Inflation in Weyl Scaling Invariant Gravity with $R^3$ Extensions

TL;DR

This paper introduces a Weyl scaling invariant gravity model with $R^2$ and $R^3$ terms that supports two distinct inflationary patterns, predicting observable primordial perturbation features for future experiments.

Contribution

The study develops a novel $R^2+R^3$ gravity model with Weyl invariance that supports multiple inflationary scenarios, expanding the landscape of inflation models and their observational signatures.

Findings

Supports inflation with tensor-to-scalar ratio from 10^{-4} to 10^{-2}

Predicts a second inflationary pattern with oscillation-induced acceleration

Both inflation patterns are testable by future CMB and gravitational wave observations

Abstract

The cosmological observations of cosmic microwave background and large-scale structure indicate that our universe has a nearly scaling invariant power spectrum of the primordial perturbation. However, the exact origin for this primordial spectrum is still unclear. Here, we propose the Weyl scaling invariant $R^2+R^3$ gravity that gives rise to inflation that is responsible for the primordial perturbation in the early universe. We develop both analytic and numerical treatments on inflationary observables, and find this model gives a distinctive scalar potential that can support two different patterns of inflation. The first one is similar to that occurs in the pure $R^2$ model, but with a wide range of tensor-to-scalar ratio $r$ from $\mathcal O(10^{-4})$ to $\mathcal O(10^{-2})$. The other one is a new situation with not only slow-roll inflation but also a short stage of oscillation-induced accelerating expansion. Both patterns of inflation have viable parameter spaces that can be probed by future experiments on cosmic microwave background and primordial gravitational waves.