Directly comparing the 6 expansion rates 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 \pm 4.75 Km/s/Mpc .
By fitting two different two-parameter models to the observational data , 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 .