Constraints on the interacting vacuum -- geodesic CDM scenario

TL;DR

This work investigates a dark-sector interaction where vacuum energy exchanges energy with CDM while CDM remains geodesic, parameterized by a redshift-dependent coupling q_V(z). Using Planck 2015 data plus BAO, RSD, and SN measurements, the authors develop a linear perturbation framework and explore five reconstruction schemes for q_V(z), including a four-bin, model-independent case. Across all scenarios that preserve early-Universe ΛCDM behavior, the results are consistent with q_V = 0, with Planck+Low-z data driving the posterior toward ΛCDM and Planck data alone allowing broader ranges. The study finds no significant statistical preference for an interacting vacuum over ΛCDM, discusses implications for H0 and σ8 tensions, and highlights the need for non-linear analyses and richer data (e.g., future surveys) to tighten constraints on dark-sector interactions.

Abstract

We investigate an interacting dark sector scenario in which the vacuum energy is free to interact with cold dark matter (CDM), which itself is assumed to cluster under the sole action of gravity, i.e. it is in free fall (geodesic), as in $Λ$CDM. The interaction is characterised by a dimensionless coupling $q_{\rm V}$ that we constrain using cosmic microwave background data from the Planck 2015 data release, along with baryon acoustic oscillation, redshift space distortion and Type Ia supernova measurements. We present the full linear perturbation theory of this interacting scenario and use MCMC sampling to study five different cases: two cases in which we have $Λ$CDM evolution in the distant past, until a set redshift $z_{\rm trans}$, below which the interaction switches on and $q_{\rm V}$ is the single sampled parameter, with $z_{\rm trans}$ fixed at $z_{\rm trans}=3000$ and $z_{\rm trans}=0.9$ respectively; a case where we allow this transition redshift to vary along with $q_{\rm V}$; a case in which the vacuum energy is zero for $z>z_{\rm trans}$ and then begins to grow once the interaction switches on; and the final case in which we bin $q_{\rm V}(z)$ in four redshift bins to investigate the possibility of a dynamical interaction, reconstructing the redshift evolution of the function using Gaussian processes. We find that, in all cases where the high redshift evolution is not modified, the results are compatible with a vanishing coupling, thus finding no significant deviation from $Λ$CDM.

Figures (14)

• Figure 1: The evolution of the Hubble function $H(z)$ for 3 cosmologies resulting in the same angular size of the sound horizon at recombination. Except for $q_{\rm V}$ and $H_0$, whose values are shown in the label, all the other primary parameters are fixed to the Planck 2015 best fit.
• Figure 2: The evolution of the matter (dashed lines) and vacuum density (solid lines) parameters as a function of redshift, for a small positive and negative coupling. The $\Lambda$CDM case is shown in blue. Except for $q_{\rm V}$ and $H_0$, whose values are shown in the label, all the other primary parameters are fixed to the Planck 2015 best fit.
• Figure 3: The CMB TT power spectrum for 3 cosmologies resulting in the same angular size of the sound horizon at recombination. Except for $q_{\rm V}$ and $H_0$, whose values are shown in the label, all the other primary parameters are fixed to the Planck 2015 best fit. The data points are the TT observations of Planck 2015.
• Figure 4: The matter power spectrum at $z=0$ for 3 cosmologies resulting in the same angular size of the sound horizon at recombination. Except for $q_{\rm V}$ and $H_0$, whose values are shown in the label, all the other primary parameters are fixed to the Planck 2015 best fit. The $\Lambda$CDM case is plotted in blue.
• Figure 5: Cfix case with $z_{\rm trans} = 3000$: $68$% and the $95$% confidence level marginalized contours on $H_0$, $q_{\rm V}=q_{\rm V}(z\leq 3000)$ and $\Omega_m$ as obtained in the analysis with the Planck (red) and Planck + Low-z (yellow) datasets.