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

TL;DR

This work proposes a mechanism by which the Higgs–dilaton coupling makes the quantum of action $ħ$ and the speed of light $c$ vary across spacetime through a slowly varying dilaton field $χ$, while keeping $G$ effectively constant. Within local open sets around each spacetime point, the Higgs vacuum expectation value scales as $⟨Φ⟩∝χ$, leading to a local QED replica with $ħ_{*}∝χ^{-1/2}$ and $c_{*}∝χ^{1/2}$, and producing anisotropic scaling $l∝χ^{-1}$ and $τ∝χ^{-3/2}$, so that $τ^{-1}∝l^{-3/2}$. This VSL framework yields a modified cosmography: a Lifshitz-like redshift $1+z=a^{-3/2}F(z)$ and a revised Hubble relation, enabling fits to SNeIa Pantheon data with a reduced H0 around 47, and offering a CMB interpretation (BDRS) without dark energy. The model also naturally resolves the age problem and provides an astronomical route to the $H_{0}$ tension, while predicting an infinite cosmological horizon and suggesting a scale-invariant unit system anchored by the dilaton. Overall, the paper presents a coherent tie between Higgs physics, dilaton dynamics, and variable fundamental constants that yields testable cosmological consequences and an alternative to dark energy.

Abstract

We allow the Higgs field $Φ$ to interact with a dilaton field $χ$ of the background spacetime via the coupling $χ^2\,Φ^\daggerΦ$. Upon spontaneous gauge symmetry breaking, the Higgs VEV becomes proportional to $χ$. While traditionally this linkage is employed to make the Planck mass and particle masses dependent on $χ$, we present an $\textit alternative$ mechanism: the Higgs VEV will be used to construct Planck's constant $\hbar$ 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 $\hbar_*\proptoχ^{-1/2}(x^*)$ and $c_*\proptoχ^{1/2}(x^*)$, causing these ``fundamental constants'' to vary alongside the dynamical field $χ$. Moreover, in each open set around $x^*$, the prevailing value $χ(x^*)$ determines the length and time scales for physical processes occurring in this region as $l\proptoχ^{-1}(x^*)$ and $τ\proptoχ^{-3/2}(x^*)$. This leads to an $\textit anisotropic$ relation $τ^{-1}\propto l^{-3/2}$ 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 relation and the Hubble law. These modifications are capable of: (1) Accounting for the Pantheon Catalog of SNeIa $\textit{through a declining speed of light in an expanding Einstein--de Sitter universe}$, thus avoiding the need for dark energy; (2) Revitalizing Blanchard-Douspis-Rowan-Robinson-Sarkar's CMB power spectrum analysis that bypassed dark energy [A&A 412, 35 (2003)]; and (3) Resolving the $H_0$ tension without requiring a dynamical dark energy component.

Figures (3)

• Figure 1: Hubble diagram of SNeIa in the Pantheon Catalog. Open circles: 1,048 data points with error bars, listed in Ref. Scolnic-2018. In both panels, long-dashed line is the $\Lambda$CDM Formula \ref{['eq:dL-z-LCDM']} with $H_{0}=70.2$, $\Omega_{M}=0.285$, $\Omega_{\Lambda}=0.715$; dotted line is the EdS Formula \ref{['eq:dL-z-EdS']} with $H_{0}=70.2$. Upper panel: Solid line is our VSL Formula \ref{['eq:dL-z-VSL']} with $H_{0}=47.2$ and $F_{\infty}=0.93$. Lower panel: Solid line is our VSL Formula \ref{['eq:dL-z-VSL']} with $F(z)\equiv1\ \forall z$ with $H_{0}=44.4$.
• Figure 2: Solid curves: $F(z)$ and $F(a)$. Dashed curves: $H_{0}(z)/H_{0}(z\text{=}0)$ and $H_{0}(a)/H_{0}(a=1)$.
• Figure 4: The physical intuition of late-time acceleration based on VSL as explained in Section \ref{['subsec:Physical-intuition']}. In the left panel, photons from SNe A and SNe C were emitted at times $t_{A}$ and $t_{C}$ with $t_{C}-t_{0}=2\,(t_{A}-t_{0})$; thus, their redshifts satisfy $z_{C}=2\,z_{A}$. However, for the photons emitted from SNe C, the earlier segment of their trajectory had a higher speed of light than the later segment, allowing them to cover a longer distance. This results in $d_{C}>2\,d_{A}$, leading in an excess distance modulus in the Hubble diagram for high-$z$ SNe, as depicted in the right panel.