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

Is there a connection between “dark” and “light” physics?

“…In fact, several models incorporating non-minimal couplings between dark energy and the electromagnetic sector have already been proposed in the literature, as solutions to problems in contemporary cosmology [65][66][67][68][69]. Although a thorough analysis of the cosmological implications of the DE-UP has not yet been attempted, the cosmological implications of Λ ∝ α −6 e cosmology were investigated in [70,71], in the context of a time-varying fine structure constant.…”

Planckintermediate results

“…Another aspect of the variation fundamental constants, which has been much discussed in the literature (see e.g., Dicke 1962;Duff 2002;Uzan 2003;Narimani et al 2012), is that only dimensionless combinations of constants can really be measured. Because of this, many previous studies have focussed on the parameter µ ≡ m e /m p .…”

“…However, there have been other suggested scalings published, e.g., Narimani et al (2012) adopted α 5 , while Kaplinghat et al (1999) suggested a scaling motivated by the dependence of the effective recombination rate on temperature, yielding α 3.4 . We checked however that this difference in scaling has a subdominant impact on the spectra and that the results are essentially unmodified, whichever scaling we choose.…”

Cosmological constant decaying with CMB temperature

“…The self-similar symmetry (SSS) model [40] describes the CMB with a symmetrical self-similar structure. The model consists of dimensionless values, because a physical constant with a dimension would not have universality [29]. Therefore, we define the fundamental dimensionless mass ratios of the proton mass m pr , electron mass m e , and Planck mass m Pl as follows:…”

“…While the standard cosmological model assumes that Λ is invariant, recent observations in particle physics and cosmology indicate that Λ ought to be treated as a dynamical quantity rather than a simple constant [17][18][19][20][21][22][23][24][25][26][27][28]. In addition, dimensional analysis [29] and the action principle [30] suggest that Λ and G cannot vary independently. Therefore, a number of cosmological models incorporating variable Λ and G have subsequently been studied [31][32][33][34][35][36][37][38][39].…”