An Inflationary Scenario in Mimetic Gravity

Abstract

We study the Starobinsky potential model of inflation in mimetic gravity where the box of the mimetic field (d’Alembertian) is coupled to the inflation potential, and then note that the observable quantities, namely the tensor-to-scalar ratio in perturbations and the spectral index agree with observations. To that end, a review of cosmology and inflation in ordinary General Relativity is presented. The results of Higgs inflationary scenario and Starobinsky/R2 model are noted, specifically the tensor-to-scalar ratio and the spectral index which are proportional to the inverse square of the number of e-folds N and to the inverse of N respectively during inflation. Then Mimetic gravity, a modified theory of gravity which incorporates dark matter in the underlying geometry of spacetime is revisited. This incorporation is due to writing the physical metric as an auxiliary metric multiplied by a conformal mode. We then proceed to setup the theory of mimetic inflation by coupling a linear function of the d’Alembertian of the mimetic field with the inflaton potential in the action. We get the equations of motion, analyze them in the modified slow roll approximation, and show that an inflationary epoch takes place. After proving that a reheating phase indeed occurs in our model, we then carry cosmological perturbations to the background equations of motion to get the scalar and tensor power spectrum. It is shown afterwards that for our Starobinsky potential model the observable quantities (spectral index and tensor-to-scalar ratio) agree with observations and with Higgs inflationary scenario / R2 inflation. Finally, a very brief look on self-reproduction/eternal inflation and how to possibly avoid it based on this work is mentioned.