Coupled dark energy with perturbed Hubble expansion rate

The coupling between dark sectors provides a possible approach to mitigate the coincidence problem of the cosmological standard model. In this paper, dark energy is treated as a fluid with a constant equation of state, whose coupling with dark matter is proportional the Hubble parameter and energy density of dark energy, that is, Q=3ₗH{}ₗ. In particular, we consider the Hubble expansion rate to be perturbed in the perturbation evolutions of dark sectors. Using joint data sets which include cosmic microwave background radiation, baryon acoustic oscillation, type Ia supernovae, and redshift-space distortions, we perform a full Markov chain Monte Carlo likelihood analysis for the coupled model. The results show that the mean value with errors of the interaction rate is ₗ=0. 00305-₀. ₀₀₃₀₅-₀. ₀₀₃₀₅-₀. ₀₀₃₀₅^+0. 000645+0. 00511+0. 00854 for Q₀^u₂^ and ₗ=0. 00317-₀. ₀₀₃₁₇-₀. ₀₀₃₁₇-₀. ₀₀₃₁₇^+0. 000628+0. 00547+0. 00929 for Q₀^uₗ^, which means that the recent cosmic observations favor a small interaction rate which is up to the order of 10^-3. Moreover, in contrast to the coupled model with an unperturbed expansion rate, we find the perturbed Hubble expansion rate can bring about a negligible impact on the model parameter space.