Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lemaître-Robertson-Walker Metric

Abstract

In the Friedmann-Lemaître-Robertson-Walker metric, a varying speed of light (VSL) reflects a change in the clock rate across hypersurfaces, described by the lapse function. This variation is not a dynamical field evolution but a consequence of coordinate choice, as the cosmic time coincides with the proper time of comoving observers due to the Weyl postulate. From an action principle including $\tilde{c}$, we derive that $\tilde{c}$ does not have its dynamics but imposes a constraint on the scale factor $a(t)$, indicating that it is not an independent degree of freedom. This insight reframes the VSL concept as a manifestation of gauge freedom in general relativity, wherein physical laws remain invariant under smooth coordinate transformations. Here, gauge refers to the freedom of choosing the temporal coordinate (\textit{e.g.}, setting the lapse $N(t)\ne 1$), which determines how the speed of light appears in the cosmological equations. Recognizing $\tilde{c}$ as a coordinate-dependent quantity offers a new interpretation of cosmological time and observational tensions, such as the Hubble tension, without invoking new physical fields. This redefinition opens a novel theoretical pathway in interpreting cosmic expansion within a consistent relativistic framework.

25 pages, 2 figures. This is for GR and Cosmology

References in corpus (17)

• Determining the Type, Redshift, and Age of a Supernova Spectrum
• Time Dilation in Type Ia Supernova Spectra at High Redshift
• Tension of the $E_G$ statistic and RSD data with Planck/$\Lambda$CDM and implications for weakening gravity
• The minimally extended Varying Speed of Light (meVSL)
• Cosmology with relativistically varying physical constants
• Temporally Varying Universal Gravitational "Constant" and Speed of Light in Energy Momentum Squared Gravity
• Time-dependent $G$ in Einstein's equations as an alternative to the cosmological constant
• Dynamical analysis of the covarying coupling constants in scalar-tensor gravity
• The cosmological evolution condition of the Planck constant in the varying speed of light models through adiabatic expansion
• Constraining minimally extended varying speed of light by cosmological chronometers
• Testing a varying-$\Lambda$ model for dark energy within Co-varying Physical Couplings framework
• A viable varying speed of light model in the RW metric
• Constraint on the minimally extended varying speed of light using time dilations in type Ia supernovae
• Observational constraints on varying fundamental constants in a minimal CPC model
• Review on the minimally extended varying speed of light model
• Cosmography of the minimally extended Varying Speed of Light Model
• Constraints on the minimally extended varying speed of light model using the Pantheon+ dataset

Cited by in corpus (3)

• Stringent constraint on the CCC+TL cosmology with $H(z)$ Measurements
• A Unified Interpretation of Supernova, GRB, and QSO Time Dilation Signals in a Generalized Cosmological Time Framework
• Geometric Matching of Local Static Regions in Cosmological Spacetimes with an Evolving Lapse