture.

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References

G. Hinshaw et al. [WMAP Collaboration], Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Cosmological parameter results, Astrophys. J. Suppl. 208 (2013) 19 [arXiv:1212.5226]. DOI: https://doi.org/10.1088/0067-0049/208/2/19

Y. Akrami et al. [Planck Collaboration], Planck 2018 results. VII. Isotropy and statistics of the CMB, Astron. Astrophys. 641 (2020) A7 [arXiv:1906.02552].

D. Saadeh, S. M. Feeney, A. Pontzen, H. V. Peiris and J. D. McEwen, How isotropic is the Universe?, Phys. Rev. Lett. 117 (2016) 131302 [arXiv:1605.07178]; J. Soltis, A. Farahi, D. Huterer and C. M. Liberato II, Percent-level test of isotropic expansion using type Ia supernovae, Phys. Rev. Lett. 122 (2019) 091301 [arXiv:1902.07189]; N. J. Secrest, S. von Hausegger, M. Rameez, R. Mohayaee, S. Sarkar and J. Colin, A test of the cosmological principle with quasars, Astrophys. J. Lett. 908 (2021) L51 [arXiv:2009.14826]; C. Krishnan, R. Mohayaee, E. O. Colgain, M. M. Sheikh-Jabbari and L. Yin, Hints of FLRW break down from supernovae, Phys. Rev. D 105 (2022) 063514 [arXiv:2106.02532].

T. Buchert, A. A. Coley, H. Kleinert, B. F. Roukema and D. L. Wiltshire, Observational challenges for the standard FLRW model, Int. J. Mod. Phys. D 25 (2016) 1630007 [arXiv:1512.03313]. DOI: https://doi.org/10.1142/S021827181630007X

G. F. R. Ellis and M. A. H. MacCallum, A Class of homogeneous cosmological models, Commun. Math. Phys. 12 (1969) 108; G. F. R. Ellis, The Bianchi models: Then and now, Gen. Rel. Grav. 38 (2006) 1003.

D. J. Schwarz, C. J. Copi, D. Huterer and G. D. Starkman, CMB Anomalies after Planck, Class. Quant. Grav. 33 (2016) 184001 [arXiv:1510.07929]. DOI: https://doi.org/10.1088/0264-9381/33/18/184001

C. Krishnan, R. Mohayaee, E. O. Colgain, M. M. Sheikh-Jabbari and L. Yin, Does Hubble tension signal a breakdown in FLRW cosmology?, Class. Quant. Grav. 38 (2021) 184001 [arXiv:2105.09790]. DOI: https://doi.org/10.1088/1361-6382/ac1a81

A. A. Starobinsky, A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 (1980) 99; A. H. Guth, The inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23 (1981) 347; A. D. Linde, A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. B 108 (1982) 389; A. D. Linde, Chaotic inflation, Phys. Lett. B 129 (1983) 177.

C. Pitrou, T. S. Pereira and J. P. Uzan, Predictions from an anisotropic inflationary era, J. Cosmol. Astropart. Phys. 04 (2008) 004 [arXiv:0801.3596]; A. E. Gumrukcuoglu, C. R. Contaldi and M. Peloso, Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB, J. Cosmol. Astropart. Phys. 07 (2007) 005 [arXiv:0707.4179].

J. Colin, R. Mohayaee, M. Rameez and S. Sarkar, Evidence for anisotropy of cosmic acceleration, Astron. Astrophys. 631 (2019) L13 [arXiv:1808.04597]. DOI: https://doi.org/10.1051/0004-6361/201936373

G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15 (1977) 2738; S. W. Hawking and I. G. Moss, Supercooled phase transitions in the very early universe, Phys. Lett. B 110 (1982) 35.

R. M. Wald, Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant, Phys. Rev. D 28 (1983) 2118. DOI: https://doi.org/10.1103/PhysRevD.28.2118

J. D. Barrow, Cosmic no hair theorems and inflation, Phys. Lett. B 187 (1987) 12; M. Mijic and J. A. Stein- Schabes, A no-hair theorem for R2 models, Phys. Lett. B 203 (1988) 353; Y. Kitada and K. i. Maeda, Cosmic no hair theorem in power law inflation, Phys. Rev. D 45 (1992) 1416.

