A more inclusive effective dark fluid equation of state parameter: constraints from SKA and Euclid like surveys

Abstract

We forecast constraints on an effective dark fluid equation of state parameter $w_{\rm eff}$ that encapsulates modified gravity theories that modifies both the Universe background expansion as well as its large scale structures growth. This is achieved through relating Friedmann equations' dark fluid pressure and density content, thus $w_{\rm eff}$, to modified gravity parameterized models by mean of the Newtonian potential equation parameter $\mu_0$, the gravitational slip parameter $\eta_0$ and a redshift dependent Hubble parameter $H_{0,{\rm bck}}$. We adopt next stage SKA survey specifications, alone or in combination with concurrently expected DR3 Euclid survey release, paying attention to the modeling and recipe of the implementation of the galaxy clustering and lensing probes obtained from the two surveys. We consider two data mock models: one with deviation of the intermediate parameters at the level of 10 \% (yielding however $w_{\rm eff}=-1.03$) and another sub-percently close to $\Lambda$CDM. We found that the three parameters deviation from $\Lambda$CDM could only be detected at 1 $\sigma$ from SKA alone, while this improves to $\sim$ 2 $\sigma$ when we combine with Euclid. An improvement of the order of 30\% on the bounds is reached after projecting the three parameters into a single $w_{\rm eff}$ parameter. However, this affects both cases and thus it does not change much, though it improves the level of detection with respect to $\Lambda$CDM values. We conclude that synergy from both surveys benefits to tighten our constraints, but also that our highly generalized parameterization, although impacting at both the background and the perturbation level, will be hard to disentangle from $\Lambda$CDM at the level at which our forecast is performed and it still needs, to the least, data from more advanced stages of the adopted surveys to hope reach this target.