Redshifting the Cosmological Constant in Unimodular Gravity via Nonlinear Quantum Mechanics

TL;DR

This paper proposes a novel modification to unimodular gravity using nonlinear quantum mechanics, which causes the shadow cosmological constant to redshift away, resolving fine-tuning issues and aligning with cosmological observations.

Contribution

It introduces state-dependent nonlinear quantum terms into gravity equations, enabling the shadow energy to diminish over time without fine-tuning.

Findings

Shadow energy density redshifts away with cosmic expansion.

Cosmology remains matter and radiation dominated without fine-tuning.

The modified gravity is consistent with local and cosmological tests.

Abstract

The cosmological constant problem represents a profound conflict between quantum field theory and general relativity. Unimodular gravity offers a compelling starting point by de-gravitating the vacuum energy of the Standard Model, but this framework traditionally trades the problem of vacuum energy for a fine-tuning of initial conditions, which manifest as a ``shadow" cosmological constant. In this paper, we resolve this initial conditions problem by proposing a novel modification to gravity based on nonlinear quantum mechanics. We introduce specific state-dependent terms to the Hamiltonian, constructed from expectation values of the metric such as the average Ricci scalar. These terms alter the dynamical equations of gravity such that the shadow energy density associated with unconstrained initial conditions redshifts away with cosmic expansion, rendering it negligible at late times. The resulting cosmology is naturally dominated by matter and radiation without fine-tuning. We demonstrate that this significant infrared modification of gravity is consistent with local and cosmological tests of gravity. We comment on the possibility of testing this solution in cosmological measurements of Newton's constant.