Adiabatic regularization and preferred vacuum state for the $\lambda \phi^4$ field theory in cosmological spacetimes

TL;DR

This paper extends adiabatic regularization for a self-interacting scalar field in cosmological spacetimes, introducing a parameter to define a preferred vacuum state at a fixed time, with applications to common cosmological backgrounds.

Contribution

It introduces an extended adiabatic regularization method with an arbitrary parameter to define a preferred vacuum state for $ ext{λ} ext{φ}^4$ theory in FLRW spacetimes.

Findings

Defined a preferred vacuum state at a fixed time using the extended method.

Computed the vacuum state for two cosmological background fields.

Provided a prescription for choosing the parameter μ.

Abstract

We extend the method of adiabatic regularization by introducing an arbitrary parameter $\mu$ for a scalar field with quartic self-coupling in a Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime at one-loop order. The subtraction terms constructed from this extended version allow us to define a preferred vacuum state at a fixed time $\eta = \eta_0$ for this theory. We compute this vacuum state for two commonly used background fields in cosmology. We also give a possible prescription for an adequate value for $\mu$.