118345110
Scale‐dependent halo bias in the excursion set approach
If one accounts for correlations between scales, then non-local, k-dependent halo bias is part and parcel of the excursion set approach, and hence of halo model predictions for galaxy bias. We present an analysis that distinguishes between a number of different effects, each of which contributes to scale-dependent bias in real space. We show how to isolate these effects and remove the scale dependence, order by order, by cross-correlating the halo field with suitably transformed versions of the mass field. These transformations may be thought of as simple one-point, two-scale measurements that allow one to estimate quantities which are usually constrained using n-point statistics. As part of our analysis, we present a simple analytic approximation for the first-crossing distribution of walks with correlated steps which are constrained to pass through a specified point, and demonstrate its accuracy. Although we concentrate on non-linear, non-local bias with respect to a Gaussian random field, we show how to generalize our analysis to more general fields.
17381559
Nonlinear Structure Formation, Backreaction and Weak Gravitational Fields
There is an ongoing debate in the literature concerning the effects of averaging out inhomogeneities (“backreaction”) in cosmology. In particular, some simple models of structure formation studied in the literature seem to indicate that the backreaction can play a significant role at late times, and it has also been suggested that the standard perturbed FLRW framework is no longer a good approximation during structure formation, when the density contrast becomes nonlinear. In this work we use Zalaletdinov's covariant averaging scheme (macroscopic gravity or MG) to show that as long as the metric of the Universe can be described by the perturbed FLRW form, the corrections due to averaging remain negligibly small. Further, using a fully relativistic and reasonably generic model of pressureless spherical collapse, we show that as long as matter velocities remain small (which is true in our model), the perturbed FLRW form of the metric can be explicitly recovered. Together, these results imply that the backreaction remains small even during nonlinear structure formation, and we confirm this within the toy model with a numerical calculation.
18963472
Structure formation, backreaction and weak gravitational fields
There is an ongoing debate in the literature as to whether the effects of averaging out inhomogeneities ('backreaction') in cosmology can be large enough to account for the acceleration of the scale factor in the Friedmann–Lemaitre–Robertson–Walker (FLRW) models. In particular, some simple models of structure formation studied in the literature seem to indicate that this is indeed possible, and it has also been suggested that the perturbed FLRW framework is no longer a good approximation during structure formation, when the density contrast becomes non-linear. In this work we attempt to clarify the situation to some extent, using a fully relativistic model of pressureless spherical collapse. We find that whereas averaging during structure formation can lead to acceleration via a selective choice of averaging domains, the acceleration is not present when more generic domains are used for averaging. Further, we show that for most of the duration of the collapse, matter velocities remain small, and the perturbed FLRW form of the metric can be explicitly recovered, in the structure formation phase. We also discuss the fact that the magnitude of the average effects of inhomogeneities depends on the scale of averaging, and while it may not be completely negligible on intermediate scales, it is expected to remain small when averaging on suitably large scales.
119303188
Non-Gaussian halo abundances in the excursion set approach with correlated steps
We study the effects of primordial non-Gaussianity on the large scale structure in the excursion set approach, accounting for correlations between steps of the random walks in the smoothed initial density field. These correlations are induced by realistic smoothing filters (as opposed to a filter that is sharp in k-space), but have been ignored by many analyses to date. We present analytical arguments -- building on existing results for Gaussian initial conditions -- which suggest that the effect of the filter at large smoothing scales is remarkably simple, and is in fact identical to what happens in the Gaussian case: the non-Gaussian walks behave as if they were smooth and deterministic, or 'completely correlated'. As a result, the first crossing distribution (which determines, e.g., halo abundances) follows from the single-scale statistics of the non-Gaussian density field -- the so-called 'cloud-in-cloud' problem does not exist for completely correlated walks. Also, the answer from single-scale statistics is simply one half that for sharp-k walks. We explicitly test these arguments using Monte Carlo simulations of non-Gaussian walks, showing that the resulting first crossing distributions, and in particular the factor 1/2 argument, are remarkably insensitive to variations in the power spectrum and the defining non-Gaussian process. We also use our Monte Carlo walks to test some of the existing prescriptions for the non-Gaussian first crossing distribution. Since the factor 1/2 holds for both Gaussian and non-Gaussian initial conditions, it provides a theoretical motivation (the first, to our knowledge) for the common practice of analytically prescribing a ratio of non-Gaussian to Gaussian halo abundances.
19943745
Spatial averaging limit of covariant macroscopic gravity: Scalar corrections to the cosmological equations
It is known that any explicit averaging scheme of the type essential for describing the large scale behavior of the Universe must necessarily yield corrections to the Einstein equations applied in the cosmological setting. The question of whether or not the resulting corrections to the Einstein equations are significant is still a subject of debate, partly due to possible ambiguities in the averaging schemes available. In particular, it has been argued in the literature that the effects of averaging could be gauge artifacts. We apply the formalism of Zalaletdinov's macroscopic gravity (MG), which is a fully covariant and nonperturbative averaging scheme, in an attempt to construct gauge independent corrections to the standard Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) equations. We find that whereas one cannot escape the problem of dependence on one gauge choice\char22{}which is inherent in the assumption of large scale homogeneity and isotropy\char22{}it is however possible to construct space-time scalar corrections to the standard FLRW equations. This partially removes the criticism concerning the corrections being gauge artifacts. For a particular initial choice of gauge which simplifies the formalism, we explicitly construct these scalars in terms of the underlying inhomogeneous geometry, and incidentally demonstrate that the formal structure of the corrections with this gauge choice is identical to that of analogous corrections derived by Buchert in the context of spatial averaging of scalars.
118443233
Backreaction of Cosmological Perturbations in Covariant Macroscopic Gravity
The problem of corrections to Einstein's equations arising from averaging of inhomogeneities (backreaction) in the cosmological context has gained considerable attention recently. We present results of analyzing cosmological perturbation theory in the framework of Zalaletdinov's fully covariant macroscopic gravity. We show that this framework can be adapted to the setting of cosmological perturbations in a manner which is free from gauge related ambiguities. We derive expressions for the backreaction which can be readily applied in any situation (not necessarily restricted to the linear perturbations considered here) where the metric can be brought to the perturbed Friedmann-Lemaitre-Robertson-Walker form. In particular, these expressions can be employed in toy models studying nonlinear structure formation, and possibly also in N-body simulations. Additionally, we present results of example calculations which show that the backreaction remains negligible well into the matter dominated era.
5059816
Cosmological sector for localized mass and spin in 2+1 dimensional topologically massive gravity
Abstract The cosmological sector to the full non-linear topologically massive gravity (TMG) is obtained for localized sources of mass m and spin σ besides the asymptotically spinning conical flat sector previously obtained [A. Edery, M.B. Paranjape, gr-qc/9606029, to be published]. In a small region near but outside the sources, the metric resembles the spinning conical flat metric but we find that the mass m creates a negative deficit angle of 3 m as opposed to m . Furthermore, it is not possible to recover the results of pure Einstein gravity in the limit μ →∞ unlike the flat sector.