Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation

TL;DR

This paper explores a string-inspired 4D Chern-Simons gravity model of inflation, highlighting quantum effects that induce metastability and estimating the inflation lifetime, with implications for string energy scales and cosmological observations.

Contribution

It introduces quantum-ordering effects on the gCS condensate, providing a second-order calculation of inflation metastability and constraining the string scale relative to Planck mass.

Findings

Inflation may be metastable due to quantum effects in gCS condensate.

Estimated inflation lifetime based on quantum-ordering ambiguities.

Constraint on string scale to Planck mass ratio, approximately 0.1.

Abstract

In this work, we elaborate further on a 4D cosmological Running-Vacuum-type Model (RVM) of inflation that characterises string-inspired Chern-Simons (CS) gravity. It has been shown that inflation in such models is caused by a condensation of the gravitational CS (gCS) terms induced by primordial gravitational waves (GW), which leads to a linear-axion potential, thus breaking the shift symmetry, and lifting its periodicity (monodromy). We demonstrate here that this inflationary phase may be metastable, due to the existence of non-trivial imaginary parts of the gCS condensate. These imaginary parts are quantum effects, proportional to appropriate commutators of GW perturbations. As we stress, their existence is quantum-ordering-scheme dependent. We argue here in favor of a physical importance of such imaginary parts, which we compute to second order in the GW (tensor) perturbations in the framework of a specific gauge-fixed effective Lagrangian, within a (mean field) weak-quantum-gravity path integral approach. We pay specific attention to the various space-time boundary terms. We thus provide an estimate of the life time of inflation. On matching our results with the relevant inflationary phenomenology, we fix the quantum-ordering ambiguities, and obtain an order-of-magnitude constraint on the ratio of the string energy scale $M_s$ in this model to the (four-spacetime-dimensional) reduced Planck mass $M_{\rm Pl}$, specifically, $M_s/M_{\rm Pl} = \mathcal{O}(10^{-1})$. This is consistent with the corresponding estimate obtained in previous analyses by the authors in this framework, based on a dynamical-system approach to linear-axion RVM inflation. Finally, we examine the role of periodic modulations in the axion potential induced by non-perturbative stringy effects on the slow-roll inflationary parameters, and find compatibility with the cosmological data.