Model independent parametrization of the late time cosmic acceleration: Constraints on the parameters from recent observations

In this work, we have considered a model independent approach to study the nature of the late time cosmic acceleration. We have used the Pade approximation to parametrize the comoving distance. Consequently, from this comoving distance, we derive a parametrization for the Hubble parameter. Our parametrization is completely analytic and valid for the late time and matter dominated eras only. This parametrization possesses subpercentage accuracy compared to any arbitrary cosmological model or parametrization up to the matter dominated era. Using this parametrization, we put constraints on the parameters from recent low redshift cosmological observations including Planck 2018 distance priors. Our results show that the $\mathrm{\Lambda }\mathrm{CDM}$ model is $1\sigma$ to $2\sigma$ away for lower redshifts. We find that the phantom crossing is allowed by all the combinations of datasets considered. We also find that the dynamical dark energy models are preferable at lower redshifts. Our study also shows that, at lower redshifts ($z<0.5$), phantom models are allowed at an almost $1\sigma$ confidence level.

Figure 1

Percentage deviations in the Hubble parameter [using Eq. (27)] in our series vs Taylor series vs normal Padé series compared to the fiducial model 1 (denoted by fid1, which is the $\mathrm{\Lambda }\mathrm{CDM}$ model). Black, blue, and red lines correspond to the results from the Taylor series, normal Padé series, and our series, respectively.

Figure 2

Percentage deviations in the Hubble parameter [using Eq. (27)] in our series vs Taylor series vs normal Padé series compared to the fiducial model 2 (denoted by fid2, which is the $w_0=-1.2$, $w_a=-0.2$ model in CPL parametrization). Black, blue, and red lines correspond to the results from the Taylor series, normal Padé series, and our series, respectively.

Figure 3

Percentage deviations in the Hubble parameter [using Eq. (27)] in our series vs Taylor series vs normal Padé series compared to the fiducial model 3 (denoted by fid3, which is the $w_0=-0.8$, $w_a=0.2$ model in CPL parametrization). Black, blue, and red lines correspond to the results from the Taylor series, normal Padé series, and our series, respectively.

Figure 4

Triangle plot for the parameters (parameters in our series and the cosmological parameters) using recent cosmological observations mentioned in the text (in Sec. 5).

Figure 5

Derived Hubble parameter. The color codes are the same as in Fig. 4. The error bars are from the OHD data for the Hubble parameter as a function of redshifts.

Figure 6

Derived deceleration parameter [using Eq. (28)]. The color codes are the same as in Fig. 4. The horizontal black line corresponds to $q=0$, i.e., no acceleration.

Figure 7

Derived equation of state of the dark energy [using Eq. (29)]. The color codes are the same as in Fig. 4. The horizontal black line corresponds to the $\mathrm{\Lambda }\mathrm{CDM}$ value. The lower and upper regions of this horizontal black line correspond to the phantom and nonphantom regions, respectively.

Figure 8

Percentage deviations in the best-fit evolution of the Hubble parameter in our series compared to the same in the CPL parametrization. The color codes are the same as in Fig. 4.

Figure 9

Percentage deviations in the best-fit evolution of the comoving distance in our series compared to the same in the CPL parametrization. The color codes are the same as in Fig. 4.