The most general four-derivative Unitary String Effective Action with Torsion and Stringy-Running-Vacuum-Model Inflation: Old ideas from a modern perspective

TL;DR

This paper revisits string-inspired effective actions with curvature-squared terms, demonstrating that additional four-derivative terms are negligible and confirming the phenomenological completeness of the stringy running vacuum model for inflation.

Contribution

It identifies a new class of four-derivative terms compatible with unitarity and torsion in 3+1 dimensions, showing they are phenomenologically insignificant for inflation.

Findings

Additional four-derivative terms are subleading and have no practical impact on inflation.

The string-inspired effective action can be fully embedded in a UV-complete string theory framework.

The torsion interpretation of the Kalb-Ramond field is consistent with unitarity in 3+1 dimensions.

Abstract

The string-inspired running vacuum model (StRVM) of inflation is based on a Chern-Simons (CS) gravity effective action, in which the only four-spacetime-derivative-order term is a gravitational anomalous CS Pontryagin density coupled to an axion. In this work, we revisit curvature-squared string-inspired effective actions, from the point of view of appropriate local field redefinitions, leaving the perturbative string scattering matrices invariant. We require simultaneously unitarity and torsion interpretation of the field strength of the Kalb-Ramond antisymmetric tensor, features characterising the (3+1)-dimensional StRVM Cosmology. Unlike the higher dimensional case, the above feature is possible in the context of (3+1)-dimensional spacetimes, obtained after string compactification. We demonstrate that the unitarity and torsion-interpretation requirements lead to a single-type of extra four-derivative terms in the effective gravitational action, not discussed in the previous literature of StRVM, which however is shown to be subleading by many orders of magnitude, compared to the terms of the StRVM framework. Hence, its presence has no practical implications for the relevant inflationary (and, hence, postinflationary) physics of the StRVM. This demonstrates the phenomenological completeness of the StRVM cosmological scenario, which is thus fully embeddable in the UV complete (quantum-gravity compatible) string theory framework.