New varying speed of light theories

TL;DR

New varying speed of light theories surveys the meaning, mechanisms, and observational status of a non-constant $c$, framing the discussion around Lorentz-breaking, bimetric, Lorentz-invariant, color-dependent, extra-dimensional, and field-theoretic realizations. It connects VSL to quantum gravity concepts such as non-linear Lorentz realizations and doubly special relativity, and discusses implications for horizon/flatness problems, structure formation, and black-hole physics. The paper highlights potential observational signals (e.g., redshift evolution of $\alpha$, high-energy cosmic-ray thresholds, and GRB timing) while acknowledging tight but not insurmountable constraints, and it outlines concrete predictions and falsifiability pathways for future experiments and observations. Overall, VSL offers a unifying phenomenology linking cosmology, quantum gravity, and astrophysical tests, with the potential to explain or complement inflationary insights under specific dynamical implementations.

Abstract

We review recent work on the possibility of a varying speed of light (VSL). We start by discussing the physical meaning of a varying $c$, dispelling the myth that the constancy of $c$ is a matter of logical consistency. We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a color dependent speed of light; varying $c$ induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation. We show how VSL scenarios may solve the cosmological problems usually tackled by inflation, and also how they may produce a scale-invariant spectrum of Gaussian fluctuations, capable of explaining the WMAP data. We then review the connection between VSL and theories of quantum gravity, showing how ``doubly special'' relativity has emerged as a VSL effective model of quantum space-time, with observational implications for ultra high energy cosmic rays and gamma ray bursts. Some recent work on the physics of ``black'' holes and other compact objects in VSL theories is also described, highlighting phenomena associated with spatial (as opposed to temporal) variations in $c$. Finally we describe the observational status of the theory. The evidence is currently slim -- redshift dependence in the atomic fine structure, anomalies with ultra high energy cosmic rays, and (to a much lesser extent) the acceleration of the universe and the WMAP data. The constraints (e.g. those arising from nucleosynthesis or geological bounds) are tight, but not insurmountable. We conclude with the observational predictions of the theory, and the prospects for its refutation or vindication.

Figures (5)

• Figure 1: A conformal diagram (in which light travels at $45^\circ$). This diagram reveals that the sky is a cone in 4-dimensional space-time. When we look far away we look into the past; there is an horizon because we can only look as far away as the Universe is old. The fact that the horizon is very small in the very early Universe, means that we can now see regions in our sky outside each others' horizon. This is the horizon problem of standard Big Bang cosmology.
• Figure 2: Diagram showing the horizon structure in a model in which at time $t_c$ the speed of light changed from $c^-$ to $c^+\ll c^-$. Light travels at $45^\circ$ after $t_c$ but it travels at a much smaller angle to the spatial axis before $t_c$. Hence it is possible for the horizon at $t_c$ to be much larger than the portion of the Universe at $t_c$ intersecting our past light cone. All regions in our past have then always been in causal contact. This is the VSL solution of the horizon problem.
• Figure 3: The flux of cosmic rays at high energies. The dashed line illustrates the GZK cut-off. (I thank Masahiro Takeda for permission to use this Figure.)
• Figure 4: The data points are the QSO results for the changing $\alpha$. The solid line depict theoretical prediction in several varying-$\alpha$ models.
• Figure 5: The Hubble diagram built from Supernovae results (data points) suggests a Universe with 30% normal matter and 70% cosmological constant (plotted curve). However any other form of repulsive gravity could be made to fit the data.