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

We allow the Higgs field $\mathrm{\Phi }$ to interact with a dilaton field $\chi$ of the background spacetime via the coupling ${\chi }^2{\mathrm{\Phi }}^{†}\mathrm{\Phi }$. Upon spontaneous gauge symmetry breaking, the Higgs VEV becomes proportional to $\chi$. While traditionally this linkage is employed to make the Planck mass and particle masses dependent on $\chi$, we present an $\mathit{\text{a}}lternative$ mechanism: the Higgs VEV will be used to construct Planck’s constant $\mathrm{\hslash }$ and speed of light $c$. Specifically, each open set vicinity of a given point $x^{\ast }$ on the spacetime manifold is equipped with a replica of the Glashow-Weinberg-Salam action operating with its own effective values of ${\mathrm{\hslash }}_{\ast }$ and $c_{\ast }$ per ${\mathrm{\hslash }}_{\ast }\propto {\chi }^{-1\mathrm{/}2}(x^{\ast })$ and $c_{\ast }\propto {\chi }^{1\mathrm{/}2}(x^{\ast })$, causing these ``fundamental constants’’ to vary alongside the dynamical field $\chi$. Moreover, in each open set around $x^{\ast }$, the prevailing value $\chi (x^{\ast })$ determines the length and time scales for physical processes occurring in this region as $l\propto {\chi }^{-1}(x^{\ast })$ and $\tau \propto {\chi }^{-3\mathrm{/}2}(x^{\ast })$. This leads to an $\mathit{\text{a}}nisotropic$ relation ${\tau }^{-1}\propto l^{-3\mathrm{/}2}$ 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 relation and the Hubble law. These modifications are capable of: (1) Accounting for the Pantheon Catalog of SNeIa $\mathit{\text{through}}\mathit{\text{a}}\mathit{\text{declining}}\mathit{\text{speed}}\mathit{\text{of}}\mathit{\text{light}}\mathit{\text{in}}\mathit{\text{an}}\mathit{\text{expanding}}\mathit{\text{Einstein–de}}\mathit{\text{Sitter}}\mathit{\text{universe}}$, thus avoiding the need for dark energy; (2) Revitalizing Blanchard-Douspis-Rowan-Robinson-Sarkar’s CMB power spectrum analysis that bypassed dark energy [A&A 412, 35 (2003)]; and (3) Resolving the $H_0$ tension without requiring a dynamical dark energy component.