New analysis of SNeIa Pantheon Catalog: Variable speed of light as an alternative to dark energy

In ref. [4] Blanchard, Douspis, Rowan-Robinson, and Sarkar (BDRS) slightly modified the primordial fluctuation spectrum and produced an excellent fit to WMAP's CMB power spectrum for an Einstein-de Sitter (EdS) universe, bypassing dark energy. Curiously, they obtained a Hubble value of H0 ≈ 46, in sharp conflict with the canonical range ∼ 67–73. However, we will demonstrate that the reduced value of H0 ≈ 46 achieved by BDRS is fully compatible with the use of variable speed of light in analyzing the late-time cosmic acceleration observed in Type Ia supernovae (SNeIa). In ref. [6] we considered a generic class of scale-invariant actions that allow matter to couple non-minimally with gravity via a dilaton field χ. We discovered a hidden aspect of these actions: the dynamics of the dilaton can induce a variation in the speed of light c as c ∝ χ1/2, thereby causing c to vary alongside χ across spacetime. For an EdS universe with varying c, besides the effects of cosmic expansion, light waves emitted from distant SNeIa are further subject to a refraction effect, which alters the Lemaître redshift relation to 1 + z = a3/2. Based on this new formula, we achieve a fit to the SNeIa Pantheon Catalog exceeding the quality of the ΛCDM model. Crucially, our approach does not require dark energy and produces H0 = 47.2±0.4 (95% CL) in strong alignment with the BDRS finding of H0 ≈ 46. The reduction in H0 in our work, compared with the canonical range ∼ 67–73, arises due to the 3/2-exponent in the modified Lemaître redshift formula. Hence, BDRS's analysis of the (early-time) CMB power spectrum and our variable-c analysis of the (late-time) Hubble diagram of SNeIa fully agree on two counts: (i) the dark energy hypothesis is avoided, and (ii) H0 is reduced to ∼ 47, which also yields an age t0 = 2/(3H0)=13.8Gy for an EdS universe, without requiring dark energy. Most importantly, we will demonstrate that the late-time acceleration can be attributed to the declining speed of light in an expanding EdS universe, rather than to a dark energy component.