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We use a set of N-body simulations employing a modified gravity (MG) model with Vainshtein screening to study matter and halo hierarchical clustering. As test-case scenarios we consider two normal branch Dvali-Gabadadze-Porrati (nDGP) gravity models with mild and strong growth rate enhancement. We study higher-order correlation functions $\xi_n(R)$ up to $n=9$ and associated hierarchical amplitudes $S_n(R)\equiv\xi_n(R)/\sigma(R)^{2n-2}$. We find that the matter PDFs are strongly affected by the fifth-force on scales up to $50h^{-1}$Mpc, and the deviations from GR are maximised at $z=0$. For reduced cumulants $S_n$, we find that at small scales $R\leq10h^{-1}$Mpc the MG is characterised by lower values, with the deviation growing from $7\%$ in the reduced skewness up to even $40\%$ in $S_5$. To study the halo clustering we use a simple abundance matching and divide haloes into thee fixed number density samples. The halo two-point functions are weakly affected, with a relative boost of the order of a few percent appearing only at the smallest pair separations ($r\leq 5h^{-1}$Mpc). In contrast, we find a strong MG signal in $S_n(R)$'s, which are enhanced compared to GR. The strong model exhibits a $>3\sigma$ level signal at various scales for all halo samples and in all cumulants. In this context, we find that the reduced kurtosis to be an especially promising cosmological probe of MG. Even the mild nDGP model leaves a $3\sigma$ imprint at small scales $R\leq3h^{-1}$Mpc, while the stronger model deviates from a GR-signature at nearly all scales with a significance of $>5\sigma$. Since the signal is persistent in all halo samples and over a range of scales, we advocate that the reduced kurtosis estimated from galaxy catalogues can potentially constitute a strong MG-model discriminatory as well as GR self-consistency test., Comment: 19 pages, 11 figures, comments are welcome

In this Letter, we report the observational constraints on the Hu-Sawicki f(R) theory derived from weak lensing peak abundances, which are closely related to the mass function of massive halos. In comparison with studies using optical or x-ray clusters of galaxies, weak lensing peak analyses have the advantages of not relying on mass-baryonic observable calibrations. With observations from the Canada-France-Hawaii-Telescope Lensing Survey, our peak analyses give rise to a tight constraint on the model parameter |f_{R0}| for n=1. The 95% C.L. is log_{10}|f_{R0}

Current constraints on f(R) gravity from the large-scale structure are at the verge of penetrating into a region where the modified forces become nonlinearly suppressed. For a consistent treatment of observables at these scales, we study cluster quantities produced in chameleon and linearized Hu-Sawicki f(R) gravity dark matter N-body simulations. We find that the standard Navarro-Frenk-White halo density profile and the radial power law for the pseudo phase-space density provide equally good fits for f(R) clusters as they do in the Newtonian scenario. We give qualitative arguments for why this should be the case. For practical applications, we derive analytic relations, e.g., for the f(R) scalar field, the gravitational potential, and the velocity dispersion as seen within the virialized clusters. These functions are based on three degrees of freedom fitted to simulations, i.e., the characteristic density, scale, and velocity dispersion. We further analyze predictions for these fitting parameters from the gravitational collapse and the Jeans equation, which are found to agree well with the simulations. Our analytic results can be used to consistently constrain chameleon f(R) gravity with future observations on virialized cluster scales without the necessity of running a large number of simulations., 14 pages, 4 figures, 1 table; v2 matches published version

We explore the complementarity of weak lensing and galaxy peculiar velocity measurements to better constrain modifications to General Relativity. We find no evidence for deviations from GR on cosmological scales from a combination of peculiar velocity measurements (for Luminous Red Galaxies in the Sloan Digital Sky Survey) with weak lensing measurements (from the CFHT Legacy Survey). We provide a Fisher error forecast for a Euclid-like space-based survey including both lensing and peculiar velocity measurements, and show that the expected constraints on modified gravity will be at least an order of magnitude better than with present data, i.e. we will obtain 5% errors on the modified gravity parametrization described here. We also present a model--independent method for constraining modified gravity parameters using tomographic peculiar velocity information, and apply this methodology to the present dataset., 8 pages, 5 figures

We perform high resolution N-body simulations for f(R) gravity based on a self-adaptive particlemesh code MLAPM. The Chameleon mechanism that recovers General Relativity on small scales is fully taken into account by self-consistently solving the non-linear equation for the scalar field. We independently confirm the previous simulation results, including the matter power spectrum, halo mass function and density profiles, obtained by Oyaizu et al. (Phys.Rev.D 78, 123524, 2008) and Schmidt et al. (Phys.Rev.D 79, 083518, 2009), and extend the resolution up to k � 20 h/Mpc for the measurement of the matter power spectrum. Based on our simulation results, we discuss how the Chameleon mechanism affects the clustering of dark matter and halos on full non-linear scales.

