Constraints on the interaction and self-interaction of dark energy from cosmic microwave background

TL;DR

This paper investigates constraints on dark-energy self-interaction and its coupling to dark matter using high-precision CMB data. By modeling a coupled scalar field with potential $U$ (characterized by $U' = B U^N$) and a coupling parameter $\beta$, the authors identify distinct post-equivalence epochs (the $\phi$MDE and tracking phases) that yield nearly constant equations of state, enabling cosmological constraints. The main result is that current CMB data tightly constrain the coupling $\beta$ (e.g., $\beta < 0.16$ at 95% c.l.) but are only weakly informative about the potential unless strong priors on the Hubble parameter $h$ are imposed; Planck-like data could tighten $\beta$ to $<0.05$. This work demonstrates the CMB’s potential to test gravitational interactions in the dark sector beyond simple kinematic constraints.

Abstract

It is well-known that even high quality cosmic microwave background (CMB) observations are not sufficient on their own to determine the equation of state of the dark energy, due to the effect of the so-called geometric degeneracy at large multipoles and the cosmic variance at small ones. In contrast, we find that CMB data can put tight constraints on another fundamental property of the dark energy, namely its coupling to dark matter. We compare the current high-resolution CMB data to models of dark energy characterized by an inverse power law or exponential potential and by the coupling to dark matter. We determine the curve of degeneracy between the dark energy equation of state and the dimensionless Hubble parameter h and show that even an independent perfect determination of h may be insufficient to distinguish dark energy from a pure cosmological constant with the current dataset. On the other hand, we find that the interaction with dark matter is firmly bounded, regardless of the potential. In terms of the dimensionless ratio βof the dark energy interaction to gravity, we find β<0.16 (95% c.l.). This implies that the effective equation of state between equivalence and tracking has been close to the pure matter equation of state within 1% and that scalar gravity is at least 40 times weaker than tensor gravity. Further, we show that an experiment limited by cosmic variance only, like the Planck mission, can put an upper bound β< 0.05 (95% c.l.). This shows that CMB observations have a strong potentiality not only as a test of cosmic kinematics but also as a gravitational probe.

Figures (4)

• Figure 1: Numerical solutions of the system (\ref{['gensyst']}) for $N=2,\beta =0.1,\omega _{c}=0.1,\omega _{b}=0.02,h=0.65$ plotted against the redshift. Upper panel. Long dashed line: radiation; short dashed line: CDM; unbroken thin line: baryons; unbroken thick line: scalar field; dotted line: scalar field potential energy. The horizontal thin line marks the kinetic energy density of $\phi$MDE, reached just after equivalence. Lower panel. Thick line: effective equation of state; thin line: dark energy equation of state. The labels mark the $\phi$MDE, the tracking (T) and the final attractor (A).
• Figure 2: CMB spectra for increasing values of the coupling constant (the other parameters are $N=1.5,h=0.65,\omega _{b}=0.01,\omega _{c}=0.1$). Notice that the peaks not only move to the right but also change in height.
• Figure 3: Likelihood contour plots in the space $N,h$ marginalizing over the other parameters at the 68,90 and 95% c.l.. The white thick lines refer to the coupled case, the black curves to the uncoupled case. The dotted line is the likelihood degeneracy curve, the dashed line is the expected degeneracy curve. Notice that only fixing $h$ smaller than 0.65 it would be possible to exclude the cosmological constant at 95% c.l..
• Figure 4: Marginalized likelihood for tracking trajectories. The equation of state in panel $a$ is $w_{\phi }=1/(2N-1)$. In panels a and b we plot as a dotted line the likelihood assuming $h=0.65\pm 0.05$ and as dashed line $h=0.75\pm 0.05$ (gaussian prior). In panel $b$ the long-dashed line is the Planck-like likelihood. In panel $d$ the long-dashed line is for $\beta =0$.