Cosmological constraints on a dynamical electron mass

Abstract

Motivated by recent astrophysical observations of quasar absorption systems, we formulate a simple theory where the electron to proton mass ratio µ = me/mp is allowed to vary in space-time. In such a minimal theory only the electron mass varies, with α and mp kept constant. We find that changes in µ will be driven by the electronic energy density after the electron mass threshold is crossed. Particle production in this scenario is negligible. The cosmological constraints imposed by recent astronomical observations are very weak, due to the low mass density in electrons. Unlike in similar theories for spacetime variation of the fine structure constant, the observational constraints on variations in µ imposed by the weak equivalence principle are much more stringent constraints than those from quasar spectra. Any time-variation in the electron-proton mass ratio must be less than one part in 10 9 since redshifts z ≈ 1.This is more than one thousand times smaller than current spectroscopic sensitivities can achieve. Astronomically observable variations in the electron-proton must therefore arise directly from effects induced by varying fine structure 'constant' or by processes associated with internal proton structure. We also place a new upper bound of 2 × 10 −8 on any large-scale spatial variation of µ that is compatible with the isotropy of the microwave background radiation.

The status of varying constants: a review of the physics, searches and implications

“…Observationally, this leads to a varying proton-to-electron mass ratio, µ. (Note that [152] uses a definition of µ which is opposite to the one we follow here, specifically it defines it as m e /m p .) As before we can assume that the field driving these variations, in this case denoted φ, does not significantly contribute to the Friedmann equation.…”

“…However, we note that the recently launched MICROSCOPE satellite is expected to improve the sensitivity of local bounds to η ∼ 10 −15 [151], thus enabling additional constraints. The Bekenstein-Barrow-Magueijo model for varying µ was introduced in [152]. It is again a dilatontype model and to a large extent analogous to the α Astrophysical and cosmological constraints on Bekenstein-type models, specifically 2D likelihood contours on the ζα − Ωm plane (top panel) and the ζµ − Ωm plane (bottom panel).…”

On a possible variation of the proton-to-electron mass ratio: H2 spectra in the line of sight of high-redshift quasars and in the laboratory

“…Besides the older Kaluza-Klein theories that relate such variations to compactified extra dimensions [15,16], also modern superstring and M-theories predict similar variations [17]. Barrow and coworkers [18,19] have developed a theoretical scenario that would allow variation of l. In a 'minimal theory', where m e varies and a and m p are kept constant, selfconsistent extensions of general relativity are imposed ensuring energy and momentum conservation. We note that in a theoretical scenario it is very well conceivable that dimensional parameters vary, whereas in experiments only variation of dimensionless parameters can be probed on a cosmological time scale.…”

Observable effects of scalar fields and varying constants

“…This only starts to occur during the matter era; at these epochs it is an acceptable approximation to consider the Universe to be comprised of only pressureless dust (baryonic and dark matter), density ε, and some cosmological constant, Λ. We usually expect that the scalar field φ will couple only to some fraction of the total dust density; for example, in varying-α em theories it couples to the fraction that feels the electromagnetic force, and in varying m e theories it couples only to the electron density [9]. We will assume, as is almost always the case, that the fraction of matter to which it couples is approximately constant during the epoch of interest.…”

“…Included in this formulation are all standard theories for varying constants, like those for the variation of the Newtonian gravitation 'constant' G, α em , and the electron-proton mass ratio, as described in refs. [5,6,7,9].…”