Searching for dark matter-dark energy interactions: Going beyond the conformal case

We consider several cosmological models which allow for nongravitational direct couplings between dark matter and dark energy. The distinguishing cosmological features of these couplings can be probed by current cosmological observations, thus enabling us to place constraints on these specific interactions which are composed of the conformal and disformal coupling functions. We perform a global analysis in order to independently constrain the conformal, disformal, and mixed interactions between dark matter and dark energy by combining current data from: Planck observations of the cosmic microwave background radiation anisotropies, a combination of measurements of baryon acoustic oscillations, a supernova type Ia sample, a compilation of Hubble parameter measurements estimated from the cosmic chronometers approach, direct measurements of the expansion rate of the Universe today, and a compilation of growth of structure measurements. We find that in these coupled dark-energy models, the influence of the local value of the Hubble constant does not significantly alter the inferred constraints when we consider joint analyses that include all cosmological probes. Moreover, the parameter constraints are remarkably improved with the inclusion of the growth of structure data set measurements. We find no compelling evidence for an interaction within the dark sector of the Universe.

Figure 1

Cosmological parameter constraints in three coupled DE models with all data set combinations considered in this paper. The colored intervals correspond to the marginalized $1\sigma$ two-tail limits of each parameter.

Figure 2

(Upper) Comparison of the marginalized constraints on the dimensionless age of the Universe in the conformal, disformal, and mixed coupled DE models using all data set combinations considered in this paper. (Lower) Constraints on $H_{\text{astro}}{t}_{\text{astro}}$ from astrophysical objects [101, 102, 103] with their names specified on the vertical axis. In the upper panel the colored intervals correspond to the inferred $1\sigma$ two-tail limits on the dimensionless age of the Universe, whereas in the lower panel these intervals show the estimated $1\sigma$ constraints.

Figure 3

Marginalized two-dimensional likelihood constraints for conformally coupled DE with different data set combinations. We show the degeneracy of the conformal coupling parameter $\alpha$ with $\lambda ,{\mathrm{\Omega }}_m,{\sigma }_8$, and $H_0$.

Figure 4

Marginalized one-dimensional posterior distributions for the conformal coupling parameter $\alpha$, with the different data set combinations indicated in the figure. The respective parameter constraints are tabulated in Table 2.

Figure 5

Marginalized two-dimensional likelihood constraints on the parameters $\alpha ,\lambda ,{\mathrm{\Omega }}_m,{\sigma }_8$, and $H_0$ in the conformal model. The respective parameter constraints are tabulated in Table 3.

Figure 6

Marginalized one-dimensional posterior distributions for the conformal coupling parameter $\alpha$, with the different data set combinations considered in Table 3, together with two other combinations making use of both the ACA and CA measurements (denoted by FCA).

Figure 7

Marginalized constraints on parameters of the conformal model using the data sets indicated in the figure. The shaded band depicts the Planck $\mathrm{TT}+\mathrm{lensing}$ constraint, whereas the region enclosed by the dashed $(1\sigma )$ and dotted $(2\sigma )$ lines shows the constraint from Planck lensing alone [69].

Figure 8

A comparison of the marginalized two-dimensional constraints on the conformal coupling parameter $\alpha$ and the slope of the exponential potential $\lambda$, using the local values of the Hubble constant $H_0^{\mathrm{E}}$ (left) and $H_0^{\mathrm{R}}$ (right).

Figure 9

Marginalized two-dimensional constraints on the redshift of reionization $z_{\mathrm{reio}}$ and ${\sigma }_8$, together with samples from the $\mathrm{TT}+\mathrm{BSHR}$ data sets color coded with the value of the conformal coupling parameter $\alpha$. The gray band denotes the excluded region by observations of the spectra of high-redshift quasars [113].

Figure 10

Marginalized two-dimensional constraints on parameters of the constant disformal model using the data sets indicated in the figure. The shaded band depicts the Planck $\mathrm{TT}+\mathrm{lensing}$ constraint, whereas the region enclosed by the dashed $(1\sigma )$ and dotted $(2\sigma )$ lines shows the constraint from Planck lensing alone [69].

Figure 11

Marginalized constraints on parameters of the constant disformal model using the data sets indicated in the figure. The sample points are taken from the $\mathrm{TT}+\mathrm{BSHR}$ data sets and color coded with the value of the disformal coupling parameter $D_M/{\mathrm{meV}}^{-1}$.

Figure 12

Marginalized constraints on the disformal coupling parameter $D_M/{\mathrm{meV}}^{-1}$, and the slope of the exponential scalar field potential $\lambda$, in the constant disformally coupled DE model. In the upper two panels we use the $H_0^{\mathrm{E}}$ local value of the Hubble constant, and in the lower two panels we use $H_0^{\mathrm{R}}$. The sample points in the top right and lower right panels are color coded with the value of ${\sigma }_8$ and are taken from the data sets represented by the black solid contour lines of each panel.

Figure 13

Marginalized two-dimensional constraints on the exponential disformal coupling parameter $\beta$ and the slope of the exponential potential $\lambda$. In these panels we use the local value of the Hubble constant $H_0^{\mathrm{E}}$ (left), and also of $H_0^{\mathrm{R}}$ (right). In this model we set $D_M{V}_0=1$.

Figure 14

Marginalized two-dimensional constraints on the conformal coupling parameter $\alpha$, and the slope of the exponential potential $\lambda$, in the mixed model with the parameter constraints tabulated in Table 8. In these panels we use the local value of the Hubble constant $H_0^{\mathrm{E}}$ (left), and also of $H_0^{\mathrm{R}}$ (right).

Figure 15

A comparison of the marginalized two-dimensional constraints on the conformal coupling parameter $\alpha$, and the scalar field’s potential parameter $\lambda$, in mixed models and the conformally coupled model. The mixed model with variable $D_M$ is denoted by mixed, whereas the other mixed model makes use of the relationship $D_M{V}_0=1$. In both mixed models, a constant disformal coupling ($\beta =0$) was considered.