Growth of matter fluctuations in $f(R,T)$ Gravity. (arXiv:2004.06884v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Bhattacharjee_S/0/1/0/all/0/1">Snehasish Bhattacharjee</a>
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.
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.
http://arxiv.org/icons/sfx.gif
