[Paper Review] The Classification of Universes

James D. Bjorken|arXiv (Cornell University)|Apr 12, 2004

Cosmology and Gravitation Theories1 references4 citations

TL;DR

This paper proposes a phenomenologically grounded multiverse framework by defining a 'universe' as a comoving spacetime box containing all measurable phenomena, from which a local ensemble of similar universes is constructed. By assuming strong correlations between standard model parameters and the inverse Hubble parameter (size), it estimates the range of sizes allowing life and suggests a natural distribution favoring small sizes, offering a novel, testable approach to the hierarchy problem in particle physics.

ABSTRACT

We define a universe as the contents of a spacetime box with comoving walls, large enough to contain essentially all phenomena that can be conceivably measured. The initial time is taken as the epoch when the lowest CMB modes undergo horizon crossing, and the final time taken when the wavelengths of CMB photons are comparable with the Hubble scale, i.e. with the nominal size of the universe. This allows the definition of a local ensemble of similarly constructed universes, using only modest extrapolations of the observed behavior of the cosmos. We then assume that further out in spacetime, similar universes can be constructed but containing different standard model parameters. Within this multiverse ensemble, it is assumed that the standard model parameters are strongly correlated with size, i.e. with the value of the inverse Hubble parameter at the final time, in a manner as previously suggested. This allows an estimate of the range of sizes which allow life as we know it, and invites a speculation regarding the most natural distribution of sizes. If small sizes are favored, this in turn allows some understanding of the hierarchy problems of particle physics. Subsequent sections of the paper explore other possible implications. In all cases, the approach is as bottoms up and as phenomenological as possible, and suggests that theories of the multiverse so constructed may in fact lay some claim of being scientific.

Motivation & Objective

• To establish a scientifically defensible framework for the multiverse by defining a universe as a comoving spacetime box large enough to contain all measurable phenomena.
• To construct a local ensemble of universes with similar cosmological and particle physics properties, extrapolated from our own universe’s observed behavior.
• To investigate whether standard model parameters are strongly correlated with the size of the universe (inverse Hubble parameter), particularly in relation to life-supporting conditions.
• To explore whether such a correlation can provide a natural explanation for the hierarchy problem in particle physics.
• To argue that this approach, though speculative, is more scientific and phenomenologically grounded than broader multiverse proposals, due to its reliance on observable data and minimal assumptions.

Proposed method

• Define a universe as the contents of a spacetime box with comoving walls, spanning from the CMB horizon crossing epoch to the time when CMB photon wavelengths match the Hubble scale.
• Construct a local ensemble of universes by extrapolating the physical laws and initial conditions of our universe to causally disconnected but nearby spacetime regions.
• Assume that standard model parameters (e.g., coupling constants, masses) are strongly correlated with the final inverse Hubble parameter, i.e., the size of the universe at the end of the evolution.
• Use the Friedmann-Robertson-Walker (FRW) equations to model cosmic expansion across radiation, matter, and dark energy-dominated epochs, with equations of state ω = 0, 1/3, and -1 respectively.
• Apply the scaling hypothesis that physical parameters scale with the size of the universe, particularly linking the hierarchy problem to critical exponents like 1/3 (QCD) and 1/4 (electroweak).
• Use the event horizon distance E(t) = H⁻¹ in the de Sitter era and E(t) ≈ a(t)η₀ in earlier epochs to model observable limits and cosmic size evolution.

Experimental results

Research questions

• RQ1 Can a local, phenomenologically motivated multiverse ensemble be constructed using only modest extrapolations of observed cosmological and particle physics data?
• RQ2 Are standard model parameters strongly correlated with the size of the universe (as parameterized by the inverse Hubble parameter at the final time)?
• RQ3 What range of universe sizes allows for the existence of life as we know it, given the observed values of fundamental parameters?
• RQ4 Can the observed fine-tuning of standard model parameters be explained by a natural distribution of universe sizes within such a multiverse?
• RQ5 Does this multiverse model provide a testable or predictive explanation for the hierarchy problem in particle physics?

Key findings

• The paper proposes that the inverse Hubble parameter at the final time (i.e., the size of the universe) is strongly correlated with standard model parameters, particularly those governing the hierarchy problem.
• The scaling hypothesis—wherein parameters scale with cosmic size—leads to a natural explanation for the observed hierarchy in particle physics, such as the 1/3 exponent in QCD and 1/4 in the electroweak sector.
• The model suggests that small-sized universes are naturally favored in the ensemble, which may explain why the hierarchy problem appears fine-tuned in our universe.
• The analysis shows that the event horizon distance E(t) scales as H⁻¹ in the de Sitter era and as a(t)η₀ in earlier epochs, with log E(t) vs. log a showing a slope of +1 during matter and radiation domination.
• The model provides a phenomenological framework that links real physical issues—such as QCD vacuum structure and reheating after inflation—to multiverse reasoning, suggesting testable implications within our own universe.
• By grounding the multiverse in observable cosmological data and minimal assumptions, the paper argues that such a framework can lay claim to scientific status, despite its speculative nature.