Viable Intermediate Inflation in the Mimetic DBI Model

We study the intermediate inflation in the mimetic Dirac-Born-Infeld model. By considering the scale factor as $a=a_{0}\exp(bt^{\beta})$, we show that in some ranges of the intermediate parameters $b$ and $\beta$, the model is free of the ghost and gradient instabilities. We study the scalar spectral index, tensor spectral index, and the tensor-to-scalar ratio in this model and compare the results with Planck2018 TT, TE, EE+lowE+lensing +BAO +BK14 data at $68\%$ and $95\%$ CL. In this regard, we find some constraints on the intermediate parameters that lead to the observationally viable values of the perturbation parameters. We also seek the non-gaussian features of the primordial perturbations in the equilateral configuration. By performing the numerical analysis on the nonlinearity parameter in this configuration, we show that the amplitude of the non-gaussianity in the intermediate mimetic DBI model is predicted to be in the range $-16.7<f^{equil}<-12.5$. We show that, with $0<b\leq 10$ and $0.345<\beta<0.387$, we have an instabilities-free intermediate mimetic DBI model that gives the observationally viable perturbation and non-gaussianity parameters.