[Paper Review] A simple varying-speed-of-light hypothesis is enough for explaining high-redshift supernovae data

Yves‐Henri Sanejouand|arXiv (Cornell University)|Sep 20, 2005

Gamma-ray bursts and supernovae1 references3 citations

TL;DR

This paper proposes that a time-varying speed of light—decreasing by approximately 2 cm s⁻¹ per year—can explain the observed high-redshift supernovae data without invoking dark energy. By modeling the speed of light as a linear function of time, the study derives a modified Hubble law that matches the redshift-distance relationship of type Ia supernovae, offering a phenomenological alternative to the cosmological constant.

ABSTRACT

The hypothesis that the speed of light decreases by nearly 2 cm per sec and per year is discussed within the frame of a simple phenomenological model. It is shown that this hypothesis can provide an alternative explanation for the redshift-distance relationship of type Ia supernovae, which is nowadays given in terms of a new form of (dark) energy of unknown origin.

Motivation & Objective

• To explore whether a time-varying speed of light can explain the accelerating expansion of the universe observed in high-redshift type Ia supernovae.
• To provide a phenomenological alternative to the cosmological constant by assuming a slowly decreasing speed of light over cosmic time.
• To test the consistency of this hypothesis with existing observational data, particularly from the Hubble Space Telescope's 'gold set' of 156 supernovae.
• To investigate whether lunar laser ranging data, showing a 3.82 cm/year apparent recession, could be explained by a time-varying speed of light rather than tidal forces alone.

Proposed method

• Assumes the speed of light varies linearly with time: $ c_d = c_0 + a_c \Delta t $, where $ a_c $ is the rate of change of the speed of light.
• Derives the photon time-of-flight $ \Delta t $ from the distance $ d $, using the relation $ d = c_0 \Delta t + \frac{1}{2} a_c \Delta t^2 $, leading to a quadratic solution for $ \Delta t $.
• Uses the redshift relation $ z = \frac{c_d}{c_0} - 1 $ and substitutes $ c_d $ from the time-dependent model to derive $ z = \sqrt{1 + \frac{2a_c d}{c_0^2}} - 1 $.
• Matches the derived redshift-distance relation to the Hubble law by setting $ a_c = H_0 c_0 $, yielding $ z = \sqrt{1 + \frac{2H_0 d}{c_0}} - 1 $, a modified Hubble law.
• Compares the model’s predictions directly to the observed redshifts of 156 type Ia supernovae from the 'gold set' without fitting, using a fixed $ H_0 = 72 \, \text{km s}^{-1} \text{Mpc}^{-1} $.
• Evaluates the model against lunar laser ranging data, predicting a pseudo-recession rate of $ v_{\text{mes}} = H_0 d_0 $, which matches the observed 3.82 cm/year trend if $ H_0 = 72 \, \text{km s}^{-1} \text{Mpc}^{-1} $.

Experimental results

Research questions

• RQ1 Can a time-varying speed of light explain the redshift-distance relationship of high-redshift type Ia supernovae without invoking dark energy?
• RQ2 Is the observed apparent recession of the Moon, as measured by laser ranging, consistent with a time-varying speed of light?
• RQ3 Does the derived model reproduce the Hubble law at low redshifts while modifying it at higher redshifts?
• RQ4 What is the required rate of change of the speed of light to match both supernova and lunar laser ranging data?
• RQ5 Could the observed Hubble-like expansion of the solar system be an artifact of a varying speed of light rather than actual dynamical expansion?

Key findings

• The model predicts a redshift-distance relationship $ z = \sqrt{1 + \frac{2H_0 d}{c_0}} - 1 $, which closely matches the observed data of 156 high-redshift type Ia supernovae without fitting.
• The required rate of change of the speed of light is $ a_c = H_0 c_0 $, corresponding to approximately -2 cm s⁻¹ per year for $ H_0 = 72 \, \text{km s}^{-1} \text{Mpc}^{-1} $.
• The model predicts a pseudo-lunar recession rate of 2.8 cm/year due to the varying speed of light, which is consistent with the observed 3.82 cm/year trend when combined with tidal effects.
• The observed 3.82 cm/year recession from lunar laser ranging is partially explained by the varying speed of light, with the remaining ~1 cm/year attributed to tidal forces.
• The model is consistent with the measured Hubble constant and reproduces the Hubble law at low redshifts while modifying it at higher redshifts.
• The hypothesis is compatible with the lack of detectable variation in the fine-structure constant and vacuum permittivity/permeability, as long as the speed of light variation is slow and consistent with current experimental limits.