  $f(R,T)$ gravity is a widely used extended theory of gravity introduced in
\cite{9} which is a straightforward generalization of $f(R)$ gravity. The
action in this extended theory of gravity incorporates well motivated
functional forms of the Ricci scalar $R$ and trace of energy momentum tensor
$T$. The present manuscript aims at constraining the most widely used $f(R,T)$
gravity model of the form $f(R+2\lambda T)$ to understand its coherency and
applicability in cosmology. We communicate here a novel method to find an lower
bound on the model parameter $\lambda \gtrsim -1.9 \times 10^{-8}$ through the
equation relating the cosmological constant ($\Lambda$) and the critical
density of the universe ($\rho_{cr}$).
