A new paper has been put on the arXiv by new CosmoStat member Valeria Pettorino, her PhD student Santiago Casas, in collaboration with Martin Kunz (Geneva) and Matteo Martinelli (Leiden).
The authors discuss forecasts in Modified Gravity cosmologies, described by two generic functions of time and space [Planck Dark Energy and Modified Gravity 2015, Asaba et al 2013,Bull 2015, Alonso et al 2016]. Their amplitude is constrained in different redshift bins. The authors elaborate on the impact of non-linear scales, showing that their inclusion (via a non-linear semi-analytical prescription applied to Modified Gravity) enables to highly reduce correlation among different redshift bins, even before any decorrelation procedure is applied. This is visually seen in the figure below (Fig.4 of arXiv), for the case of Galaxy Clustering: the correlation Matrix of the cosmological parameters (including the amplitudes of the Modified Gravity functions, binned in redshift) is much more diagonal in the non-linear case (right panel) than in the linear one (left panel).
A decorrelation procedure (Zero-phase Component Analysis, ZCA) is anyway used to extract those combinations which are best constrained by future surveys such as Euclid. With respect to Principal Component Analysis, ZCA allows to find a new vector of uncorrelated variables that is as similar as possible to the original vector of variables.
The authors further consider two smooth time functions whose main allowed to depart from General Relativity only at late times (late-time parameterization) or able to detach also at early times (early-time parameterization). The Fisher Matrix forecasts for standard and Modified gravity parameters, for different surveys (Euclid, SKA1, SKA2) is shown in the plot below (extracted from Fig.15 of arXiv), in which Galaxy Clustering and Weak Lensing probes are combined. Left panel refers to linear analysis, right panel includes a non-linear treatment.