Resolving Hubble Tension with Quintom Dark Energy Model
  Recent low-redshift observations give value of the present-time Hubble
parameter $H_{0}\simeq 74~\rm{km s}^{-1}\rm{Mpc}^{-1}$, roughly 10\% higher
than the predicted value $H_{0}=67.4~\rm{km s}^{-1}\rm{Mpc}^{-1}$ from Planck's
observations of the Cosmic Microwave Background radiation~(CMB) and the
$\Lambda$CDM model. Phenomenologically, we show that by adding an extra
component X with negative density in the Friedmann equation, it can relieve the
Hubble tension without changing the Planck's constraint on the matter and dark
energy densities. For the extra negative density to be sufficiently small, its
equation-of-state parameter must satisfy $1/3\leq w_{X}\leq1$. We propose a
quintom model of two scalar fields that realizes this condition and potentially
alleviate the Hubble tension. One scalar field acts as a quintessence while
another "phantom" scalar conformally couples to matter in such a way that
viable cosmological scenario can be achieved. The model depends only on two
parameters, $\lambda_{\phi}$ and $\delta$ which represent rolling tendency of
the self-interacting potential of the quintessence and the strength of
conformal phantom-matter coupling respectively. The toy quintom model with
$H_{0}=73.4~\rm{km s}^{-1}\rm{Mpc}^{-1}$~(Quintom I) gives good Supernovae-Ia
luminosity fits, decent $r_{\rm BAO}$ fit, but slightly small acoustic
multipole $\ell_{A}=285.54$. Full parameter scan reveals that quintom model
provide better model than the $\Lambda$CDM model in certain region of the
parameter space, $0.02<\delta<0.10, \Omega_{m}^{(0)}<0.31$, while significantly
relieving Hubble tension even though not completely resolving it. A benchmark
quintom model, Quintom II, is presented as an example.
