A small but nonzero cosmological constant

TL;DR

This paper explores how unimodular gravity can explain the small, nonzero, and positive cosmological constant as a dynamical quantity evolving with the universe's scale factor, addressing longstanding cosmological puzzles.

Contribution

It proposes that unimodular gravity makes the cosmological constant dynamical, evolving with the universe's scale factor, offering a unified approach to the smallness, nonzero value, and positivity.

Findings

Cosmological constant becomes dynamical in unimodular gravity.

Lambda varies as (R(t_0)/R(t))^2 after redshift z ~ 1.

Provides a potential solution to the cosmological constant problem.

Abstract

Recent astrophysical observations seem to indicate that the cosmological constant is small but nonzero and positive. The old cosmological constant problem asks why it is so small; we must now ask, in addition, why it is nonzero (and is in the range found by recent observations), and why it is positive. In this essay, we try to kill these three metaphorical birds with one stone. That stone is the unimodular theory of gravity, which is the ordinary theory of gravity, except for the way the cosmological constant arises in the theory. We argue that the cosmological constant becomes dynamical, and eventually, in terms of the cosmic scale factor $R(t)$, it takes the form $\Lambda(t) = \Lambda(t_0)(R(t_0)/R(t))^2$, but not before the epoch corresponding to the redshift parameter $z \sim 1$.