Dimensionless cosmology

Abstract

Although it is well known that any consideration of the variations of fundamental constants should be restricted to their dimensionless combinations, the literature on variations of the gravitational constant $G$ is entirely dimensionful. To illustrate applications of this to cosmology, we explicitly give a dimensionless version of the parameters of the standard cosmological model, and describe the physics of Big Bang Neucleosynthesis and recombination in a dimensionless manner. The issue that appears to have been missed in many studies is that in cosmology the strength of gravity is bound up in the cosmological equations, and the epoch at which we live is a crucial part of the model. We argue that it is useful to consider the hypothetical situation of communicating with another civilization (with entirely different units), comparing only dimensionless constants, in order to decide if we live in a Universe governed by precisely the same physical laws. In this thought experiment, we would also have to compare epochs, which can be defined by giving the value of any {\it one} of the evolving cosmological parameters. By setting things up carefully in this way one can avoid inconsistent results when considering variable constants, caused by effectively fixing more than one parameter today. We show examples of this effect by considering microwave background anisotropies, being careful to maintain dimensionlessness throughout. We present Fisher matrix calculations to estimate how well the fine structure constants for electromagnetism and gravity can be determined with future microwave background experiments. We highlight how one can be misled by simply adding $G$ to the usual cosmological parameter set.

References in corpus (19)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Varying constants, Gravitation and Cosmology
• Primordial Nucleosynthesis: from precision cosmology to fundamental physics
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Evolving Newton's Constant, Extended Gravity Theories and SnIa Data Analysis
• Observational signatures of Jordan-Brans-Dicke theories of gravity
• An upper limit to the secular variation of the gravitational constant from white dwarf stars
• From Cavendish to PLANCK: Constraining Newton's Gravitational Constant with CMB Temperature and Polarization Anisotropy
• Planck constraints on scalar-tensor cosmology and the variation of the gravitational constant
• Tilted Physics: A Cosmologically Dipole-Modulated Sky
• CMB constraints on the fine structure constant
• Varying couplings in the early universe: correlated variations of $\alpha$ and $G$
• The WiggleZ Dark Energy Survey: constraining the evolution of Newton's constant using the growth rate of structure
• Constraining the Variation of G by Cosmic Microwave Background Anisotropies
• Black Hole Constraints on Varying Fundamental Constants
• Let's talk about varying G
• Cosmic microwave background constraints on the strong equivalence principle
• Big bang nucleosynthesis as a probe of fundamental "constants"
• Black Hole Entropy Constraints on Variation of the Gravitational Constant

Cited by in corpus (7)

• Planck intermediate results. XXIV. Constraints on variation of fundamental constants
• How fundamental are fundamental constants?
• A 5% measurement of the gravitational constant in the Large Magellanic Cloud
• Is there a connection between "dark" and "light" physics?
• The role of $T_0$ in CMB anisotropy measurements
• How does pressure gravitate? Cosmological constant problem confronts observational cosmology
• Dimensionless constants and cosmological measurements