A mechanism to generate varying speed of light via Higgs-dilaton coupling: theory and cosmological applications - Hoang Ky Nguyen (European Physical Journal C: Particles and Fields)
Abstract We probe into a class of scale-invariant actions, which allow the Higgs field $$Φ $$ Φ to interact with a dilaton field $$χ $$ χ of the background spacetime through the term $$χ ^{2}\,Φ ^{\dagger }Φ $$ χ 2 Φ † Φ . Upon spontaneous gauge symmetry breaking, the vacuum expectation value (VEV) of the Higgs field becomes proportional to $$χ $$ χ . Although this linkage is traditionally employed to make the Planck mass and particle masses dependent on $$χ $$ χ , we present an alternative mechanism: the Higgs VEV will be used to construct Planck’s quantum of action $$\hbar $$ ħ 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 $$\hbar _{*}$$ ħ ∗ and $$c_{*}$$ c ∗ per $$\hbar _{*}\propto χ ^{-1/2}(x^{*})$$ ħ ∗ ∝ χ - 1 / 2 ( x ∗ ) and $$c_{*}\propto χ ^{1/2}(x^{*})$$ c ∗ ∝ χ 1 / 2 ( x ∗ ) , causing these “fundamental constants” to vary alongside the dynamical field $$χ $$ χ . Moreover, in each open set around $$x^{*}$$ x ∗ , the prevailing value $$χ (x^{*})$$ χ ( x ∗ ) determines the length and time scales for physical processes occurring in this region as $$l\propto χ ^{-1}(x^{*})$$ l ∝ χ - 1 ( x ∗ ) and $$τ \propto χ ^{-3/2}(x^{*})$$ τ ∝ χ - 3 / 2 ( x ∗ ) . This leads to an anisotropic relation $$τ ^{-1}\propto l^{-3/2}$$ τ - 1 ∝ 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.