Tachyon Mimetic Inflation as an Instabilities-Free Model

Abstract: We consider the mimetic tachyon model in the Lagrange multiplier approach. We study both the linear and non-linear perturbations and find the perturbation and non-gaussianity parameters in this setup. By adopting two types of the scale factor as the power-law ($a=a_{0}\,t^{n}$) and intermediate ($a=a_{0}\exp(bt^{\beta})$) scale factors, we perform a numerical analysis on the model which is based on Planck2018 TT, TE, EE+lowE+lensing +BAO +BK14 and Planck2018 TTT, EEE, TTE and EET data sets. We show that the mimetic tachyon model with both the power-law and intermediate scale factors, in some ranges of its parameter space is instabilities-free and observationally viable. The power-law mimetic tachyon model with $26.3<n<33.0$ and the intermediate mimetic tachyon model with $0.116<\beta<0.130$ are consistent with observational data and free of the ghost and gradient instabilities.