Twisting inflation to sub-Planckian axion decay constants

TL;DR

This paper explores how torsion in Einstein-Cartan gravity, coupled with specific topological terms, can effectively increase the axion decay constant, enabling sub-Planckian inflation with certain potentials consistent with observational data.

Contribution

It introduces non-minimal topological couplings in Einstein-Cartan gravity that modify the axion decay constant, allowing steep potentials to drive inflation compatible with observations.

Findings

Torsion and topological couplings can increase the axion decay constant.

Natural inflation remains incompatible with data, but hilltop potentials can be viable.

Parity violation leads to chiral gravitational waves.

Abstract

We study pseudoscalar inflation in the Einstein-Cartan-Palatini (first-order) formulation of gravity while allowing for torsion. We introduce two non-minimal interactions in the gravitational sector: pseudoscalar couplings to the Pontryagin density (Chern-Simons term) and the Nieh-Yan topological invariant. In the presence of these terms, the rolling pseudoscalar sources non-trivial torsional fields during inflation. We show that pathological gradient and ghost instabilities limit the strength of the coupling to the Pontryagin density during inflation. Furthermore, we show that the interaction with the Nieh-Yan term induces a new contribution to the pseudoscalar kinetic term, which parametrically increases its decay constant and allows for inflation on steep potentials. The torsion field generated by the background is parity violating, which is manifest in the resulting chiral gravitational wave spectrum. We find that the scalar sector is largely unaffected beyond the remapping of the axion decay constant to a larger value. Consequently, we show that while natural inflation with a cosine potential remains inconsistent with observations, the squared quartic hilltop potential can be made consistent with Planck 2018 data even for sub-Planckian decay constants by coupling to the Nieh-Yan term.