Constraining early and interacting dark energy with gravitational wave standard sirens: the potential of the eLISA mission

TL;DR

This work forecasts eLISA's ability to constrain beyond-\ΛCDM expansion histories using standard sirens from MBHB mergers with EM counterparts. It employs a Fisher-matrix approach across three eLISA configurations (N2A1M5L6, N2A2M5L6, N2A5M5L6) and three MBHB seed models (popIII, Q3d, Q3nod), deriving $d_L(z)$ constraints from GW signals and redshift measurements. EDE is parametrized by $\Omega_{de}^e$ and a transition redshift $z_e$, with $H^2/H_0^2$ and $\Omega_{de}(z)$ specified; IDE uses two forms, IDE1 with $Q=\epsilon_1 H \rho_{dm}$ and IDE2 with $Q=\epsilon_2 H \rho_{de}$, activated up to $z_i$, and the paper reports degeneracy-driven behavior in the constraints. The main finding is that eLISA can place competitive bounds on $\Omega_{de}^e$, $\epsilon_1$, and $\epsilon_2$ when the onset of deviation occurs at $z \lesssim 6$, whereas deviations from $\Lambda$CDM in the pre-recombination era are better constrained by CMB data, highlighting eLISA's role as a complementary cosmological probe in the intermediate redshift range.

Abstract

We perform a forecast analysis of the capability of the eLISA space-based interferometer to constrain models of early and interacting dark energy using gravitational wave standard sirens. We employ simulated catalogues of standard sirens given by merging massive black hole binaries visible by eLISA, with an electromagnetic counterpart detectable by future telescopes. We consider three-arms mission designs with arm length of 1, 2 and 5 million km, 5 years of mission duration and the best-level low frequency noise as recently tested by the LISA Pathfinder. Standard sirens with eLISA give access to an intermediate range of redshift $1\lesssim z \lesssim 8$, and can therefore provide competitive constraints on models where the onset of the deviation from $Λ$CDM (i.e. the epoch when early dark energy starts to be non-negligible, or when the interaction with dark matter begins) occurs relatively late, at $z\lesssim 6$. If instead early or interacting dark energy is relevant already in the pre-recombination era, current cosmological probes (especially the cosmic microwave background) are more efficient than eLISA in constraining these models, except possibly in the interacting dark energy model if the energy exchange is proportional to the energy density of dark energy.

Figures (11)

• Figure 1: Evolution of $\Omega_{de}(z)$ in early dark energy models with $\Omega_{de}^e = 0.03$ and $z_e = 6$ (solid blue line) or $z_e \rightarrow\infty$ (dashed blue line). The EDE model considered by Pettorino et al Pettorino:2013ia, with the cut of EDE set to $z=6$, is also shown for comparison (dotted-dashed red line). The dotted black line represents $\Lambda$CDM.
• Figure 2: EDE: 2$\sigma$ contours for $z_e = 2$ (blue) and $z_e = 6$ (red) with N2A2M5L6 for the three MBHB formation scenarios in the two-parameter cosmological models where $\Omega_{de}^e$ is a free parameter together with $\Omega_m^0$, $h$ and $w_0$, respectively.
• Figure 3: 1$\sigma$ errors in the one-parameter cosmological model with only $\Omega_{de}^e$ (left panels) and in the two-parameter cosmological models with both $\Omega_{de}^e$ and $w_0$ (right panel) for three 6-link eLISA configurations. In the right panels empty and filled markers denote the uncertainties on $w_0$ and $\Omega_{de}^e$, respectively.
• Figure 4: Evolution of $\Omega_{de}(z)$ in interacting dark energy models. From top to bottom of the curves: the red line denotes IDE1 with $\epsilon_1 = 0.1$ and $z_i = 6$ (solid line) or $z_i \rightarrow\infty$ (dashed line). The green line denotes IDE2 with $\epsilon_2 = 0.1$ and $z_i = 6$ (solid line) or $z_i \rightarrow\infty$ (dotted-dashed line). The black, dotted line denotes $\Lambda$CDM.
• Figure 5: IDE1: 2$\sigma$ contours for $z_i = 2$ (blue) and $z_i = 6$ (red) with N2A2M5L6 for three MBHB scenarios in the two-parameter cosmological models where $\epsilon_1$ is a free parameter together with $\Omega_{m}^0$, $h$ and $w_0$, respectively.