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 freefall (geodesic), as in ΛCDM. The interaction is characterized by a dimensionless coupling qV(z), in general a function of redshift. Aiming to reconstruct the evolution of the coupling, we use cosmic microwave background data from Planck 2015, along with baryon acoustic oscillation, redshift space distortion, and Type Ia supernova measurements to constrain various parametrizations of qV(z). We present the full linear perturbation theory of this interacting scenario and use Monte Carlo Markov Chains (MCMC) sampling to study five different cases: two cases in which we have ΛCDM evolution in the distant past, until a set redshift ztrans, below which the interaction switches on and qV is the single-sampled parameter, with ztrans fixed at ztrans = 3000 and 0.9, respectively; a case where we allow this transition redshift to vary along with qV; a case in which the vacuum energy is zero for z > ztrans and then begins to grow once the interaction switches on; and the final case in which we bin qV(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 ΛCDM.
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