Anisotropic inflation with a non-minimally coupled electromagnetic field to gravity

Abstract

We consider the non-minimal model of gravity in Y (R)F 2 -form. We investigate a particular case of the model, for which the higher order derivatives are eliminated but the scalar curvature R is kept to be dynamical via the constraintThe effective fluid obtained can be represented by interacting electromagnetic field and vacuum depending on Y (R), namely, the energy density of the vacuum tracks R while energy density of the conventional electromagnetic field is dynamically scaled with the factor2 . We give exact solutions for anisotropic inflation by assuming the volume scale factor of the Universe exhibits a power-law expansion. The directional scale factors do not necessarily exhibit power-law expansion, which would give rise to a constant expansion anisotropy, but expand non-trivially and give rise to a non-monotonically evolving expansion anisotropy that eventually converges to a non-zero constant. Relying on this fact, we discuss the anisotropic e-fold during the inflation by considering observed scale invariance in CMB and demanding the Universe to undergo the same amount of e-folds in all directions. We calculate the residual expansion anisotropy at the end of inflation, though as a result of non-monotonic behaviour of expansion anisotropy all the axes of the Universe undergo the same of amount of e-folds by the end of inflation. We also discuss the generation of the modified electromagnetic field during the first few e-folds of the inflation and its persistence against to the vacuum till end of inflation.

Anisotropic power-law inflation for a conformal-violating Maxwell model

“…It would be interesting to examine the validity of the cosmic no-hair conjecture for some other possible coupling terms in the conformal-violating theory. For example, those models that have been discussed recently, e.g., I R, R μν , R μνλκ [79,80,[91][92][93][94][95][96], I = I A 2 [97], I = I (G) [98,99], and I = I (k F ) αβμν [100,101]. The result shown in this paper focusing on the late-time evolution is a new approach to the selection rules for the compatible models.…”

“…A conformal-violating Maxwell theory can be described by the general action given by [82][83][84] [79,80,[91][92][93][94][95][96], I = I A 2 [97], I = I (G) [98,99], and I = I (k F ) αβμν [100,101] have been considered extensively in the literature. Note that the Planck mass M p has been set as one for convenience.…”

“…One might also consider some subclasses of the conformal-violating Maxwell theory to see whether the cosmic no-hair conjecture breaks down. In particular, a model with a Ricci scalar non-minimally coupled to the electromagnetic field via a coupling Y (R)F μν F μν [91] has already been considered.…”

Inflation of the universe by the non-minimal Y (R )F 2 models

“…From (45) we see that p = −ρ + 2ρ 3n (47) and by considering the Planck data and perfect fluid approach f (ρ) ρ = 2 3n = 5.3 × 10 −3 , gives n ≈ 126 at the inflation. We note that the anisotropic solutions which obtained in [40] with the mean scale factor v = v 1 t α−1/3 have the same cosmological parameters (the mean Hubble and deceleration parameters) with the isotropic scale factor a = a 0 t n , where n = α − 1/3. Therefore the analysis of the mean quantities in [40] gives the same results with this isotropic case.…”

“…Also the RF 2 type couplings and their effects on gravity are studied in [28][29][30], and they were derived from reduction of higher dimensional gravity theories [31][32][33] and the calculation of vacuum polarization in a curved background [34]. Furthermore it is important to note that they also have used to explain the generation of primordial magnetic fields [27,[35][36][37][38][39][40][41].…”