Forecasting Coupled Dark Energy Parameters with the One-Loop Galaxy Power Spectrum

We forecast constraints on the parameters of the coupled dark energy model using DESI and Euclid data with the one-loop galaxy power spectrum. We investigate the distinguishability of our model from the zero-coupling scenario at the 1σ level and explore how the parameter constraints depend on the fiducial coupling β fid, the fixed potential slope parameter ν, the maximum wavenumber k, and different prior choices. We find that the inclusion of mildly non-linear scales improves the constraints on the coupling by roughly a factor of five. Then, we address the question of which is the minimum value of β that can be distinguished from zero at 1σ. We find that for our reference case k max=0.2 h/ Mpc, β=0.15 lies roughly 1σ above zero. In the most optimistic case with k max=0.3 h/ Mpc and including a Planck prior on Ω m0, this value can be reduced to 0.05. These values are substantially larger than the current constraints on β, but the latter have been obtained assuming β to be constant from at least the decoupling epoch to today, while we only employ late-time data. We conclude therefore that only models that allow for time-varying couplings can be detected with late-time datasets.