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 constraint $Y_R{F}_{mn}{F}^{mn}=-\frac{2}{{\kappa }^2}$. The 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 factor $\frac{Y(R)}{2}$. 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.

28 pages, 12 figures; improved considerably; matches the version published in JCAP

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• Cosmology with variable $G$ and nonlinear electrodynamics
• Compact Stars in the Non-minimally Coupled Electromagnetic Fields to Gravity
• Anisotropic inflation in non-minimal kinetic coupling model
• Noether Symmetry Approach to the Non-Minimally Coupled $Y(R)F^2$ Gravity
• Anisotropic Stars in the Non-minimal $Y(R)F^2$ Gravity
• Inflation of the Universe by the Non-minimal $Y(R)F^2$ Models
• Anisotropic power-law inflation for the Sáez-Ballester theory non-minimally coupled to a vector field
• A model of non-minimally coupled gravitation and electromagnetism in (1+2) dimensions
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