Birefringent Gravitational Waves and the Consistency Check of Inflation

TL;DR

This paper investigates how the gravitational Chern-Simons term affects super-horizon gravitational waves during inflation, providing a potential probe of string-inspired leptogenesis mechanisms through the CMB, though the observable effects are very small.

Contribution

It calculates the impact of the gravitational Chern-Simons term on inflationary gravitational waves and the tensor-to-scalar ratio, linking stringy physics to observable cosmological signals.

Findings

The amplitude of super-Hubble gravitational waves is modified by the Chern-Simons term.

The spectral index of gravitational waves remains unchanged at leading order.

The correction to the tensor-to-scalar ratio T/S is very small and likely unobservable.

Abstract

In this work we show that the gravitational Chern-Simons term, aside from being a key ingredient in inflationary baryogenesis, modifies super-horizon gravitational waves produced during inflation. We compute the super-Hubble gravitational power spectrum in the slow-roll approximation and show that its overall amplitude is modified while its spectral index remains unchanged (at leading order in the slow-roll parameters). Then, we calculate the correction to the tensor to scalar ratio, T/S. We find a correction of T/S which is dependent on $\cal{N}$ (more precisely quadratic in ${\cal N}$), the parameter characterizing the amplitude of the Chern-Simons terms. In a stringy embedding of the leptogenesis mechanism, $\cal{N}$ is the ratio between the Planck scale and the fundamental string scale. Thus, in principle, we provide a direct probe of leptogenesis due to stringy dynamics in the Cosmic Microwave Background (CMB). However, we demonstrate that the corresponding correction of T/S is in fact very small and not observable in the regime where our calculations are valid. To obtain a sizable effect, we argue that a non-linear calculation is necessary.