Power law Starobinsky model of inflation from no-scale SUGRA

We consider a power law $\frac{1}{M^2}{R}^{\beta }$ 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 $\beta =2$ 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 $\beta \approx 1.83$ thereby breaking global Weyl symmetry. We show that the general $R^{\beta }$ model can be obtained from a SUGRA construction by adding a power law $(\mathrm{\Phi }+\bar{\mathrm{\Phi }}{)}^n$ term to the minimal no-scale SUGRA K"ahler 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 ${\mathrm{\Phi }}^4$- potentials i.e. models of the form $\xi \Phi^{a} R^{b} + \lambda \Phi^{4(1+\gamma)}$ and thus the power law Starobinsky model is the most economical parametrization of such models.