Theories of the Cosmological Constant

TL;DR

The paper surveys the cosmological constant problem, contrasting the large quantum vacuum energy with the tiny observed value, and surveys three directions to resolve it: deep symmetries, cancellation mechanisms, and anthropic constraints. It emphasizes that, beyond speculative symmetry-based ideas, a practical path lies in anthropic reasoning within a multiverse of subuniverses where $\rho_V$ differs, and in computing the observer-weighted probability distribution of $\rho_V$. By applying a Gunn–Gott spherical-collapse model, it derives an observer-weighted distribution $\mathcal{P}_{obs}(\rho_V)$ that favors values permitting structure formation, and expresses the mean $\langle\rho_V\rangle$ in terms of recombination-era density fluctuations. The analysis highlights how the spectrum of primordial fluctuations and the handling of critical overdensities critically influence the predicted range of $\rho_V$, and discusses related work (e.g., Efstathiou) and ongoing numerical efforts to refine the distribution.

Abstract

This is a talk given at the conference ``Critical Dialogues in Cosmology'' at Princeton University, June 24-- 27, 1996. It gives a brief summary of our present theoretical understanding regarding the value of the cosmological constant, and describes how to calculate the probability distribution of the observed cosmological constant in cosmological theories with a large number of subuniverses (i. e., different expanding regions, or different terms in the wave function of the universe) in which this constant takes different values.