Nonperturbative renormalization group for scalar fields in de Sitter space: beyond the local potential approximation

TL;DR

This paper advances the nonperturbative renormalization group approach for scalar fields in de Sitter space by including derivative expansions and field renormalization, revealing significant anomalous dimensions but preserving the gravitational dimensional reduction phenomenon.

Contribution

It develops a formalism beyond the local potential approximation, incorporating derivative expansion and field renormalization for scalar fields in curved spacetime.

Findings

Large anomalous dimensions can occur along the flow.

The effective potential remains unchanged despite the anomalous dimension effects.

The flow is slowed down by the running anomalous dimension.

Abstract

Nonperturbative renormalization group techniques have recently proven a powerful tool to tackle the nontrivial infrared dynamics of light scalar fields in de Sitter space. In the present article, we develop the formalism beyond the local potential approximation employed in earlier works. In particular, we consider the derivative expansion, a systematic expansion in powers of field derivatives, appropriate for long wavelength modes, that we generalize to the relevant case of a curved metric with Lorentzian signature. The method is illustrated with a detailed discussion of the so-called local potential approximation prime which, on top of the full effective potential, includes a running (but field-independent) field renormalization. We explicitly compute the associated anomalous dimension for O(N) theories. We find that it can take large values along the flow, leading to sizable differences as compared to the local potential approximation. However, it does not prevent the phenomenon of gravitationally induced dimensional reduction pointed out in previous studies. We show that, as a consequence, the effective potential at the end of the flow is unchanged as compared to the local potential approximation, the main effect of the running anomalous dimension being merely to slow down the flow.