M. Kleban and L. Senatore, Inhomogeneous anisotropic cosmology, J. Cosmol. Astropart. Phys. 10 (2016) 022 [arXiv:1602.03520]; W. E. East, M. Kleban, A. Linde and L. Senatore, Beginning inflation in an inhomogeneous universe, J. Cosmol. Astropart. Phys. 09 (2016) 010 [arXiv:1511.05143].

S. M. Carroll and A. Chatwin-Davies, Cosmic equilibration: A holographic no-hair theorem from the generalized second law, Phys. Rev. D 97 (2018) 046012 [arXiv:1703.09241]. DOI: https://doi.org/10.1103/PhysRevD.97.046012

F. Azhar and D. I. Kaiser, Flows into de Sitter from anisotropic initial conditions: An effective field theory approach, arXiv:2207.08355.

A. A. Starobinsky, Isotropization of arbitrary cosmological expansion given an effective cosmological constant, JETP Lett. 37 (1983) 66; V. Muller, H. J. Schmidt and A. A. Starobinsky, Power law inflation as an attractor solution for inhomogeneous cosmological models, Class. Quant. Grav. 7 (1990) 1163.

J. D. Barrow and J. Stein-Schabes, Inhomogeneous cosmologies with cosmological constant, Phys. Lett. A 103 (1984) 315; L. G. Jensen and J. A. Stein-Schabes, Is inflation natural?, Phys. Rev. D 35 (1987) 1146; J. A. Stein- Schabes, Inflation in spherically symmetric inhomogeneous models, Phys. Rev. D 35 (1987) 2345.

M. a. Watanabe, S. Kanno and J. Soda, Inflationary universe with anisotropic hair, Phys. Rev. Lett. 102 (2009) 191302 [arXiv:0902.2833]. DOI: https://doi.org/10.1103/PhysRevLett.102.191302

S. Kanno, J. Soda and M. a. Watanabe, Anisotropic power-law inflation, J. Cosmol. Astropart. Phys. 12 (2010) 024 [arXiv:1010.5307]. DOI: https://doi.org/10.1088/1475-7516/2010/12/024

R. Emami, H. Firouzjahi, S. M. Sadegh Movahed and M. Zarei, Anisotropic inflation from charged scalar fields, J. Cosmol. Astropart. Phys. 02 (2011) 005 [arXiv:1010.5495]; K. Murata and J. Soda, Anisotropic inflation with non-Abelian gauge kinetic function, J. Cosmol. Astropart. Phys. 06 (2011) 037 [arXiv:1103.6164]; S. Hervik, D. F. Mota and M. Thorsrud, Inflation with stable anisotropic hair: is it cosmologically viable?, J. High Energy Phys. 11 (2011) 146 [arXiv:1109.3456]; M. Thorsrud, D. F. Mota and S. Hervik, Cosmology of a scalar field coupled to matter and an isotropy-violating Maxwell field, J. High Energy Phys. 10 (2012) 066 [arXiv:1205.6261]; J. Holland, S. Kanno and I. Zavala, Anisotropic inflation with derivative couplings, Phys. Rev. D 97 (2018) 103534 [arXiv:1711.07450]; T. Q. Do and W. F. Kao, Anisotropic power-law inflation for a conformal-violating Maxwell model, Eur. Phys. J. C 78 (2018) 360 [arXiv:1712.03755]; T. Q. Do and W. F. Kao, Anisotropic power-law inflation for a model of two scalar and two vector fields, Eur. Phys. J. C 81 (2021) 525 [arXiv:2104.14100]; P. Gao, K. Takahashi, A. Ito and J. Soda, Cosmic no-hair conjecture and inflation with an SU(3) gauge field, Phys. Rev. D 104 (2021) 103526 [arXiv:2107.00264]; C. B. Chen and J. Soda, Anisotropic hyperbolic inflation, J. Cosmol. Astropart. Phys. 09 (2021) 026 [arXiv:2106.04813]; T. Q. Do and W. F. Kao, Anisotropic hyperbolic inflation for a model of two scalar and two vector fields, Eur. Phys. J. C 82 (2022) 123 [arXiv:2110.13516]; C. B. Chen and J. Soda, Geometric structure of multi-form-field isotropic inflation and primordial fluctuations, J. Cosmol. Astropart. Phys. 05 (2022) 029 [arXiv:2201.03160].

