  We revisit the Fujii-Wetterich model [Phys.Rev.D 26, 2580 (1982) and
Nucl.Phys.B 302, 645 (1988)] which allows the Higgs doublet to couple with a
"cosmon" scalar $\chi$ of the background spacetime as $\chi^2\,\Phi^2$. Upon
the SSB of the $SU(2)$ gauge, the VEV of the Higgs doublet is proportional to
the field $\chi$. Fujii and Wetterich employed this linkage to make particle
masses dependent on $\chi$. We shall present an $\textit alternative$
mechanism: at a given point $x^*$, the prevailing Higgs VEV will be used to
$\textit construct$ a quantum of action $\hbar_*$ and a speed of light $c_*$ in
association with $\chi(x^*)$. Specifically, each open set vicinity of a given
point $x^*$ on the manifold is equipped with a replica of the
Glashow-Weinberg-Salam action operating with its own effective values of
$\hbar_*$ and $c_*$, whereas particle masses induced via Higgs SSB remain
independent of $\chi(x^*)$. Our mechanism unambiguously generates the
dependencies $\hbar_*\propto\chi^{-1/2}(x^*)$ and $c_*\propto\chi^{1/2}(x^*)$,
causing these "fundamental constants" to vary along with the dynamical field
$\chi$ across the manifold. For late-time cosmology, a varying $c$ along the
trajectory of light waves from distant supernovae towards Earth renders the
classic Lema\^itre redshift formula $1+z=a^{-1}$ inapplicable. Using the
dependency $c_*\propto\chi^{1/2}(x^*)$, we derive the new (variable-$c$)
Lema\^itre redshift relation and apply it to analyze the Pantheon Catalog of
SneIa $\textit without$ invoking the dark energy hypothesis. Key consequences
are: (1) Accounting for the Pantheon Catalog with a fit exceeding the quality
of the $\Lambda$CDM model; (2) Explaining the late-time cosmic acceleration
based on variable $c$, eliminating the need for dark energy; (3) Revitalizing
Blanchard-Douspis-Rowan-Robinson-Sarkar's CMB power spectrum analysis that
bypassed dark energy [A&A 412, 35 (2003)].
