Future constraints on dynamical dark-energy using gravitational-wave standard sirens

The detection of gravitational waves (GW) by the LIGO and Virgo collaborations offers a whole new range of possible tests and opens up a new window that may shed light on the nature of dark energy and dark matter. In the present work we investigate how future gravitational-wave data could help to constrain different dynamical dark energy models. In particular, we perform cosmological forecastings of a class of well-known and most used dynamical dark energy models using the third-generation gravitational wave detector, the Einstein Telescope. We have considered 1000 simulated GW events in order to constrain the parameter space of the dynamical dark energy models. Our analyses show that the inclusion of the GW data from the Einstein Telescope significantly improves the parameter space of the dynamical dark energy models compared to their constraints extracted from the standard cosmological probes, namely, the cosmic microwave observations, baryon acoustic oscillations distance measurements, supernove type Ia, and the Hubble parameter measurements.

Figure 1

Error of luminosity distance based on two sets of simulations. It is clear from the figure that the results of these two methods are quite close. In the plot we also show the contribution of gravitational lensing, which takes majority in the whole error budget, i.e., ${\sigma }_{d_{\mathrm{L}}}^{\mathrm{lens}}>{\sigma }_{d_{\mathrm{L}}}^{\mathrm{inst}}$.

Figure 2

For the fiducial CPL model, we first constrain the cosmological parameters using the datasets CMB, $\mathrm{CMB}+\mathrm{BAO}$, $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}$, and $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}+\mathrm{CC}$ and then we use the best-fit values of the parameters for “each dataset” to generate the corresponding GW catalogue. Following this, in each panel we show $d_L(z)$ vs $z$ catalogue with the corresponding error bars for 1000 simulated GW events. The upper left and upper right panels respectively present the catalogue ($z$, $d_L(z)$) with the corresponding error bars for 1000 simulated events derived using the CMB alone and $\mathrm{CMB}+\mathrm{BAO}$ dataset. The lower left and lower right panels respectively present the catalogue ($z$, $d_L(z)$) with the corresponding error bars for 1000 simulated events derived using the $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}$ and $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}+\mathrm{CC}$ datasets.

Figure 3

Sixty-eight percent and 95% C.L. contour plots for various combinations of some selected parameters of the CPL model (10) using different observational data in the presence (absence) of the GW data.

Figure 4

The evolution of the dark energy equation of state for the CPL parametrziation is shown for different datasets taking the mean values of the key parameters $w_0$ and $w_a$ from the corresponding analysis with and without the GW data. The solid curves stand for the evolution of $w_x(z)$ for the standard cosmological probes while the dotted curves stand for the dataset in the presence of the GW data. The shaded regions show the 68% C.L. constraints on these two parameters.

Figure 5

For the fiducial logarithmic model, we first constrain the cosmological parameters using the datasets CMB, $\mathrm{CMB}+\mathrm{BAO}$, $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}$, and $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}+\mathrm{CC}$ and then we use the best-fit values of the parameters for each dataset to generate the corresponding GW catalogue. Following this, in each panel we show $d_L(z)$ vs $z$ catalogue with the corresponding error bars for 1000 simulated GW events. The upper left and upper right panels respectively present the catalogue ($z$, $d_L(z)$) with the corresponding error bars for 1000 simulated GW events derived using the CMB alone and $\mathrm{CMB}+\mathrm{BAO}$ dataset. The lower left and lower right panels respectively present the catalogue ($z$, $d_L(z)$) with the corresponding error bars for 1000 simulated GW events derived using the $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}$ and $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}+\mathrm{CC}$ datasets.

Figure 6

In this figure we have shown the 68% and 95% confidence-level contour plots for various combinations of some selected parameters of the logarithmic parametrization (11) using different observational data in the presence (absence) of the GW data.

Figure 7

The evolution of the dark energy equation of state for the logarithmic parametrization has been shown for different datasets taking the mean values of the key parameters $w_0$ and $w_a$ from the analyses with and without the GW data. The solid curves stand for the evolution of $w_x(z)$ for the standard cosmological probes while the dotted curves stand for the dataset in the presence of the GW data. The shaded regions show the 68% C.L. constraints on these two parameters.

Figure 8

For the fiducial JBP model, we first constrain the cosmological parameters using the datasets CMB, $\mathrm{CMB}+\mathrm{BAO}$, $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}$, and $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}+\mathrm{CC}$ and then we use the best-fit values of the parameters for each dataset to generate the corresponding GW catalogue. Following this, in each panel we show $d_L(z)$ vs $z$ catalogue with the corresponding error bars for 1000 simulated GW events. The upper left and upper right panels respectively present the catalogue ($z$, $d_L(z)$) with the corresponding error bars for 1000 simulated GW events derived using the CMB alone and $\mathrm{CMB}+\mathrm{BAO}$ dataset. The lower left and lower right panels respectively present the catalogue ($z$, $d_L(z)$) with the corresponding error bars for 1000 simulated GW events derived using the $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}$ and $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}+\mathrm{CC}$ datasets.

Figure 9

Sixty-eight percent and 95% C.L. contour plots for various combinations of some selected parameters of the JBP model (12) using different observational data in the presence (absence) of the GW data.

Figure 10

The evolution of the dark energy equation of state for the JBP parametrziation has been shown for different datasets taking the mean values of the key parameters $w_0$ and $w_a$ from the analyses with and without the GW data. The solid curves stand for the evolution of $w_x(z)$ for the standard cosmological probes while the dotted curves stand for the dataset in the presence of the GW data. The shaded regions show the 68% C.L. constraints on these two parameters.

Figure 11

For the fiducial BA model, we first constrain the cosmological parameters using the datasets CMB, $\mathrm{CMB}+\mathrm{BAO}$, $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}$, and $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}+\mathrm{CC}$ and then we use the best-fit values of the parameters for each dataset to generate the corresponding GW catalogue. Following this, in each panel we show $d_L(z)$ vs $z$ catalogue with the corresponding error bars for 1000 simulated GW events. The upper left and upper right panels respectively present the catalogue ($z$, $d_L(z)$) with the corresponding error bars for 1000 simulated GW events derived using the CMB alone and $\mathrm{CMB}+\mathrm{BAO}$ dataset. The lower left and lower right panels respectively present the catalogue ($z$, $d_L(z)$) with the corresponding error bars for 1000 simulated GW events derived using the $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}$ and $\mathrm{CMB}+\mathrm{BAO}+\mathrm{JLA}+\mathrm{CC}$ datasets.

Figure 12

Sixty-eight percent and 95% C.L. contour plots for various combinations of some selected parameters of the BA model (13) using different observational data in the presence (absence) of the GW data.

Figure 13

The evolution of the dark energy equation of state for the BA parametrization has been shown for different datasets taking the mean values of the key parameters $w_0$ and $w_a$ from the analyses with and without the GW data. The solid curves stand for the evolution of $w_x(z)$ for the standard cosmological probes while the dotted curves stand for the dataset in the presence of the GW data. The shaded regions show the 68% C.L. constraints on these two parameters.