Growth of matter fluctuations in $f(R,T)$ Gravity

Abstract

In this work, I present for the first time the analysis concerning the growth of matter fluctuations in the framework of $f(R,T)$ modified gravity where I presume $f(R,T)=R+\lambda T$, where $R$ denote the Ricci scalar, $T$ the trace of the energy-momentum tensor and $\lambda$ a constant. I first solve the Friedman equations assuming a dust universe ($\omega =0$) for the Hubble parameter $H(z)$ and then employ it in the equation of matter density fluctuations $\delta (z)$ to solve for $\delta (z)$ and the growth rate $f(z)$. Next, I proceed to show the behavior of $f(z)$ and $\delta (z)$ with redshift for some values of $\lambda$ with observational constraints. Finally, following the prescription of \cite{growft41}, I present an analytical expression for the growth index $\gamma$ which is redshift dependent and the expression reduces to $3/5$ for $\lambda =0$, which is the growth index for a dust universe.

arXiv commentPublished in Chinese Journal of Physics

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• Growth of cosmic perturbations in the modified $f(R,T)$ gravity
• Configurational Entropy in Chaplygin Gas Models
• White dwarf cooling in $f(R,T)$ gravity