We compute the critical density of collapse for spherically symmetric overdensities in a class of f (R) modified gravity models. For the first time we evolve the Einstein, scalar field and non-linear fluid equations, making the minimal simplifying assumptions that the metric potentials and scalar field remain quasi-static throughout the collapse. Initially evolving a top hat profile, we find that the density threshold for collapse depends significantly on the initial conditions imposed, specifically the choice of size and shape. By imposing 'natural' initial conditions, we obtain a fitting function for the spherical collapse δ c as a function of collapse redshift, mass of the overdensity and f R0 , the background scalar field value at z = 0. By extending δ c into drifting and diffusing barrier within the context of excursion set theory, we obtain a realistic mass function that might be used to confront this class of scalar-tensor models with observations of dark matter halos. The proposed analytic formula for the halo mass function was tested against Monte Carlo random walks for a wide class of moving barriers and can therefore be applied to other modified gravity theories.

No abstract

We use the Excursion Set formalism to compute the properties of the halo mass distribution for a stochastic barrier model which encapsulates the main features of the ellipsoidal collapse of dark matter halos. Non-markovian corrections due to the sharp filtering of the linear density field in real space are computed with the path-integral technique introduced by Maggiore & Riotto [20]. Here, we provide a detailed derivation of the results presented in [22] and extend the mass function analysis to higher redshift. We also derive an analytical expression for the linear halo bias. We find the analytically derived mass function to be in remarkable agreement with N-body simulation data from Tinker et al. [10] with differences 5% over the range of mass probed by the simulations. The excursion set solution from Monte Carlo generated random walks shows the same level of agreement, thus confirming the validity of the path-integral approach for the barrier model considered here. Similarly the analysis of the linear halo bias shows deviations no greater than 20%. Overall these results indicate that the Excursion Set formalism in combination with a realistic modeling of the conditions of halo collapse can provide an accurate description of the halo mass distribution.

We compute the dark matter halo mass function using the excursion set formalism for a diffusive barrier with linearly drifting average which captures the main features of the ellipsoidal collapse model. We evaluate the non-Markovian corrections due to the sharp filtering of the linear density field in real space with a path-integral method. We find an unprecedented agreement with N-body simulation data with deviations ≲5% over the range of masses probed by the simulations. This indicates that the excursion set in combination with a realistic modeling of the collapse threshold can provide a robust estimation of the halo mass function.

The excursion set approach provides a framework for predicting how the abundance of dark matter halos depends on the initial conditions. A key ingredient of this formalism is the specification of a critical overdensity threshold (barrier) which protohalos must exceed if they are to form virialized halos at a later time. However, to make its predictions, the excursion set approach explicitly averages over all positions in the initial field, rather than the special ones around which halos form, so it is not clear that the barrier has physical motivation or meaning. In this Letter we show that once the statistical assumptions which underlie the excursion set approach are considered a drifting diffusing barrier model does provide a good self-consistent description both of halo abundance as well as of the initial overdensities of the protohalo patches.

We test the imprint of f (R) modified gravity on the halo mass function, using N-body simulations and a theoretical model developed in [43]. We find a good agreement between theory and simulations ∼ 5%. We extend the theoretical model to the conditional mass function and apply it to the prediction of the linear halo bias in f (R) gravity. Using the halo model we obtain a prediction for the non-linear matter power spectrum accurate to ∼ 10% at z = 0 and up to k = 2h/Mpc. We also study halo profiles for the f (R) models and find a deviation from the standard general relativity result up to 40%, depending on the halo masses and redshift. This has not been pointed out in previous analysis. Finally we study the number density and profiles of voids identified in these f (R) N-body simulations. We underline the effect of the bias and the sampling to identify voids. We find significant deviation from GR when measuring the f (R) void profiles with fR0 < −10 −6 .

We present a new analysis of the inferred growth rate of cosmic structure measured around voids, using the LOWZ and the CMASS samples in the twelfth data release (DR12) of SDSS. Using a simple multipole analysis we recover a value consistent with ΛCDM for the inferred linear growth rate normalized by the linear bias: the β parameter. This is true in both the mock catalogues and the data, where we find β = 0.33 ± 0.06 for the LOWZ sample and β = 0.36 ± 0.05 for the CMASS sample. This work demonstrates that we can expect redshift-space distortions around voids to provide unbiased and accurate constraints on the growth rate, complementary to galaxy clustering, using simple linear modelling.

We compare analytical predictions of void volume functions to those measured from Nbody simulations, detecting voids with the zobov void finder. We push to very small, nonlinear voids, below few h −1 .Mpc radius, by considering the unsampled DM density field. We also study the case where voids are identified using halos. We develop analytical formula for the void abundance of both the excursion set approach and the peaks formalism. These formula are valid for random walks smoothed with a top-hat filter in real space, with a large class of realistic barrier models. We test the extent to which the spherical evolution approximation, which forms the basis of the analytical predictions, models the highly aspherical voids that occur in the cosmic web, and are found by a watershed-based algorithm such as zobov. We show that the volume function returned by zobov is quite sensitive to the choice of treatment of sub-voids, a fact that has not been appreciated previously. For reasonable choices of sub-void exclusion, we find that the Lagrangian density δ v of the zobov voids -which is predicted to be a constant δ v ≈ −2.7 in the spherical evolution model -is different from the predicted value, showing substantial scatter and scale dependence. This result applies to voids identified at z = 0 with effective radius between 1 and 10M pc.h −1 . Our analytical approximations are flexible enough to give a good description of the resulting volume function; however, this happens for choices of parameter values that are different from those suggested by the spherical evolution assumption. We conclude that analytical models for voids must move away from the spherical approximation in order to be applied successfully to observations, and we discuss some possible ways forward.