Constraining interactions in cosmology’s dark sector

We consider the cosmological constraints on theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the universe, in light of the most recent supernovae, large scale structure and cosmic microwave background data. For a variety of models, we show that the strength of the coupling of dark matter to a quintessence field is constrained to be less than 7% of the coupling to gravity. We also show that long-range interactions between fermionic dark matter particles mediated by a light scalar with a Yukawa coupling are constrained to be less than 5% of the strength of gravity at a distance scale of 10 Mpc. We show that all of the models we consider are quantum mechanically weakly coupled, and argue that some other models in the literature are ruled out by quantum mechanical strong coupling.

Figure 1

Examples of evolution of the effective equation of state, $w_{\mathrm{eff}}$, in coupled scalar field dark matter models with an exponential potential $V(\varphi )\propto \exp (-\varphi /M_p)$ (left panel) and a power law potential $V(\varphi )\propto 1/\varphi$ (right panel). Cosmological parameters are fixed to $H_0=70$, ${\Omega }_c=0.25$, ${\Omega }_b=0.05$, and $C=0.1$ (black) and $C=0.5$ (red). Both models follow the coupling dependent attractor in the matter dominated era and asymptote to coupling independent attractors at late times. The timing of the transition between these two attractors is sensitive to both the potential and coupling parameters. For the exponential potential the dynamical attractor leads to a negligible dependence on initial conditions, shown here through comparing evolution with two different initial values of ${\varphi }_i\equiv \varphi (a={10}^{-8})$, ${\varphi }_i=1M_p$ (full line) and ${10}^{-10}{M}_p$ (dashed line). For the power law potential, however, a sensitivity to initial conditions can exist in the transition era. This is accounted for in the analysis by marginalizing over initial conditions.

Figure 2

Joint 68% (dark shaded) and 95% (light shaded) constraints in the exponential potential model for the the fractional matter density, ${\Omega }_m$ and the effective scalar equation of state, $w_{\varphi }$(left panel), and the coupling, $C$ (right panel). The complementary constraints arising separately from the WMAP CMB spectra, SDSS matter power spectrum plus SDSS and 2dFGRS baryon acoustic oscillation data sets, and the “union” Type 1a supernovae data set, and a HST prior on $H_0$ are shown.

Figure 3

Joint 68% (dark shaded) and 95% (light shaded) constraints using combined WMAP CMB, SDSS matter power spectrum, SDSS and 2dFGRS baryon acoustic oscillation, “union” type 1a supernovae datasets and HST $H_0$ prior for the power law potential (blue) and exponential potential (red) for the fractional matter density, ${\Omega }_m$ and the effective scalar equation of state, $w_{\varphi }$, (left panel), and the coupling, $C$ (right panel).

Figure 4

CMB temperature power spectrum comparing a fiducial minimally coupled $\Lambda \mathrm{CDM}$ model ( gray) with four models with the Yukawa interaction with ${\alpha }_{\mathrm{Yuk}}=10$, $r_s=2\mathrm{Mpc}$ (red), ${\alpha }_{\mathrm{Yuk}}=5$, $r_s=2\mathrm{Mpc}$ (green) ${\alpha }_{\mathrm{Yuk}}=10$, $r_s=5\mathrm{Mpc}$ (magenta), ${\alpha }_{\mathrm{Yuk}}=5$, $r_s=5\mathrm{Mpc}$ (blue). Data from WMAP 5 yr (blue points) and ACBAR (black points) experiments are also shown. The inset plot shows a blow up of the small scale anisotropies measured by ACBAR.

Figure 5

1D likelihood constraints on $G_c/G$ at 1 Mpc (left panel) and 10 Mpc (right panel) for the Yukawa dark matter interaction, in light of WMAP 5 yr and ACBAR CMB anisotropy, and SDSS LRG matter power spectrum observations.