Power law Starobinsky model of inflation from no-scale SUGRA

Abstract

We consider a power law $\frac{1}{M^2}R^β$ correction to Einstein gravity as a model of inflation. The interesting feature of this form of generalization is that small deviations from the Starobinsky limit $β=2$ can change the value of tensor to scalar ratio from $r \sim \mathcal{O}(10^{-3})$ to $r\sim \mathcal{O}(0.1)$. We find that in order to get large tensor perturbation $r\approx 0.1$ as indicated by BKP measurements, we require the value of $β\approx 1.83$ thereby breaking global Weyl symmetry. We show that the general $R^β$ model can be obtained from a SUGRA construction by adding a power law $(Φ+\bar Φ)^n$ term to the minimal no-scale SUGRA Kähler potential. We further show that this two parameter power law generalization of the Starobinsky model is equivalent to generalized non-minimal curvature coupled models with quantum corrected $Φ^{4}$- potentials i.e. models of the form $ξΦ^{a} R^{b} + λΦ^{4(1+γ)}$ and thus the power law Starobinsky model is the most economical parametrization of such models.