Axi-Higgs cosmology: Cosmic Microwave Background and cosmological
  tensions
  Non-canonical cosmology with an uplifted Higgs vacuum expectation value
(Higgs-VEV) in the early universe is believed to provide the solution for
existing tensions within the $\Lambda$CDM regime. We recently proposed a
theoretical model called axi-Higgs to explore this framework. The axi-Higgs
model features an ultralight axion with mass $m_a \sim 10^{-29}$ eV, which
couples to the Higgs field such that the Higgs-VEV is driven by the axion
background evolution. In this paper, we perform Markov Chain Monte Carlo (MCMC)
analyses with our modified Boltzmann solver to investigate the parameter space
of axi-Higgs beside other models including $\Lambda$CDM, $\Lambda$CDM+$m_e$,
$\Lambda$CDM+$\omega_a$. Combining cosmological data from Cosmic Microwave
Background (CMB), Baryon Acoustic Oscillations (BAO), weak-lensing (WL) cosmic
shear survey, we found $H_0 = 69.3^{+1.2}_{-1.4}$ km/s/Mpc and $S_8 = 0.797 \pm
0.012$, which reduces the Hubble tension to approximately $2.5\sigma$ and
slightly alleviates the $S_8$ tension. The presence and behavior of this
Higgs-VEV-driving axion may be tested by atomic clock measurements in
laboratory and/or quasar spectral measurements in the near future.
