Determination of dark energy by the Einstein Telescope: Comparing with CMB, BAO, and SNIa observations

A design study is currently in progress for a third-generation gravitational-wave (GW) detector called the Einstein Telescope (ET). An important kind of source for ET will be the inspiral and merger of binary neutron stars up to $z\sim 2$. If binary neutron star mergers are the progenitors of short-hard $\gamma$-ray bursts, then some fraction of them will be seen both electromagnetically and through GW, so that the luminosity distance and the redshift of the source can be determined separately. An important property of these “standard sirens” is that they are self-calibrating: the luminosity distance can be inferred directly from the GW signal, with no need for a cosmic distance ladder. Thus, standard sirens will provide a powerful independent check of the $\Lambda \mathrm{CDM}$ model. In previous work, estimates were made of how well ET would be able to measure a subset of the cosmological parameters (such as the dark energy parameter $w_0$) it will have access to, assuming that the others had been determined to great accuracy by alternative means. Here we perform a more careful analysis by explicitly using the potential Planck cosmic microwave background data as prior information for these other parameters. We find that ET will be able to constrain $w_0$ and $w_a$ with accuracies $\Delta w_0=0.099$ and $\Delta w_a=0.302$, respectively. These results are compared with projected accuracies for the JDEM baryon acoustic oscillations project and the SNAP type Ia supernovae observations.

Figure 1

The averaged quantity $A^{-1/2}(z)$ [defined in (31)] as a function of redshift $z$. The red dots denote the results based on the Monte Carlo sampling, and the solid line denotes the fit results.

Figure 2

The normalized distribution of the GW sources.

Figure 3

The two-dimensional uncertainty contours of the dark energy parameters $w_0$ and $w_a$ in the case with uniform distribution.

Figure 4

The two-dimensional uncertainty contours for the dark energy parameters $w_0$ and $w_a$, in the different cases.

Figure 5

The two-dimensional uncertainty contours of the cosmological parameters. The black (larger) curves denote the results of $\mathrm{CMB}+\mathrm{BAO}+\mathrm{SNIa}$, and the red (smaller) curves denote the results of $\mathrm{CMB}+\mathrm{BAO}+\mathrm{SNIa}+\mathrm{GW}$. Here, we have assumed the GW with nonuniform distribution (The case with uniform distribution gives the nearly overlapped results).