Solutions to the cosmological constant problems

TL;DR

The paper analyzes two cosmological constant problems: the small observed value of $\rho_\Lambda$ and the coincidence of galaxy-formation time with $\Lambda$-domination. It compares discrete-$\Lambda$ models (brane-induced four-forms and Abbott-like washboard potentials) and continuous-$\Lambda$ models (slowly varying scalar potentials) within inflationary cosmology, emphasizing anthropic selection and the computation of the prior ${\cal P}_*$ and the conditions under which observers are likely to measure $\rho_\Lambda$ in the anthropic window. It finds that both discrete and continuous approaches can, in principle, address both CCPs but require highly tuned parameter regimes or special mechanisms (e.g., flat priors, suppressed brane nucleation, or slow-roll conditions); M-theory–motivated four-form models face significant viability constraints. The authors also discuss non-anthropic avenues, such as explaining the coincidence by a fixed $\Lambda$ with a random $Q$, or alternative dynamical scenarios like $k$-essence, and highlight that the precise form of the initial-condition prior ${\cal P}_*$ is critical for any predictive anthropic explanation. Overall, the work clarifies the strengths and limitations of anthropic versus non-anthropic solutions and underscores the central role of inflationary dynamics and priors in interpreting the cosmological constant problems.

Abstract

We critically review several recent approaches to solving the two cosmological constant problems. The "old" problem is the discrepancy between the observed value of $Λ$ and the large values suggested by particle physics models. The second problem is the "time coincidence" between the epoch of galaxy formation $t_G$ and the epoch of $Λ$-domination $t_Ł$. It is conceivable that the "old" problem can be resolved by fundamental physics alone, but we argue that in order to explain the "time coincidence" we must account for anthropic selection effects. Our main focus here is on the discrete-$Λ$ models in which $Λ$ can change through nucleation of branes. We consider the cosmology of this type of models in the context of inflation and discuss the observational constraints on the model parameters. The issue of multiple brane nucleation raised by Feng {\it et. al.} is discussed in some detail. We also review continuous-$Ł$ models in which the role of the cosmological constant is played by a slowly varying potential of a scalar field. We find that both continuous and discrete models can in principle solve both cosmological constant problems, although the required values of the parameters do not appear very natural. M-theory-motivated brane models, in which the brane tension is determined by the brane coupling to the four-form field, do not seem to be viable, except perhaps in a very tight corner of the parameter space. Finally, we point out that the time coincidence can also be explained in models where $Λ$ is fixed, but the primordial density contrast $Q=δρ/ρ$ is treated as a random variable.

Figures (3)

• Figure 1: The washboard potential.
• Figure 2: Inflaton potential
• Figure 3: Probability distribution for $t_G/t_{\Lambda}$, the time of galaxy formation as compared to the time when the cosmological constant starts dominating. Here, $\Lambda$ is taken to be a fundamental constant but the density contrast $Q$ is treated as a random variable with a priori volume distribution $\propto Q^{-\alpha}$ at the time of thermalization. The plot is shown for $\alpha=1.5,\ 3$ and $5$. The distributions present rather well defined peaks at $t_G \sim t_\Lambda$.