Novel higher-curvature variations of $R^2$ inflation

TL;DR

This paper introduces new higher-curvature modifications to $R^2$ inflation that maintain second-order equations, explores their inflationary dynamics, derives holographic bounds, and analyzes their impact on primordial perturbations, with potential observational implications.

Contribution

It presents novel geometric higher-curvature extensions of Starobinsky inflation with second-order equations and holographic bounds, advancing the understanding of inflationary models and their observational signatures.

Findings

Identified models with extended slow roll inflation as attractors.

Derived holographic unitarity bounds on higher-curvature corrections.

Calculated modifications to primordial perturbation spectra and consistency relations.

Abstract

We put forward novel extensions of Starobinsky inflation, involving a class of 'geometric' higher-curvature corrections that yield second-order Friedmann-Lema\^itre equations and second-order-in-time linearized equations around cosmological backgrounds. We determine the range of models within this class that admit an extended phase of slow roll inflation as an attractor. By embedding these theories in anti-de Sitter space, we derive holographic 'unitarity' bounds on the two dominant higher-order curvature corrections. Finally we compute the leading corrections to the spectral properties of scalar and tensor primordial perturbations, including the modified consistency relation $r=-8n_{T}$. Remarkably, the range of models singled out by holography nearly coincides with the current observational bounds on the scalar spectral tilt. Our results indicate that future observations have the potential to discriminate between different higher-curvature corrections considered here.