T. Q. Do and W. F. Kao, Anisotropic power-law inflation for the Dirac-Born-Infeld theory, Phys. Rev. D 84 (2011) 123009. DOI: https://doi.org/10.1103/PhysRevD.84.123009

J. Ohashi, J. Soda and S. Tsujikawa, Anisotropic power-law k-inflation, Phys. Rev. D 88 (2013) 103517 [arXiv:1310.3053]. DOI: https://doi.org/10.1103/PhysRevD.88.103517

T. Q. Do, Stable small spatial hairs in a power-law k-inflation model, Eur. Phys. J. C 81 (2021) 77 [arXiv:2007.04867]. DOI: https://doi.org/10.1140/epjc/s10052-021-08866-7

A. Ito and J. Soda, Anisotropic constant-roll inflation, Eur. Phys. J. C 78 (2018) 55 [arXiv:1710.09701]. DOI: https://doi.org/10.1140/epjc/s10052-018-5534-5

D. H. Nguyen, T. M. Pham and T. Q. Do, Anisotropic constant-roll inflation for the Dirac–Born–Infeld model, Eur. Phys. J. C 81 (2021) 839 [arXiv:2107.14115]. DOI: https://doi.org/10.1140/epjc/s10052-021-09652-1

A. Maleknejad, M. M. Sheikh-Jabbari and J. Soda, Gauge fields and inflation, Phys. Rept. 528 (2013) 161 [arXiv:1212.2921]; J. Soda, Statistical anisotropy from anisotropic inflation, Class. Quant. Grav. 29 (2012) 083001 [arXiv:1201.6434].

H. Motohashi, A. A. Starobinsky and J. Yokoyama, Inflation with a constant rate of roll, J. Cosmol. Astropart. Phys. 09 (2015) 018 [arXiv:1411.5021]. DOI: https://doi.org/10.1088/1475-7516/2015/09/018

H. Motohashi and A. A. Starobinsky, Constant-roll inflation: confrontation with recent observational data, Europhys. Lett. 117 (2017) 39001 [arXiv:1702.05847]; J. T. Galvez Ghersi, A. Zucca and A. V. Frolov, Observational constraints on constant roll inflation, J. Cosmol. Astropart. Phys. 05 (2019) 030 [arXiv:1808.01325]; S. D. Odintsov and V. K. Oikonomou, Inflationary dynamics with a smooth slow-roll to constant-roll era transition, J. Cosmol. Astropart. Phys. 04 (2017) 041 [arXiv:1703.02853]; S. Nojiri, S. D. Odintsov and V. K. Oikonomou, Constant-roll inflation in F(R) gravity, Class. Quant. Grav. 34 (2017) 245012 [arXiv:1704.05945]; H. Motohashi and A. A. Starobinsky, f (R) constant-roll inflation, Eur. Phys. J. C 77 (2017) 538 [arXiv:1704.08188]; V. K. Oikonomou, Reheating in constant-roll F(R) gravity, Mod. Phys. Lett. A 32 (2017) 1750172 [arXiv:1706.00507]; L. Anguelova, P. Suranyi and L. C. R. Wijewardhana, Systematics of constant roll inflation, J. Cosmol. Astropart. Phys. 02 (2018) 004 [arXiv:1710.06989]; A. Karam, L. Marzola, T. Pappas, A. Racioppi and K. Tamvakis, Constant-roll (quasi-)linear inflation, J. Cosmol. Astropart. Phys. 05 (2018) 011 [arXiv:1711.09861]; A. Mohammadi, K. Saaidi and H. Sheikhahmadi, Constant-roll approach to non-canonical inflation, Phys. Rev. D 100 (2019) 083520 [arXiv:1803.01715]; A. Mohammadi, T. Golanbari and K. Saaidi, Observational constraints on DBI constant-roll inflation, Phys. Dark Univ. 27, 100456 (2020) [arXiv:1808.07246]; W. C. Lin, M. J. P. Morse and W. H. Kinney, Dynamical analysis of attractor behavior in constant roll inflation, J. Cosmol. Astropart. Phys. 09 (2019) 063 [arXiv:1904.06289]; H. Motohashi and A. A. Starobinsky, Constant-roll inflation in scalar-tensor gravity, J. Cosmol. Astropart. Phys. 11 (2019) 025 [arXiv:1909.10883]; H. Motohashi, S. Mukohyama and M. Oliosi, Constant roll and primordial black holes, J. Cosmol. Astropart. Phys. 03 (2020) 002 [arXiv:1910.13235]; I. Antoniadis, A. Lykkas and K. Tamvakis, Constant-roll in the Palatini-R2 models, J. Cosmol. Astropart. Phys. 04 (2020) 033 [arXiv:2002.12681]; V. K. Oikonomou and F. P. Fronimos, A nearly massless graviton in Einstein-Gauss-Bonnet inflation with linear coupling implies constant-roll for the scalar field, Europhys. Lett. 131 (2020) 30001 [arXiv:2007.11915]; T. J. Gao, Gauss–Bonnet inflation with a constant rate of roll, Eur. Phys. J. C 80 (2020) 1013 [arXiv:2008.03976]; M. Guerrero, D. Rubiera-Garcia and D. Saez-Chillon Gomez, Constant roll inflation in multifield models, Phys. Rev. D 102 (2020) 123528 [arXiv:2008.07260]; J. Sadeghi and S. Noori Gashti, Anisotropic constant-roll inflation with noncommutative model and swampland conjectures, Eur. Phys. J. C 81 (2021) 301 [arXiv:2104.00117]; M. Shokri, J. Sadeghi, M. R. Setare and S. Capozziello, Non- minimal coupling inflation with constant slow roll, Int. J. Mod. Phys. D 30 (2021) 2150070 [arXiv:2104.00596]. M. Shokri, M. R. Setare, S. Capozziello and J. Sadeghi, Constant-roll f (R) inflation compared with Cosmic Microwave Background anisotropies and swampland criteria, Eur. Phys. J. Plus 137 (2022) 639 [arXiv:2108.00175].

