Euclid preparation

Context. The Euclid mission has the potential to determine the fundamental physical nature of late-time cosmic acceleration and, as such, of deviations from the standard cosmological model, Λ cold dark matter. In this paper we focus on model-independent methods for modifying the evolution of scalar perturbations on linear scales. We considered two powerful and convenient approaches: The first is based on the two phenomenological modified gravity (PMG) parameters, μ mg and Σ mg , which are phenomenologically connected to the clustering of matter and weak lensing (WL), respectively. The second is the effective field theory (EFT) of dark energy and modified gravity, which we used to parameterise the braiding function, α B , which defines the mixing between the metric and the dark energy field typical of Galileon theories. Aims. We estimate cosmological parameters based on spectroscopic and photometric primary probes by Euclid for a given set of additional parameters using the PMG and EFT models. Methods. We used the Fisher matrix method applied to spectroscopic galaxy clustering, WL, photometric galaxy clustering (GC ph ), and the cross-correlation between GC ph and WL. To model photometric predictions on nonlinear scales, we used the halo model reaction approach to cover two limiting cases for the screening mechanism: the unscreened (US) case, for which the screening mechanism is not present; and the super-screened (SS) case, which assumes strong screening. We also assumed scale cuts to account for our uncertainties when modelling nonlinear perturbation evolution. We chose a time-dependent form for { μ mg , Σ mg }, with two fiducial sets of values for the corresponding model parameters at the present time, { μ ¯ 0 ,Σ¯ 0 }, and two forms for α B , with one fiducial set of values for each of the model parameters, α B, 0 and { α B, 0 , m }. Results. At the 68.3% confidence level, the percentage relative errors obtained with Euclid alone and our conservative settings for the full combination of probes for the US case are: for { μ ¯ 0 ,Σ¯ 0 }, with a ΛCDM fiducial, we obtain {23.3%, 2.6%}; for a fiducial { μ ¯ 0 ,Σ¯ 0 } = {0.5,0.5} we obtain {36.2%, 2.7%}; for α B, 0 whose fiducial is 0.2, we have 31.1%; and for { α B, 0 , m } with fiducial {0.9, 2.4} we have 11.6% and 11.8%. The constraints we obtain with the SS prescription provide similar values. We also computed constraints for different combinations of probes to assess their standalone and complementary constraining power.

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