Stationarity of Inflation and Predictions of Quantum Cosmology

TL;DR

The paper analyzes how inflationary cosmology can exhibit different regimes, from non-reproducing to eternally self-reproducing universes, and how the resulting volume-weighted, stationary or runaway probability distributions influence quantum cosmology predictions. It integrates chaotic inflation, nonminimal coupling, and Starobinsky-type conformal anomaly corrections to map where self-reproduction occurs and how fractal growth governs the growth of inflating volume. The authors apply these frameworks to the cosmological constant problem, suggesting, in certain models, a tendency toward Λ = 0, while also highlighting significant measure, time-slicing, and anthropic caveats. Overall, the work explores how inflationary model choice shapes observable predictions through the behavior of P_p and related growth exponents, offering potential mechanisms for addressing fundamental constants within a quantum cosmology context.

Abstract

We describe several different regimes which are possible in inflationary cosmology. The simplest one is inflation without self-reproduction of the universe. In this scenario the universe is not stationary. The second regime, which exists in a broad class of inflationary models, is eternal inflation with the self-reproduction of inflationary domains. In this regime local properties of domains with a given density and given values of fields do not depend on the time when these domains were produced. The probability distribution to find a domain with given properties in a self-reproducing universe may or may not be stationary, depending on the choice of an inflationary model. We give examples of models where each of these possibilities can be realized, and discuss some implications of our results for quantum cosmology. In particular, we propose a new mechanism which may help solving the cosmological constant problem.