Non-Local Modification of Gravity and the Cosmological Constant Problem

TL;DR

The paper confronts the cosmological constant problem by proposing a phenomenological, generally covariant non-local modification of gravity at infrared scales that deamplifies the gravitational impact of vacuum energy. By treating Newton's constant as a high-pass filter through a non-local operator ${\cal F}(L^2\nabla^2)$, it preserves standard short-distance gravity while suppressing homogeneous, long-wavelength sources; in the $L\to\infty$ limit this yields a universal equation coupling the Einstein tensor to the space-time-averaged curvature, effectively driving the observed curvature to tiny values in asymptotically de Sitter spaces. The framework accommodates acausality as a feature that resolves the CCP, explores connections to dS/CFT, and discusses finite-$L$ extensions that offer novel inflationary dynamics and potential observational consequences. Overall, the approach provides a coherent infrared mechanism to degravitate vacuum energy without fine-tuning, while maintaining compatibility with conventional cosmology and offering new directions for inflation and holography.

Abstract

We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. The effective Newton constant becomes very small at large length scales, so that sources with immense wavelengths and periods -- such as the vacuum energy-- produce minuscule curvature. Conventional astrophysics, cosmology and standard inflationary scenaria are unaffected, as they involve shorter length scales. A new possibility emerges that inflation may ``self-terminate'' naturally by its own action of stretching wavelengths to enormous sizes. In a simple limit our proposal leads to a modification of Einstein's equation by a single additional term proportional to the average space-time curvature of the Universe. It may also have a qualitative connection with the dS/CFT conjecture.