A Caveat on Building Nonlocal Models of Cosmology

TL;DR

This paper critically examines methods for constructing nonlocal cosmological models, highlighting that existing techniques may not accurately reflect models derived from fundamental theories due to their differing approaches to causality and conservation.

Contribution

It clarifies that current methods for building nonlocal cosmological models access different classes of models and may not correspond to those emerging from fundamental theory.

Findings

Different techniques access distinct classes of models.

Neither method may accurately represent models from fundamental theory.

Abstract

Nonlocal models of cosmology might derive from graviton loop corrections to the effective field equations from the epoch of primordial inflation. Although the Schwinger-Keldysh formalism would automatically produce causal and conserved effective field equations, the models so far proposed have been purely phenomenological. Two techniques have been employed to generate causal and conserved field equations: either varying an invariant nonlocal effective action and then enforcing causality by the ad hoc replacement of any advanced Green's function with its retarded counterpart, or else introducing causal nonlocality into a general ansatz for the field equations and then enforcing conservation. We point out here that the two techniques access very different classes of models, and that neither one of them may represent what would actually arise from fundamental theory.