We test General Relativity (GR) using current cosmological data: the cosmic microwave background (CMB) from WMAP5 (Komatsu et al. 2009), the integrated Sachs-Wolfe (ISW) effect from the cross-correlation of the CMB with six galaxy catalogs (Giannantonio et al. 2008), a compilation of supernovae Type Ia (SNe) including the latest SDSS SNe (Kessler et al. 2009), and part of the weak lensing (WL) data from CFHTLS (Fu et al. 2008, Kilbinger et al. 2009) that probe linear and mildly non-linear scales. We first test a model where the effective Newton's constant, mu, and the ratio of the two gravitational potentials, eta, transit from the GR value to another constant at late times; in this case, we find that standard GR is fully consistent with the combined data. The strongest constraint comes from the ISW effect which would arise from this gravitational transition; the observed ISW signal imposes a tight constraint on a combination of mu and eta that characterizes the lensing potential. Next, we consider four pixels in time and space for each function mu and eta, and perform a Principal Component Analysis (PCA) finding that seven of the resulting eight eigenmodes are consistent with GR within the errors. Only one eigenmode shows a 2-sigma deviation from the GR prediction, which is likely to be due to a systematic effect. However, the detection of such a deviation demonstrates the power of our time- and scale-dependent PCA methodology when combining observations of structure formation and expansion history to test GR., 14 pages, 10 figures. Minor modifications, version published by Phys. Rev. D

We report the constraints on the dark energy equation-of-state w(z) using the latest 'Constitution' SNe sample combined with the WMAP5 and SDSS data. Based on the localized principal component analysis and the model selection criteria, we find that the LCDM model is generally consistent with the current data, yet there exists weak hint of the possible dynamics of dark energy. In particular, a model predicting w(z)-1 at z\in[0.5,0.75), which means that w(z) crosses -1 in the range of z\in[0.25,0.75), is mildly favored at 95% confidence level. Given the best fit model for current data as a fiducial model, we make future forecast from the joint data sets of JDEM, Planck and LSST, and we find that the future surveys can reduce the error bars on the w bins by roughly a factor of 10 for a 5-w-bin model., Comment: Accepted by PRD; minor changes from v1

We investigate the correlation between the neutrino mass limit and dark energy with time evolving equation of state. Parameterizing dark energy as w=w_0+w_1*z/(1+z), we make a global fit using Markov Chain Monte Carlo technique to determine w_0, w_1, neutrino mass as well as other cosmological parameters simultaneously. We pay particular attention to the correlation between neutrino mass \Sigma m_{\nu} and w_1 using current cosmological observations as well as the future simulated datasets such as PLANCK, SNAP and LAMOST., Comment: 9 pages, 5 figures, 1 table

We probe the time dependence of the dark energy equation of state (EOS) in light of three-year WMAP (WMAP3) and the combination with other tentative cosmological observations from galaxy clustering (SDSS) and Type Ia Supernova (SNIa). We mainly focus on cases where the EOS is oscillating or with local bumps. By performing a global analysis with the Markov Chain Monte Carlo (MCMC) method, we find the current observations, in particular the WMAP3 + SDSS data combination, allow large oscillations of the EOS which can leave oscillating features on the (residual) Hubble diagram, and such oscillations are potentially detectable by future observations like SNAP, or even by the CURRENTLY ONGOING SNIa observations. Local bumps of dark energy EOS can also leave imprints on CMB, LSS and SNIa. In cases where the bumps take place at low redshifts and the effective EOS are close to -1, CMB and LSS observations cannot give constraints on such possibilities. However, geometrical observations like (future) SNIa can possibly detect such features. On the other hand when the local bumps take place at higher redshifts beyond the detectability of SNIa, future precise observations like Gamma-ray bursts, CMB and LSS may possibly detect such features. In particular, we find that bump-like dark energy EOS on high redshifts might be responsible for the features of WMAP on ranges l \sim 30-50, which is interesting and deserves addressing further., 14 pages, 7 figures Revtex4