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 ≤ 10 and 0.345 < β < 0.387, we have an instabilities-free intermediate mimetic DBI model that gives the observationally viable perturbation and non-Gaussianity parameters.