[Paper Review] Constraints on the time variation of the speed of light using Strong lensing

Seokcheon Lee|arXiv (Cornell University)|Apr 19, 2021

Adaptive optics and wavefront sensing4 citations

TL;DR

This study uses 161 galaxy-scale strong gravitational lensing (SGL) systems to constrain the varying speed of light in the meVSL model, employing lens mass models and cosmological distance relations. Results show that Planck priors on Ωₘ₀ yield negative meVSL parameters (b < 0), implying a faster speed of light and stronger gravity in the past, while WMAP priors yield null results within 1-σ, highlighting sensitivity to prior assumptions and the need for more SGL data.

ABSTRACT

Due to the recent growth of discoveries of strong gravitational lensing (SGL) systems, one can statistically study both lens properties and cosmological parameters from 161 galactic scale SGL systems. We analyze meVSL model with the velocity dispersion of lenses by adopting the redshift and surface mass density depending power-law mass model. Analysis shows that meVSL models with various dark energy models including $Λ$CDM, $ω$CDM, and CPL provide the negative values of meVSL parameter, $b$ when we put the prior to the $Ω_{m 0}$ value from Planck. These indicate the faster speed of light and the stronger gravitational force in the past. However, if we adopt the WMAP prior on $Ω_{m0}$, then we obtain the null results on $b$ within 1-$σ$ CL for the different dark energy models.

Motivation & Objective

• To constrain the time variation of the speed of light using strong gravitational lensing (SGL) systems.
• To investigate the impact of different cosmological priors (Planck vs. WMAP) on the inferred meVSL parameter b.
• To assess the consistency of SGL data with varying light speed and gravitational coupling in dark energy models (ΛCDM, ωCDM, CPL).
• To evaluate the statistical power and systematic effects in SGL-based cosmological constraints.

Proposed method

• Employs a redshift- and surface mass density-dependent power-law mass model for lensing systems.
• Uses the angular Einstein radius (θ_E) and stellar velocity dispersion (σ_DM) to derive the observable ratio R^obs = (c₀² θ_E)/(4π σ_DM²).
• Compares R^obs with theoretical R^th derived from meVSL cosmological models using comoving and angular diameter distances.
• Applies a χ² minimization to fit cosmological parameters, including the meVSL parameter b, under different dark energy models (ΛCDM, ωCDM, CPL).
• Imposes priors on Ωₘ₀ from WMAP and Planck to assess prior sensitivity in the analysis.
• Uses 161 SGL systems with measured redshifts, velocity dispersions, and image separations to constrain model parameters.

Experimental results

Research questions

• RQ1 Does strong gravitational lensing data provide evidence for a time-varying speed of light in the meVSL model?
• RQ2 How do different priors on Ωₘ₀ (from WMAP vs. Planck) affect the inferred value of the meVSL parameter b?
• RQ3 Are the constraints on b consistent across different dark energy models (ΛCDM, ωCDM, CPL)?
• RQ4 How do the results compare with those from supernovae or growth rate data?
• RQ5 What is the statistical significance and robustness of SGL-based constraints on varying light speed?

Key findings

• Under Planck priors on Ωₘ₀, the meVSL parameter b is constrained to negative values (b ≈ -0.339 ± 0.091 for CPL model), indicating a faster speed of light and stronger gravitational force in the past.
• For ΛCDM and ωCDM models with Planck priors, b is also negative (b ≈ -0.95 ± 0.054 and -0.944 ± 0.054 respectively), consistent with faster light in the early universe.
• With WMAP priors on Ωₘ₀, b is consistent with zero within 1-σ CL for all dark energy models, indicating no significant time variation in the speed of light.
• The results are sensitive to the choice of Ωₘ₀ prior, with opposite signs for b depending on whether WMAP or Planck priors are used.
• The analysis shows that current SGL data alone cannot reliably constrain b without strong priors on Ωₘ₀, highlighting the need for larger, more precise SGL samples.
• The findings are inconsistent with constraints from growth rate and supernova data, suggesting potential systematics or model dependencies in SGL-based analyses.