Null test for interactions in the dark sector

Since there is no known symmetry in nature that prevents a nonminimal coupling between the dark energy (DE) and cold dark matter (CDM) components, such a possibility constitutes an alternative to standard cosmology, with its theoretical and observational consequences being of great interest. In this paper, we propose a new null test on the standard evolution of the dark sector based on the time dependence of the ratio between the CDM and DE energy densities which, in the standard $\mathrm{\Lambda }\mathrm{CDM}$ scenario, scales necessarily as $a^{-3}$. We use the latest measurements of type Ia supernovae, cosmic chronometers and angular baryonic acoustic oscillations to reconstruct the expansion history using model-independent machine learning techniques, namely, the linear model formalism and Gaussian processes. We find that while the standard evolution is consistent with the data at $3\sigma$ level, some deviations from the $\mathrm{\Lambda }\mathrm{CDM}$ model are found at low redshifts, which may be associated with the current tension between local and global determinations of $H_0$.

Figure 1

The black dots are the cosmic chronometer data. The solid lines are the reconstructions of the Hubble function using the linear model formalism. The data is presented in [25, Table I].

Figure 2

Distance modulus as a function of the redshift. The black dots are the Pantheon data (subtracting $M=-19.25$). The solid lines are the reconstructions of the distance modulus using the linear model formalism.

Figure 3

Angular BAO scale as a function of the redshift. The black dots are the data of Table 1. The solid line is the reconstruction of the BAO angular scale using the linear model formalism.

Figure 4

Statistical analysis for the $\mathrm{\Lambda }\mathrm{CDM}$ model using the Pantheon sample of type Ia SN data. The result in red was obtained fixing $H_0$ to (22) (model independent priors), and the blue result was obtained fixing $H_0$ to (24).

Figure 5

Learning curve analysis for the CC data with ${\alpha }_{\max }=0$, 1, 2, 3 from top to bottom.

Figure 6

Learning curve analysis for the Pantheon data set with ${\alpha }_{\max }=1$, 2, 3, 4 from top to bottom.

Figure 7

Learning curve analysis for the angular BAO data with ${\alpha }_{\max }=1$ (top) e ${\alpha }_{\max }=2$ (bottom).

Figure 8

$r_0(z)$ obtained from CC data using a LM with ${\alpha }_{\max }=1$ (top) and ${\alpha }_{\max }=2$ (bottom).

Figure 9

$r_0(z)$ obtained from type Ia SN data using a LM with ${\alpha }_{\max }=2$ (top) and ${\alpha }_{\max }=3$ (bottom).

Figure 10

$r_0(z)$ obtained from BAO data using a LM with ${\alpha }_{\max }=1$.

Figure 11

$r_0(z)$ obtained from CC data using GPs.

Figure 12

$r_0(z)$ obtained from type Ia SNe data using GPs.