Cosmological constraints on a dark matter -- dark energy interaction

TL;DR

This paper investigates cosmological constraints on models with a direct interaction between dark matter (DM) and dark energy (DE), where the DM particle mass is $m=\lambda\phi$ and the DE component arises from a scalar field with potential $V(\phi)$. Using an inverse power-law potential $V(\phi)=K\phi^{−α}$, the authors derive the background dynamics and perturbation equations, compute the luminosity-distance relation and the CMB anisotropy spectrum, and compare with SN Ia and WMAP data. They find that the simplest interacting models are ruled out by current observations, primarily due to an enhanced ISW effect and a low DM density at last scattering, which cannot be reconciled with the data. The work highlights strong constraints on late-time DM–DE couplings and guides future model-building in the dark sector.

Abstract

It is generally assumed that the two dark components of the energy density of the universe, a smooth component called dark energy and a fluid of nonrelativistic weakly interacting particles called dark matter, are independent of each other and interact only through gravity. In this paper, we consider a class of models in which the dark matter and dark energy interact directly. The dark matter particle mass is proportional to the value of a scalar field, and the energy density of this scalar field comprises the dark energy. We study the phenomenology of these models and calculate the luminosity distance as a function of redshift and the CMB anisotropy spectrum for several cases. We find that the phenomenology of these models can differ significantly from the standard case, and current observations can already rule out the simplest models.

Figures (6)

• Figure 1: The effective potential, $V_{\rm eff}(\phi)$ changes as the universe expands due to the term that depends on the number density of dark matter particles. In all four pictures, the dotted line is the scalar field potential, the dashed line is the rest energy of the dark matter particles as a function of $\phi$, and the solid line is the effective potential. In the early universe (top left), the number density of the dark matter particles is large causing the line associated with it to be steep. The field rapidly settles to the minimum of the effective potential. As the universe evolves (top right), this line becomes less steep, and the minimum moves to larger $\phi$. The field (solid circle) follows the minimum until (lower left), the $3H\dot{\phi}$ term in the field equation (\ref{['eq:EoM_phi']}) becomes comparable to the first derivative of the potential. After this time, the $3H\dot{\phi}$ term acts as an effective friction and slows the field. Eventually the field is no longer in the minimum of the potential and is moving very slowly (lower right). The open circle in the lower right plot shows the minimum of the potential, and the solid circle shows the value of the field. At this point, the field is close to constant, and the interacting dark matter starts to behave as standard cold dark matter with a fixed mass.
• Figure 2: Plot of $\log_{10}(\phi/M_P)$ versus $\log_{10}(a/a_0)$ for $\alpha = 1$. The dashed line shows the value of the field at the minimum of the effective potential, $\phi_{\rm min}/M_P$ as a function of the scale factor. The solid line represents the actual evolution of the field. In the early universe, the field sits at the minimum of the effective potential, but eventually the effective friction due to the expansion of the universe causes the field to slow down and fall behind the shifting minimum of the effective potential.
• Figure 3: The bottom panel is a plot of the relative energy density in radiation ($\Omega_R$, long-dashed line), baryons ($\Omega_B$, short-dashed line), dark matter ($\Omega_{DM}$,dotted line), and the scalar field acting as the dark energy ($\Omega_\phi$, solid line) for $\alpha = 1/2$ and $(\lambda n_0/\alpha K) \gg 1$. The top panel is the same plot for $\Lambda$CDM with $\Omega_\Lambda$, the relative energy density in the cosmological constant, replacing $\Omega_\phi$ and is included for comparison. Eventually, the dark energy will dominate in the interacting model, but this can be put off as long as desired by increasing $(\lambda n_0/\alpha K)$. Note that in this case, $\Omega_{DM}/\Omega_\phi = 1/2$ is sustained for many e-foldings of the scale factor. Another feature of this model is that the onset of dark energy density takes place over a much longer time than in the $\Lambda$CDM scenario. Finally, the universe is never dominated by dark matter, but instead goes through an epoch of baryon domination.
• Figure 4: Plots of the relative energy density in radiation ($\Omega_R$, long-dashed line), baryons ($\Omega_B$, short-dashed line), dark matter ($\Omega_{DM}$, dotted line), and the scalar field acting as the dark energy ($\Omega_\phi$, solid line) vs. $log_{10}(a/a_0)$ for various values of $\alpha$.
• Figure 5: Comparison of several models with SNe Ia data. The solid lines lines represent models with (from top to bottom) $\alpha = 1/2,1,2,5,8$. The theoretical curve for $\Lambda$CDM is shown as a dotted line for reference. The solid circles are binned SNe Ia data found in Tonry:2003zg, and the point at $z=1.7$ is the upper limit for SN1997ff from Riess:2001gk. The models with $\alpha > 2$ are disfavored by moderate redshift observations.