14386518
A COVARIANT ROAD TO SPATIAL AVERAGING IN COSMOLOGY: SCALAR CORRECTIONS TO THE COSMOLOGICAL EQUATIONS
A consistent approach to cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to Buchert has attracted considerable attention recently since it offers the tantalizing hope of explaining the phenomenon of dark energy through such corrections. This approach has been criticized, however, on the grounds that its effects may be gauge artifacts. We apply the fully covariant formalism of Zalaletdinov's macroscopic gravity and show that, after making some essential gauge choices, the cosmological equations receive space–time scalar corrections which are therefore observable in principle, and further, that the broad structure of these corrections is identical to those derived by Buchert.
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.
119551280
Explicit cosmological coarse graining via spatial averaging
The present matter density of the Universe, while highly inhomogeneous on small scales, displays approximate homogeneity on large scales. We propose that whereas it is justified to use the Friedmann–Lemaître–Robertson–Walker (FLRW) line element (which describes an exactly homogeneous and isotropic universe) as a template to construct luminosity distances in order to compare observations with theory, the evolution of the scale factor in such a construction must be governed not by the standard Einstein equations for the FLRW metric, but by the modified Friedmann equations derived by Buchert (Gen Relat Gravit 32:105, 2000; 33:1381, 2001) in the context of spatial averaging in Cosmology. Furthermore, we argue that this scale factor, defined in the spatially averaged cosmology, will correspond to the effective FLRW metric provided the size of the averaging domain coincides with the scale at which cosmological homogeneity arises. This allows us, in principle, to compare predictions of a spatially averaged cosmology with observations, in the standard manner, for instance by computing the luminosity distance versus red-shift relation. The predictions of the spatially averaged cosmology would in general differ from standard FLRW cosmology, because the scale-factor now obeys the modified FLRW equations. This could help determine, by comparing with observations, whether or not cosmological inhomogeneities are an alternative explanation for the observed cosmic acceleration.
119188055
Semiclassical environment of collapsing shells
We explore in detail the semiclassical environment of collapsing shells of matter, and determine the semiclassical flux measured by a variety of observers. This study is a preliminary step in a broader investigation of thermodynamic properties of the geometry of collapsing objects. Specifically, in this paper we consider spherically symmetric null and timelike collapsing shells which form an event horizon, and calculate the flux measured by observers both inside and outside the shell, and both inside and outside the event horizon, and find nontrivial results in most of the cases. Additionally, we also investigate the environment of a shell which collapses but does not form a horizon, halting at some radius larger than the Schwarzschild radius, and find that such an object generically gives rise to a pulse of radiation which is sharply peaked as it travels inwards and is reflected at the origin, and eventually emerges from the shell in a thermalized form. Our results have potential consequences in addressing questions pertaining, e.g. to black hole entropy and backreaction.
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.
119152649
The Extreme Tail of the Non-Gaussian Mass Function
Number counts of massive high-redshift clusters provide a window to study primordial non-Gaussianity. The current quality of data, however, forces the statistical analysis to probe a region of parameter space -- the extreme tail of the mass function -- which is neither accessible in any of the currently available theoretical prescriptions for calculating the mass function, nor calibrated in N-body simulations. In this work we present a new analytical prescription for calculating a "resummed" non-Gaussian halo mass function, which is constructed to remain stable in the extreme tail. We show that the prescription works well in the parameter regime that has been currently explored in simulations. We then use Fisher matrix techniques to compare our prescription with an extrapolated fit to N-body simulations, which has recently been used to obtain constraints from data collected by the South Pole Telecope. We show that for the current data, both prescriptions would lead to statistically consistent constraints. As the data improve, however, there is a possibility of introducing a statistically significant bias in the constraints due to the choice of prescription, especially if non-Gaussianity is scale dependent and becomes relatively large on cluster scales. It would then be necessary to test the accuracy of the prescriptions in N-body simulations that can probe clusters with high masses and redshifts in the presence of large non-Gaussianity.
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.