New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gas

Abstract

In the context of $f\left(R\right)$-gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of $f(R)$ theories for which new analytical solutions are given and closed-form solutions are provided.

14 pages, 2 figures, to appear in Physical Review D

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• Non violation of energy conditions in wormholes modelling
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• Minimal dark energy: key to sterile neutrino and Hubble constant tensions?
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• Relativistic stars in $f(Q)$-gravity: Exact analytic solution for the power-law case $f(Q)=Q+b{Q}^{\nu }$