ner_tags: O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O B-Model O B-Model I-Model I-Model I-Model I-Model O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O
tokens: from PFS are expected to be less competitive against existing cosmological probes. Notice that, observations by SDSS galaxy surveys in the low to moderate redshift range 0.15 z 0.67 is already being used to set interesting constraints on any departure from GR, e.g. Bel et al. ( 2015 ) obtained at the 2σ level. We would also like to stress that our results are based on all-sky analysis and we use an f sky scaling to take into account the effect of partial sky coverage. Surveys that cover a small fraction of sky such as PFS will have to deal with strong mode–mode coupling that drives the covariance matrix to near singularity. A detailed analysis will be presented elsewhere. Our constraints are derived for a spectroscopic survey. Inclusion of photometric redshift error will degrade the discriminating power of the survey. The comparison of the linear and non-linear curves in Figs 12 and 13 suggests that the non-linear contributions can make a significant effect. However, in the non-linear regime the covariance matrix should include the bispectrum and the trispectrum of the density field, which would reduce the χ 2 . Therefore, we can expect that a fully non-linear analysis, with a better modelling of the covariance matrix (e.g. from numerical simulations) would lower down the non-linear curves and make them closer to the linear result. However, because the departures from the ΛCDM power spectrum increase on weakly non-linear scales, non-linearities should still improve the discriminatory power of the analysis of 3D clustering as compared with the linear result. Here we follow a conservative approach as we estimate the constraints on the MG parameters by using the linear-theory χ 2 . We have studied the constraints in both f ( R ) and Dilaton models with and without RSD. We find that RSD only lead to a small broadening of the constraints. Below galaxy number density of the surveys rapidly lose their ability to discriminate. On the other hand, increasing the number density beyond does not lead to drastic improvements of the results. Our constraints are based on lower order tangential modes l ≤ 25. We find that the information contents in different l are highly degenerate. In the range 0.01 ≤ k ≤ 0.2 h Mpc −1 , we find that for more than three to four (logarithmic) bins in k the covariance matrix can become singular. Finally, our results are based on a uniform distribution of noise (constant ) while real surveys may have more complicated variations in the average galaxy number density which may depend on the radial and angular coordinates in the sky. 6 DISCUSSION AND FUTURE PROSPECTS In this paper we have studied the possibility of constraining MG theories using galaxy clustering. We have studied two different MG models: f ( R ) theories and Dilaton theories. In both cases we have used a specific parametrization and computed the χ 2 as a criterion for constraining the departure from the ΛCDM models. We used the sFB transforms and the