Observer-Specific Universes: A Bayesian Framework for Resolving Cosmological Naturalness Problems

TL;DR

This paper introduces a Bayesian, observer-specific framework for addressing cosmological naturalness problems, modeling observers as quantum detectors and analyzing the probabilistic structure of their perceived universes.

Contribution

It develops a rigorous mathematical formalism that incorporates observer-dependent likelihoods using quantum influence functionals, offering a novel approach to naturalness issues in cosmology.

Findings

Proves the positivity of the influence functional's imaginary part, ensuring likelihood normalization.

Shows that additional mechanisms are needed to suppress large vacuum energy values.

Establishes the mathematical consistency of the observer-specific probabilistic framework.

Abstract

Naturalness problems such as the hierarchy problem and the origin of dark energy remain significant challenges in modern cosmology. This paper develops a rigorous mathematical framework where each observer defines their own universe, and the observer's existence conditions the probabilistic definition of that universe. We model observers as quantum detectors and formulate the problem in Bayesian terms, deriving an observer-specific likelihood using the Schwinger-Keldysh influence-functional formalism in a flat FLRW background. We prove that the imaginary part of the influence functional is positive-definite, ensuring decoherence and likelihood normalization. Careful analysis of the posterior distribution reveals that additional mechanisms are needed to fully suppress large vacuum energy values. We establish the mathematical consistency of our observer-specific framework and demonstrate its potential to provide new insights into cosmological naturalness problems, complementing traditional approaches without requiring anthropic reasoning.