On the Validity of the Cosmic No-hair Conjecture in some Conformal-violating Maxwell Models

Abstract

Abstract: We will present main results of our recent investigations on the validity of the cosmic no-hair conjecture proposed by Hawking and his colleagues in some conformal-violating Maxwell models, in which a scalar field or its kinetic term is non-trivially coupled to the electromagnetic field. In particular, we will show that the studied models really admit the Bianchi type I metrics, which are homogeneous but anisotropic space time, as their stable cosmological solutions. Hence, these models turn out to be counterexamples to the cosmic no-hair conjecture.

Keywords: Cosmic no-hair conjecture, cosmic inflation, Bianchi type I space time, Maxwell theory.

References
[1] A.H. Guth, Inflationary universe: A possible solution to the horizon and flatness problems, Phys. Rev. D 23 (1981) 347.
[2] A.D. Linde, A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. 108B (1982) 389.
[3] A.D. Linde, Chaotic inflation, Phys. Lett. 129B (1983) 177.
[4] E. Komatsu et al. [WMAP Collaboration], Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Cosmological interpretation, Astrophys. J. Suppl. 192 (2011) 18.
[5] G. Hinshaw et al. [WMAP Collaboration], Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Cosmological parameter results, Astrophys. J. Suppl. 208 (2013) 19.
[6] P.A.R. Ade et al. [Planck Collaboration], Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20.
[7] P.A.R. Ade et al. [Planck Collaboration], Planck 2015 results. XVI. Isotropy and statistics of the CMB, Astron. Astrophys. 594 (2016) A16.
[8] T. Buchert, A.A. Coley, H. Kleinert, B.F. Roukema, D.L. Wiltshire, Observational challenges for the standard FLRW model, Int. J. Mod. Phys. D 25 (2016) 1630007.
[9] G.F.R. Ellis, M.A.H. MacCallum, A class of homogeneous cosmological models, Commun. Math. Phys. 12 (1969) 108.
[10] G.F.R. Ellis, The Bianchi models: Then and now, Gen. Rel. Grav. 38 (2006) 1003.
[11] G.W. Gibbons, S.W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15 (1977) 2738.
[12] S.W. Hawking, I.G. Moss, Supercooled phase transitions in the very early universe, Phys. Lett. 110B (1982) 35.
[13] R.M. Wald, Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant, Phys. Rev. D 28 (1983) 2118.
[14] J.D. Barrow, Cosmic no hair theorems and inflation, Phys. Lett. B 187 (1987) 12.
[15] Y. Kitada, K.I. Maeda, Cosmic no hair theorem in power law inflation, Phys. Rev. D 45 (1992) 1416.
[16] M. Kleban, L. Senatore, Inhomogeneous anisotropic cosmology, J. Cosmol. Astropart. Phys. 10 (2016) 022.
[17] W.E. East, M. Kleban, A. Linde, L. Senatore, Beginning inflation in an inhomogeneous universe, J. Cosmol. Astropart. Phys. 09 (2016) 010.
[18] S.M. Carroll, A. Chatwin-Davies, Cosmic equilibration: A holographic no-hair theorem from the generalized second law, Phys. Rev. D 97 (2018) 046012.
[19] N. Kaloper, Lorentz Chern-Simons terms in Bianchi cosmologies and the cosmic no hair conjecture, Phys. Rev. D 44 (1991) 2380.
[20] J.D. Barrow, S. Hervik, Anisotropically inflating universes, Phys. Rev. D 73 (2006) 023007.
[21] J.D. Barrow, S. Hervik, On the evolution of universes in quadratic theories of gravity, Phys. Rev. D 74 (2006) 124017.
[22] J.D. Barrow, S. Hervik, Simple types of anisotropic inflation, Phys. Rev. D 81 (2010) 023513.
[23] M.A. Watanabe, S. Kanno, J. Soda, Inflationary universe with anisotropic hair, Phys. Rev. Lett. 102 (2009) 191302.
[24] S. Kanno, J. Soda, M.A. Watanabe, Anisotropic power-law inflation, J. Cosmol. Astropart. Phys. 12 (2010) 024.
[25] J. Soda, Statistical anisotropy from anisotropic inflation, Class. Quantum Grav. 29 (2012) 083001.
[26] A. Maleknejad, M.M. Sheikh-Jabbari, J. Soda, Gauge fields and inflation, Phys. Rep. 528 (2013) 161.
[27] T.Q. Do, W.F. Kao, Anisotropic power-law inflation for the Dirac-Born-Infeld theory, Phys. Rev. D 84 (2011) 123009.
[28] T.Q. Do, W.F. Kao, Anisotropic power-law solutions for a supersymmetry Dirac-Born-Infeld theory, Class. Quantum Grav. 33 (2016) 085009.
[29] T.Q. Do, W.F. Kao, Bianchi type I anisotropic power-law solutions for the Galileon models. Phys. Rev. D 96 (2017) 023529.
[30] T.Q. Do, W.F. Kao, Anisotropic power-law inflation of the five dimensional scalar–vector and scalar-Kalb–Ramond model, Eur. Phys. J. C 78 (2018) 531.
[31] M.S. Turner, L.M. Widrow, Inflation produced, large scale magnetic fields, Phys. Rev. D 37 (1988) 2743.
[32] B. Ratra, Cosmological ’seed’ magnetic field from inflation, Astrophys. J. 391 (1992) L1.
[33] A. Dolgov, Breaking of conformal invariance and electromagnetic field generation in the universe, Phys. Rev. D 48 (1993) 2499.
[34] K. Bamba, M. Sasaki, Large-scale magnetic fields in the inflationary universe, J. Cosmol. Astropart. Phys. 02 (2007) 030.
[35] V. Demozzi, V. Mukhanov, H. Rubinstein, Magnetic fields from inflation? J. Cosmol. Astropart. Phys. 08 (2009) 025.
[36] T.Q. Do, W.F. Kao, Anisotropic power-law inflation for a conformal-violating Maxwell model, Eur. Phys. J. C 78 (2018) 360.
[37] J. Holland, S. Kanno, I. Zavala, Anisotropic inflation with derivative couplings, Phys. Rev. D. 97 (2018) 103534.
[38] T.Q. Do, W.F. Kao, I.C. Lin, Anisotropic power-law inflation for a two scalar fields model, Phys. Rev. D 83 (2011) 123002.
[39] T.Q. Do, S.H.Q. Nguyen, Anisotropic power-law inflation in a two-scalar-field model with a mixed kinetic term, Int. J. Mod. Phys. D 26 (2017) 1750072.