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Why the cosmological constant is small and positive

Paul J. Steinhardt, Neil Turok

TL;DR

The paper tackles the cosmological constant problem by proposing a cyclic universe in which a dynamical relaxation mechanism gradually reduces vacuum energy, with the relaxation time growing exponentially as the density decreases. It builds on Abbott's axion-like field idea and embeds it into a cyclic, brane-world cosmology that replenishes matter and dilutes kinetic energy, avoiding the empty-universe problem. The main result is that nearly all spacetime spends most of its history at a small, positive vacuum energy, providing a natural explanation for the observed cosmological constant without requiring fine-tuning or anthropic reasoning. The approach yields falsifiable predictions, such as signatures of a cyclic gravitational-wave background, and has implications for high-scale axions and non-inflationary cosmology, offering a distinct alternative to inflation-based anthropic arguments.

Abstract

Within conventional big bang cosmology, it has proven to be very difficult to understand why today's cosmological constant is so small. In this paper, we show that a cyclic model of the universe can naturally incorporate a dynamical mechanism that automatically relaxes the value of the cosmological constant, taking account of contributions to the vacuum density at all energy scales. Because the relaxation time grows exponentially as the vacuum density decreases, nearly every volume of space spends an overwhelming majority of the time at the stage when the cosmological constant is small and positive, as observed today.

Why the cosmological constant is small and positive

TL;DR

The paper tackles the cosmological constant problem by proposing a cyclic universe in which a dynamical relaxation mechanism gradually reduces vacuum energy, with the relaxation time growing exponentially as the density decreases. It builds on Abbott's axion-like field idea and embeds it into a cyclic, brane-world cosmology that replenishes matter and dilutes kinetic energy, avoiding the empty-universe problem. The main result is that nearly all spacetime spends most of its history at a small, positive vacuum energy, providing a natural explanation for the observed cosmological constant without requiring fine-tuning or anthropic reasoning. The approach yields falsifiable predictions, such as signatures of a cyclic gravitational-wave background, and has implications for high-scale axions and non-inflationary cosmology, offering a distinct alternative to inflation-based anthropic arguments.

Abstract

Within conventional big bang cosmology, it has proven to be very difficult to understand why today's cosmological constant is so small. In this paper, we show that a cyclic model of the universe can naturally incorporate a dynamical mechanism that automatically relaxes the value of the cosmological constant, taking account of contributions to the vacuum density at all energy scales. Because the relaxation time grows exponentially as the vacuum density decreases, nearly every volume of space spends an overwhelming majority of the time at the stage when the cosmological constant is small and positive, as observed today.

Paper Structure

This paper contains 4 sections, 3 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Dynamical Relaxation: A Worked Example
  3. Cyclic Model with Dynamical Relaxation
  4. Discussion

Figures (1)

  • Figure 1: The effective cosmological constant $\Lambda_{total}$ for the washboard potential defined in Eq. \ref{['wash']} can take discrete values depending on which minimum $\phi$ occupies. In the scenario presented here, the time spent in the lowest positive minimum is exponentially greater than the entire time spent in all other minima.