Quantum backreaction of $O(N)$-symmetric scalar fields and de Sitter spacetimes at the renormalization point: renormalization schemes and the screening of the cosmological constant

TL;DR

This paper investigates the quantum backreaction of $O(N)$-symmetric scalar fields on de Sitter spacetimes, comparing different renormalization schemes, and finds that a scheme using the classical de Sitter background is most suitable for analyzing quantum effects and cosmological constant screening.

Contribution

It introduces and compares new renormalization schemes for semiclassical Einstein equations, highlighting the scheme based on the classical de Sitter background as most effective for quantum backreaction analysis.

Findings

Quantum backreaction is suppressed by $H^2/M_{pl}^2$ without logarithmic enhancement.

The scheme using the classical de Sitter background is most appropriate for quantum effects in de Sitter space.

Quantum effects lead to a small screening of the classical cosmological constant.

Abstract

We consider a theory of $N$ self-interacting quantum scalar fields with quartic $O(N)$-symmetric potential, with a coupling constant $\lambda$, in a generic curved spacetime. We analyze the renormalization process of the Semiclassical Einstein Equations at leading order in the $1/N$ expansion for different renormailzation schemes, namely: the traditional one that sets the geometry of the spacetime to be Minkowski at the renormalization point, and new schemes (originally proposed in [1,2]) which set the geometry to be that of a fixed de Sitter spacetime. In particular, we study the quantum backreaction for fields in de Sitter spacetimes with masses much smaller than the expansion rate $H$. We find that the scheme that uses the classical de Sitter background solution at the renormalization point, stands out as the most appropriate to study the quantum effects on de Sitter spacetimes. Adopting such scheme we obtain the backreaction is suppressed by $H^2/M_{pl}^2$ with no logarithmic enhancement factor of $\ln{\lambda}$, giving only a small screening of the classical cosmological constant due to the backreaction of such quantum fields. We point out the use of the new schemes can also be more appropriate than the traditional one to study quantum effects in other spacetimes relevant for cosmology.