Scrutinizing the Cosmological Constant Problem and a possible resolution

TL;DR

This paper proposes a new perspective on the cosmological constant problem by redefining vacuum energy based on the time variation of the universe's scale factor, leading to results consistent with observations and potential inflation models.

Contribution

It introduces a novel approach to vacuum energy that depends on the universe's dynamics, offering a possible resolution to the cosmological constant problem.

Findings

Vacuum energy density is approximately proportional to the square of the Hubble constant.

For a Planck-scale cutoff, the vacuum energy matches astrophysical measurements.

A different vacuum choice could model inflation in the early universe.

Abstract

We suggest a new perspective on the Cosmological Constant Problem by scrutinizing its standard formulation. In classical and quantum mechanics without gravity, there is no definition of the zero point of energy. Furthermore, the Casimir effect only measures how the vacuum energy {\it changes} as one varies a geometric modulus. This leads us to propose that the physical vacuum energy in a Friedman-Lema\^itre-Robertson-Walker expanding universe only depends on the time variation of the scale factor $a(t)$. Equivalently, requiring that empty Minkowski space is gravitationally stable is a principle that fixes the ambiguity in the zero point energy. On the other hand, if there is a meaningful bare cosmological constant, this prescription should be viewed as a fine-tuning. We describe two different choices of vacuum, one of which is consistent with the current universe consisting only of matter and vacuum energy. The resulting vacuum energy density $\rhovac$ is constant in time and approximately $k_c^2 H_0^2$, where $k_c$ is a momentum cut-off and $H_0$ is the current Hubble constant; for a cut-off close to the Planck scale, values of $\rhovac$ in agreement with astrophysical measurements are obtained. Another choice of vacuum is more relevant to the early universe consisting of only radiation and vacuum energy, and we suggest it as a possible model of inflation.