On the Generality and Persistence of Cosmological Stasis

TL;DR

This paper investigates a new cosmological phase called stasis, where matter and radiation abundances remain constant due to hierarchical decays, using machine learning, Bayesian analysis, and theoretical modeling to demonstrate its generality and potential implications.

Contribution

The paper introduces a comprehensive analysis of cosmological stasis using machine learning, Bayesian methods, and theoretical models, revealing its robustness and connection to exponential decay rates.

Findings

Stasis can be achieved with various decay rate and abundance configurations.

Exponential models of decay rates are exact solutions and act as attractors for stasis.

The exponential model exhibits inflation-level e-folds with fewer species, unlike power-law models.

Abstract

Hierarchical decays of $N$ matter species to radiation may balance against Hubble expansion to yield stasis, a new phase of cosmological evolution with constant matter and radiation abundances. We analyze stasis with various machine learning techniques on the full $2N$-dimensional space of decay rates and abundances, which serve as inputs to the system of Boltzmann equations that governs the dynamics. We construct a differentiable Boltzmann solver to maximize the number of stasis $e$-folds $\mathcal{N}$. High-stasis configurations obtained by gradient ascent motivate log-uniform distributions on rates and abundances to accompany power-law distributions of previous works. We demonstrate that random configurations drawn from these families of distributions regularly exhibit many $e$-folds of stasis. We additionally use them as priors in a Bayesian analysis conditioned on stasis, using stochastic variational inference with normalizing flows to model the posterior. All three numerical analyses demonstrate the generality of stasis and point to a new model in which the rates and abundances are exponential in the species index. We show that the exponential model solves the exact stasis equations, is an attractor, and satisfies $\mathcal{N}\propto N$, exhibiting inflation-level $e$-folding with a relatively low number of species. This is contrasted with the $\mathcal{N}\propto \log(N)$ scaling of power-law models. Finally, we discuss implications for the emergent string conjecture and string axiverse.