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arXiv · 2004.06884

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

Snehasish Bhattacharjee
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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 $f(R,T) = R + λT$, where $R$ denote the Ricci scalar, $T$ the trace of the energy-momentum tensor and $λ$ a constant. I first solve the Friedman equations assuming a dust universe ($ω=0$) for the Hubble parameter $H(z)$ and then employ it in the equation of matter density fluctuations $δ(z)$ to solve for $δ(z)$ and the growth rate $f(z)$. Next, I proceed to show the behavior of $f(z)$ and $δ(z)$ with redshift for some values of $λ$ with observational constraints. Finally, following the prescription of \cite{growft41}, I present an analytical expression for the growth index $γ$ which is redshift dependent and the expression reduces to $3/5$ for $λ=0$, which is the growth index for a dust universe.

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Snehasish Bhattacharjee. 2020-09-16. Growth of matter fluctuations in $f(R,T)$ Gravity. https://doi.org/10.1016/j.cjph.2020.09.033

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