S. D. Odintsov and V. K. Oikonomou, Constant-roll k-inflation dynamics, Class. Quant. Grav. 37 (2020) 025003 [arXiv:1912.00475]. DOI: https://doi.org/10.1088/1361-6382/ab5c9d

J. Martin, H. Motohashi and T. Suyama, Ultra slow-roll inflation and the non-Gaussianity consistency relation, Phys. Rev. D 87 (2013) 023514 [arXiv:1211.0083]. DOI: https://doi.org/10.1103/PhysRevD.87.023514

L. F. Abbott and M. B. Wise, Constraints on generalized inflationary cosmologies, Nucl. Phys. B 244 (1984) 541; F. Lucchin and S. Matarrese, Power law inflation, Phys. Rev. D 32 (1985) 1316.

J. D. Barrow, Exact inflationary universes with potential minima, Phys. Rev. D 49 (1994) 3055. DOI: https://doi.org/10.1103/PhysRevD.49.3055

L. Boubekeur and D. H. Lyth, Hilltop inflation, J. Cosmol. Astropart. Phys. 07 (2005) 010 [hep-ph/0502047]. DOI: https://doi.org/10.1088/1475-7516/2005/07/010

C. Armendariz-Picon, T. Damour and V. F. Mukhanov, k-inflation, Phys. Lett. B 458 (1999) 209 [hep-th/9904075]; J. Garriga and V. F. Mukhanov, Perturbations in k-inflation, Phys. Lett. B 458 (1999) 219 [hep-th/9904176].

T. Q. Do and S. H. Q. Nguyen, No small hairs in anisotropic power-law Gauss-Bonnet inflation, Commun. in Phys. 29 (2019) 173 [arXiv:1905.01427]; T. M. Pham, D. H. Nguyen and T. Q. Do, k-Gauss-Bonnet inflation, arXiv:2107.05926. DOI: https://doi.org/10.15625/0868-3166/29/2/13677

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Published

03-11-2022

How to Cite

[1]
H. D. Nguyen, M. T. Pham, D. T. Le, and Q. T. Do, “Anisotropic constant-roll \(k\)-inflation model”, Comm. Phys., vol. 33, no. 1, p. 15, Nov. 2022.

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Received 23-07-2022
Accepted 24-08-2022
Published 03-11-2022