Late-time varying-speed-of-light test of the DESI DR2 geometrical preference

Abstract

The second data release of the Dark Energy Spectroscopic Instrument (DESI DR2) has sharpened the question of whether late-time geometrical observations prefer a departure from the minimal

distance–redshift relation. We examine a deliberately restricted alternative interpretation: whether the same late-time distance information can be absorbed by an effective redshift dependence of the photon propagation factor. We introduce the dimensionless ratio

$$C(z)\equiv c(z)/c_0$$ C ( z ) ≡ c ( z ) / c 0

and adopt the bounded one-parameter form

$$C(z)=1+\epsilon z/(1+z)$$ C ( z ) = 1 + ϵ z / ( 1 + z )

, with

$$\epsilon =0$$ ϵ = 0

corresponding to the constant-speed limit. The analysis uses only late-time data: DESI DR2 compressed

$$\textrm{BAO}$$ BAO

measurements, 31 cosmic-chronometer

$$H(z)$$ H ( z )

points, and Type Ia supernova Hubble diagrams from DES-Dovekie and Pantheon-plus. The sound horizon

$$r_d$$ r d

is sampled as an independent free parameter with the uniform prior

$$r_d\in [120,180]\,\textrm{Mpc}$$ r d ∈ [ 120 , 180 ] Mpc

, while the supernova intercept is profiled analytically; no CMB-calibrated sound-horizon prior and no distance-ladder prior are imposed. For the main DES-Dovekie+DESI DR2+

$$H(z)$$ H ( z )

combination we obtain

$$\epsilon =-0.096^{+0.125}_{-0.114}$$ ϵ = - 0 . 096 - 0.114 + 0.125

. Replacing DES-Dovekie by Pantheon-plus gives

$$\epsilon =-0.048^{+0.142}_{-0.122}$$ ϵ = - 0 . 048 - 0.122 + 0.142

. The VSL extension improves the minimum

$$\chi ^2$$ χ 2

by only

$$1.05$$ 1.05

relative to flat

$$\Lambda \textrm{CDM}$$ Λ CDM

, and is penalized by both AIC and BIC. Allowing spatial curvature changes the geometrical degeneracy directions but still gives

$$\epsilon $$ ϵ

consistent with zero. These results show that DESI DR2-era late-time geometry provides a useful null test of cosmological light-speed constancy, but does not support a one-parameter late-time VSL explanation of the DESI geometrical preference.