Inflation in mimetic $f(R,T)$ gravity

Abstract: In this paper, we employ mimetic $f(R,T)$ gravity coupled with Lagrange multiplier and mimetic potential to yield viable inflationary cosmological solutions consistent with latest Planck and BICEP2/Keck Array data. We present here three viable inflationary solutions of the Hubble parameter ($H$) represented by $H(N)=\left(A \exp \beta N+B \alpha ^N\right)^{\gamma }$, $H(N)=\left(A \alpha ^N+B \log N\right)^{\gamma }$, and $H(N)=\left(A e^{\beta N}+B \log N\right)^{\gamma }$, where $A$, $\beta$, $B$, $\alpha$, $\gamma$ are free parameters, and $N$ represents the number of e-foldings. We carry out the analysis with the simplest minimal $f(R,T)$ function of the form $f(R,T)= R + \chi T$, where $\chi$ is the model parameter. We report that for the chosen $f(R,T)$ gravity model, viable cosmologies are obtained compatible with observations by conveniently setting the Lagrange multiplier and the mimetic potential.