Constraining logarithmic $f(R,T)$ model using Dark Energy density parameter ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ and Hubble parameter $H_0$

Of many extended theories of gravity, $f(R,T)$ gravity has gained reasonable interest in recent times as it provides interesting results in cosmology. Logarithmic corrections in modified theories of gravity has been studied extensively. In this work, we considered logarithmic correction to the trace term T and take the functional form as $f(R,T)=R+16\pi G\alpha \ln T$ where $\alpha$ is a free parameter. The free parameter is constrained using dark energy density parameter ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ and Hubble parameter $H_0$. The lower bound is found to be $\alpha \ge -9.85\times {10}^{-29}$. The cosmological implications are also studied.