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

Hoang Ky Nguyen

doi:10.1140/epjc/s10052-025-14082-4

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 393
https://doi.org/10.1140/epjc/s10052-025-14082-4

Regular Article - Theoretical Physics

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

Hoang Ky Nguyen¹^,2^a

¹ Department of Physics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania
² Institute for Interdisciplinary Research in Science and Education, ICISE, 55121, Quy Nhon, Vietnam

^a hoang.nguyen@ubbcluj.ro

Received: 1 February 2025
Accepted: 12 March 2025
Published online: 7 April 2025

Abstract

We probe into a class of scale-invariant actions, which allow the Higgs field $Φ$ $\Phi$ to interact with a dilaton field $χ$ $\chi$ of the background spacetime through the term $χ^{2} Φ^{†} Φ$ $\chi ^{2}\,\Phi ^{\dagger }\Phi$ . Upon spontaneous gauge symmetry breaking, the vacuum expectation value (VEV) of the Higgs field becomes proportional to $χ$ $\chi$ . Although this linkage is traditionally employed to make the Planck mass and particle masses dependent on $χ$ $\chi$ , we present an alternative mechanism: the Higgs VEV will be used to construct Planck’s quantum of action $ħ$ $\hbar$ and speed of light c. Specifically, each open set vicinity of a given point $x^{*}$ $x^{*}$ on the spacetime manifold is equipped with a replica of the Glashow–Weinberg–Salam action operating with its own effective values of $ħ_{*}$ $\hbar _{*}$ and $c_{*}$ $c_{*}$ per $ħ_{*} \propto χ^{- 1 / 2} (x^{*})$ $\hbar _{*}\propto \chi ^{-1/2}(x^{*})$ and $c_{*} \propto χ^{1 / 2} (x^{*})$ $c_{*}\propto \chi ^{1/2}(x^{*})$ , causing these “fundamental constants” to vary alongside the dynamical field $χ$ $\chi$ . Moreover, in each open set around $x^{*}$ $x^{*}$ , the prevailing value $χ (x^{*})$ $\chi (x^{*})$ determines the length and time scales for physical processes occurring in this region as $l \propto χ^{- 1} (x^{*})$ $l\propto \chi ^{-1}(x^{*})$ and $τ \propto χ^{- 3 / 2} (x^{*})$ $\tau \propto \chi ^{-3/2}(x^{*})$ . This leads to an anisotropic relation $τ^{- 1} \propto l^{- 3 / 2}$ $\tau ^{-1}\propto l^{-3/2}$ 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 $H_{0}$ $H_{0}$ tension without requiring a dynamical dark energy component.

© The Author(s) 2025

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