Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lemaître-Robertson-Walker Metric
arXiv:2505.15838 · doi:10.1016/j.dark.2025.101947
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 , we derive that does not have its dynamics but imposes a constraint on the scale factor , 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 ), which determines how the speed of light appears in the cosmological equations. Recognizing 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.
arXiv comment25 pages, 2 figures. This is for GR and Cosmology
References in corpus (77)
- A Large Mass Hierarchy from a Small Extra Dimension
- An Alternative to Compactification
- Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
- Lorentz invariance with an invariant energy scale
- High-Energy Tests of Lorentz Invariance
- Gravity with a dynamical preferred frame
- Testable scenario for Relativity with minimum-length
- Determining the Type, Redshift, and Age of a Supernova Spectrum
- A time varying speed of light as a solution to cosmological puzzles
- CPT Violation Implies Violation of Lorentz Invariance
- Cosmic Ray and Neutrino Tests of Special Relativity
- Distance Measurement and Wave Dispersion in a Liouville-String Approach to Quantum Gravity
- Planck-scale deformation of Lorentz symmetry as a solution to the UHECR and the TeV- paradoxes
- Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology
- Cosmologies with Varying Light-Speed
- Doubly-Special Relativity: First Results and Key Open Problems
- New varying speed of light theories
- Deformed Boost Transformations That Saturate at the Planck Scale
- Astrophysical Probes of the Constancy of the Velocity of Light
- Observer-independent quanta of mass and length
- Gravitational Lorentz Violations and Adjustment of the Cosmological Constant in Asymmetrically Warped Spacetimes
- Covariant and locally Lorentz-invariant varying speed of light theories
- Varying- Theories and Solutions to the Cosmological Problems
- Dynamical Mechanism for Varying Light Velocity as a Solution to Cosmological Problems
- Detection of Signature Consistent with Cosmological Time Dilation in Gamma-Ray Bursts
- Loop-Generated Bounds on Changes to the Graviton Dispersion Relation
- Time Dilation in the Light Curve of the Distant Type Ia Supernovae SN 1995K
- ``Faster than Light'' Photons in Gravitational Fields -- Causality, Anomalies and Horizons
- Non-Commutative Inflation
- Time Dilation from Spectral Feature Age Measurements of Type Ia Supernovae
- Quantum Gravitational Optics
- Supergravity, D-brane Probes and thermal super Yang-Mills: a comparison
- Scalar-Tensor Gravity Theory For Dynamical Light Velocity
- Bi-metric Gravity and "Dark Matter"
- Causality of the brane universe
- Testing CPT with the Neutral-D System
- Time Dilation in Type Ia Supernova Spectra at High Redshift
- Tension of the statistic and RSD data with Planck/CDM and implications for weakening gravity
- Branes on Charged Dilatonic Backgrounds: Self-Tuning, Lorentz Violations and Cosmology
- Stars and black holes in varying speed of light theories
- Does a varying speed of light solve the cosmological problems?
- Can a changing explain the Supernovae results?
- Time Dilation and Quasar Variability
- A Definitive Measurement of Time Dilation in the Spectral Evolution of the Moderate-Redshift Type Ia Supernova 1997ex
- On The Varying Speed of Light in a Brane-Induced FRW Universe
- Cosmological Time Dilation in Durations of Swift Long Gamma-Ray Bursts
- The minimally extended Varying Speed of Light (meVSL)
- VSL theories and the Doppler peak
- Cosmological Evolution and Luminosity Function Effects on Number Counts, Redshift and Time Dilation of Bursting Sources
- Accelerating Photons with Gravitational Radiation
- Redshift drift in varying speed of light cosmology
- Cosmology with relativistically varying physical constants
- Temporally Varying Universal Gravitational "Constant" and Speed of Light in Energy Momentum Squared Gravity
- Time Dilation of BATSE Gamma-ray Bursts
- Neutrino mixing and Lorentz invariance
- Cosmological Time Dilation in Gamma Ray Bursts?
- Vector field mediated models of dynamical light velocity
- On the nature of gamma-ray burst time dilations
- Fourier Analysis of Gamma-Ray Burst Light Curves: Searching for Direct Signature of Cosmological Time Dilation
- A time-space varying speed of light and the Hubble Law in static Universe
- Dynamical analysis of the covarying coupling constants in scalar-tensor gravity
- Time-dependent in Einstein's equations as an alternative to the cosmological constant
- Constraining minimally extended varying speed of light by cosmological chronometers
- The cosmological evolution condition of the Planck constant in the varying speed of light models through adiabatic expansion
- Testing a varying- model for dark energy within Co-varying Physical Couplings framework
- Dynamical System Approach to Cosmological Models with a Varying Speed of Light
- 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
- A statefinder luminosity distance formula in varying speed of light cosmology
- A cosmology with variable c
- A varying-c cosmology
- Chi-Variable-Speed-of-Light Cosmologies
- Observational constraints on varying fundamental constants in a minimal CPC model
- Review on the minimally extended varying speed of light model
- Cosmological models with variable constants
- Constraints on the minimally extended varying speed of light model using the Pantheon+ dataset
- Cosmography of the minimally extended Varying Speed of Light Model