A mechanism to generate varying speed of light via Higgs-dilaton coupling: theory and cosmological applications

We probe into a class of scale-invariant actions, which allow the Higgs field \(\Phi \) to interact with a dilaton field \(\chi \) of the background spacetime through the term \(\chi ^{2}\,\Phi ^{\dagger }\Phi \). Upon spontaneous gauge symmetry breaking, the vacuum expectation value (VEV) of the Higgs field becomes proportional to \(\chi \). Although this linkage is traditionally employed to make the Planck mass and particle masses dependent on \(\chi \), we present an alternative mechanism: the Higgs VEV will be used to construct Planck’s quantum of action \(\hbar \) and speed of light c. Specifically, each open set vicinity of a given point \(x^{*}\) on the spacetime manifold is equipped with a replica of the Glashow–Weinberg–Salam action operating with its own effective values of \(\hbar _{*}\) and \(c_{*}\) per \(\hbar _{*}\propto \chi ^{-1/2}(x^{*})\) and \(c_{*}\propto \chi ^{1/2}(x^{*})\), causing these “fundamental constants” to vary alongside the dynamical field \(\chi \). Moreover, in each open set around \(x^{*}\), the prevailing value \(\chi (x^{*})\) determines the length and time scales for physical processes occurring in this region as \(l\propto \chi ^{-1}(x^{*})\) and \(\tau \propto \chi ^{-3/2}(x^{*})\). This leads to an anisotropic relation \(\tau ^{-1}\propto l^{-3/2}\) between the rate of clocks and the length of rods, resulting in a distinct set of novel physical phenomena. For late-time cosmology, the variation of c along the trajectory of light waves from distant supernovae towards the Earth-based observer necessitates modifications to the Lemaître redshift formula, the Hubble law, and the luminosity distance–redshift relation. These modifications are capable of: (1) Accounting for the Pantheon Catalog of Type Ia supernovae through a declining speed of light in an expanding Einstein–de Sitter universe, thus avoiding the need for dark energy; (2) Revitalizing Blanchard–Douspis–Rowan-Robinson–Sarkar’s CMB power spectrum analysis that bypassed dark energy; and (3) Resolving the \(H_{0}\) tension without requiring a dynamical dark energy component.