No evidence for dynamical dark energy in two models

To investigate whether dark energy evolves over time, we propose two null tests and constrain them using the data combination of cosmic microwave background radiation, baryonic acoustic oscillations, Type Ia supernovae, Planck-2015 lensing, and cosmic chronometers. We find that, for these two models, there is no evidence of the dynamical dark energy at the $1.2\sigma$ confidence level. Interestingly, both models could slightly alleviate (i) the current Hubble constant ($H_0$) tension between the global fitting derivation by the Planck collaboration and the local observation by Riess et al.; (ii) the root-mean-square density fluctuations (${\sigma }_8$) tension between the Planck-2015 data and several low-redshift large scale structure probes.

Figure 1

The 68% and 95% confidence regions of the M1 using the data combination CBSLC.

Figure 2

The 68% and 95% confidence regions of the M2 using the data combination CBSLC.

Figure 3

The comparison between the 1-dimensional marginalized posterior distributions of $H_0$, ${\sigma }_8$, ${\sigma }_8{\mathrm{\Omega }}_m^{0.5}$, and $t_{\text{age}}$ from the M1 and M2 using the data combination CBSLC and those from KiDS-450 and Planck-2015 results under the assumption of $\mathrm{\Lambda }\mathrm{CDM}$.

Figure 4

The comparison between the 2-dimensional confidence regions of the M1 and M2 using the data combination CBSLC and those of KiDS-450 and Planck-2015 results under the assumption of $\mathrm{\Lambda }\mathrm{CDM}$ in the planes of ${\mathrm{\Omega }}_m-{\sigma }_8$ and ${\mathrm{\Omega }}_m-{\sigma }_8{\mathrm{\Omega }}_m^{0.5}$.

Figure 5

The CMB temperature power spectrums of the $\mathrm{\Lambda }\mathrm{CDM}$ model (blue), M1(red), and M2 (purple) as well as the relative differences ${\mathrm{\Delta }}_{\text{dif}}$ between the $\mathrm{\Lambda }\mathrm{CDM}$ and two models.

Figure 6

The relations between the scale factor $a$ and the relative DE density ${\rho }_{de}/{\rho }_{de0}$, EoS of DE ${\omega }_{de}(a)$ and dimensionless Hubble parameter $E(a)$, respectively. The red lines correspond to the $\mathrm{\Lambda }\mathrm{CDM}$ model ${\rho }_{de}/{\rho }_{de0}=1$, ${\omega }_{de}=-1$ and a reference line $E(a)=1$ in the upper, medium, and lower panels, respectively. The blue (dashed), orange (dotted), and cyan (dash-dotted) lines correspond to the mean values of $\alpha$ (M1) or $\beta$ (M2), $1\sigma$ and $2\sigma$ confidence regions, respectively.