## 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_{RF}_{mn}F^{mn} =-2/κ^{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 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.

Original language | English |
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Article number | 026 |

Journal | Journal of Cosmology and Astroparticle Physics |

Volume | 2017 |

Issue number | 11 |

DOIs | |

Publication status | Published - 16 Nov 2017 |

### Bibliographical note

Publisher Copyright:© 2017 IOP Publishing Ltd and Sissa Medialab.

### Funding

Ö.A. acknowledges the support by the Science Academy in the scheme of Distinguished Young Scientist Awards (BAGEP). Ö.A. acknowledges further the financial support he received from, and hospitality of Koc¸ University and the Abdus Salam International Centre for Theoretical Physics (ICTP), where parts of this work were carried out. Ö.S. acknowledges the support from Pamukkale University Scientific Research Fund with BAP project no: 2017HZDP009.

Funders | Funder number |
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Koc¸ University | |

Pamukkale University Scientific Research Fund | 2017HZDP009 |

Abdus Salam International Centre for Theoretical Physics | |

Bilim Akademisi |

## Keywords

- cosmic magnetic fields theory
- ination
- modified gravity