On the covariant formalism of the effective field theory of gravity and leading order corrections

TL;DR

This paper develops a covariant effective field theory of gravity, including leading quantum corrections, and analyzes their phenomenological implications on curved spacetimes, highlighting less suppression of effects compared to flat spacetime.

Contribution

It constructs a covariant effective field theory of gravity with quantum corrections and provides a method to compute and analyze these effects on various spacetimes.

Findings

Leading quantum corrections are less suppressed on curved backgrounds.

The effective action is generally non-local and suitable for phenomenological studies.

Quantum corrections are computed up to quadratic order in curvature.

Abstract

We construct the covariant effective field theory of gravity as an expansion in inverse powers of the Planck mass, identifying the leading and next-to-leading quantum corrections. We determine the form of the effective action for the cases of pure gravity with cosmological constant as well as gravity coupled to matter. By means of heat kernel methods we renormalize and compute the leading quantum corrections to quadratic order in a curvature expansion. The final effective action in our covariant formalism is generally non-local and can be readily used to understand the phenomenology on different spacetimes. In particular, we point out that on curved backgrounds the observable leading quantum gravitational effects are less suppressed than on Minkowski spacetime.