Effective Nonlocal Euclidean Gravity

TL;DR

This paper explores a nonlocal modification to gravity that could address issues in Euclidean quantum gravity, remains compatible with current tests, and has potential cosmological implications, though some models face conflicts with nucleosynthesis constraints.

Contribution

It introduces a nonlocal effective gravity model that modifies Einstein's theory, aiming to resolve unboundedness and explain cosmological phenomena.

Findings

Modified gravity compatible with tests on sub-horizon scales

Induces spatial variation in effective Newton's constant

Potentially explains a universe with density parameter Ω<1

Abstract

A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newton's constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value $\Omega<1$ for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.