Self-similar cosmological solutions in f(R,T) gravity theory

Abstract

We study the $f(R,T)$ cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the Field Equations (FE) admit exact self-similar solutions through the matter collineation approach. We study two models: the case$f(R,T)=f_1(R)+f_2(T)$ and the case $f(R,T)=f_1(R)+f_2(R)f_3(T)$. In each case, we state general theorems which determine completely the form of the unknown functions $f_i$ such that the field equations admit self-similar solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous self-similar metric$.$ In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

accepted to IJGMMP. Matches the published version. arXiv admin note: text overlap with arXiv:1407.2013 by other authors

References in corpus (11)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• f(R,L_m) gravity
• The Expansion of the Universe is Faster than Expected
• Generalized curvature-matter couplings in modified gravity
• New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state
• Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity
• Slow-roll inflation in f(R,T) gravity and a modified Starobinsky-like inflationary model
• Inflation in $f(R,T)$ Gravity
• Beyond Einstein's General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings
• Generalized dark gravity