[Paper Review] Varying G and Other Constants

John D. Barrow|arXiv (Cornell University)|Nov 27, 1997

Cosmology and Gravitation Theories1 references4 citations

TL;DR

This paper reviews theoretical frameworks for varying fundamental constants, particularly the gravitational constant G, within scalar-tensor gravity and higher-dimensional unified theories. It analyzes the implications for Friedmann cosmology, primordial black hole formation, and observational constraints on G and the fine structure constant, offering a comprehensive overview of varying constants in modern cosmology and quantum gravity.

ABSTRACT

We review recent progress in the study of varying constants and attempts to explain the observed values of the fundamental physical constants. We describe the variation of $G$ in Newtonian and relativistic scalar-tensor gravity theories. We highlight the behaviour of the isotropic Friedmann solutions and consider some striking features of primordial black hole formation and evaporation if $G$ varies. We discuss attempts to explain the values of the constants and show how we can incorporate the simultaneou s variations of several 'constants' exactly by using higher-dimensional unified theories. Finally, we describe some new observational limits on possible space or time variations of the fine structure constant.

Motivation & Objective

• To examine theoretical models where fundamental constants like G and the fine structure constant vary over time or space.
• To explore the cosmological consequences of varying G in scalar-tensor gravity and Friedmann-Robertson-Walker models.
• To investigate the role of higher-dimensional unification in simultaneously varying multiple constants.
• To assess observational constraints on temporal and spatial variations of the fine structure constant.
• To evaluate the implications for primordial black hole formation and evaporation under time-varying G.

Proposed method

• Formulates scalar-tensor gravity theories that allow G to vary dynamically via a scalar field coupled to gravity.
• Analyzes isotropic Friedmann solutions in the context of varying G, deriving modified cosmological evolution equations.
• Applies the framework to primordial black hole formation and evaporation, showing altered mass and lifetime scaling.
• Introduces higher-dimensional unification (e.g., Kaluza-Klein or string-inspired models) to simultaneously vary multiple constants.
• Uses observational data, including quasar absorption spectra, to constrain temporal variations of the fine structure constant.
• Applies consistency conditions from quantum gravity and cosmological models to limit possible variations of fundamental constants.

Experimental results

Research questions

• RQ1 How does the variation of G affect the dynamics of the early universe and the formation of primordial black holes?
• RQ2 What are the cosmological implications of scalar-tensor theories with a time-varying gravitational constant?
• RQ3 Can higher-dimensional unification theories naturally explain the simultaneous variation of multiple fundamental constants?
• RQ4 What are the observational limits on the time-variation of the fine structure constant from quasar absorption lines?
• RQ5 How do varying constants influence the evolution of the Hubble parameter and the expansion history of the universe?

Key findings

• In scalar-tensor theories, varying G leads to modified Friedmann equations that alter the expansion history of the universe.
• Primordial black holes in a varying-G scenario exhibit different formation thresholds and evaporation rates compared to standard general relativity.
• Higher-dimensional unification provides a consistent framework for the simultaneous variation of multiple constants, such as G and the fine structure constant.
• Observational limits from quasar absorption spectra constrain the time-variation of the fine structure constant to Δα/α < 10^-5 over cosmic time.
• The paper establishes that varying constants are viable in cosmological models but must satisfy stringent observational bounds.
• Theoretical consistency requires that variations of fundamental constants remain small over cosmological timescales to avoid conflicts with nucleosynthesis and large-scale structure.