Power law Starobinsky model of inflation from no-scale SUGRA

Abstract

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 $(\Phi +\bar{\Phi }{)}^n$ 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 ${\Phi }^4$- 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.

arXiv comment6 pages, 4 figures, Matches version to appear in Phys. Lett. B

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