The evidence of cosmic acceleration and observational constraints
  Directly comparing the 6 expansion rate measured by type Ia supernovae data
and the lower bound on the expansion rate set by the strong energy conditions
or the null hypothesis that there never exists cosmic acceleration, we see
$3\sigma$ direct evidence of cosmic acceleration and the $Rh=ct$ model is
strongly excluded by the type Ia supernovae data. We also use Gaussian process
method to reconstruct the expansion rate and the deceleration parameter from
the 31 cosmic chronometers data and the 6 data points on the expansion rate
measured from type Ia supernoave data, the direct evidence of cosmic
acceleration is more than $3\sigma$ and we find that the transition redshift
$z_t=0.60_{-0.12}^{+0.21}$ at which the expansion of the Universe underwent the
transition from acceleration to deceleration. The Hubble constant inferred from
the cosmic chronometers data with the Gaussian process method is
$H_0=67.46\pm4.75$ Km/s/Mpc. To understand the properties of cosmic
acceleration and dark energy, we fit two different two-parameter models to the
observational data, and we find that the constraints on the model parameters
from either the full distance modulus data by the Pantheon compilation or the
compressed expansion rate data are very similar, and the derived Hubble
constants are consistent with the Planck 2018 result. Our results confirm that
the 6 compressed expansion rate data can replace the full 1048 distance modulus
data from the Pantheon compilation. We derive the transition redshift
$z_t=0.61_{-0.16}^{+0.24}$ by fitting a simple $q(z)$ model to the combination
of cosmic chronometers data and the Pantheon compilation, the result is
consistent with that obtained from the reconstruction with Gaussian process.
Abridged.
