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Aseem Paranjape

Publications and source records attributed to Aseem Paranjape.

89 records · Page 5Linked to original sources
arXiv2011

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.

astro-ph.CO↗
arXiv2011

An Improved Calculation of the Non-Gaussian Halo Mass Function

The abundance of collapsed objects in the universe, or halo mass function, is an important theoretical tool in studying the effects of primordially generated non-Gaussianities on the large scale structure. The non-Gaussian mass function has been calculated by several authors in different ways, typically by exploiting the smallness of certain parameters which naturally appear in the calculation, to set up a perturbative expansion. We improve upon the existing results for the mass function by combining path integral methods and saddle point techniques (which have been separately applied in previous approaches). Additionally, we carefully account for the various scale dependent combinations of small parameters which appear. Some of these combinations in fact become of order unity for large mass scales and at high redshifts, and must therefore be treated non-perturbatively. Our approach allows us to do this, and to also account for multi-scale density correlations which appear in the calculation. We thus derive an accurate expression for the mass function which is based on approximations that are valid over a larger range of mass scales and redshifts than those of other authors. By tracking the terms ignored in the analysis, we estimate theoretical errors for our result and also for the results of others. We also discuss the complications introduced by the choice of smoothing filter function, which we take to be a top-hat in real space, and which leads to the dominant errors in our expression. Finally, we present a detailed comparison between the various expressions for the mass functions, exploring the accuracy and range of validity of each.

astro-ph.CO↗
arXiv2011

Excursion Sets and Non-Gaussian Void Statistics

Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the distribution of collapsed objects (i.e. dark matter halos and the galaxies and galaxy clusters that reside in them) to probe primordial NG. An equally interesting and complementary probe however is the abundance of extended underdense regions or voids in the LSS. The calculation of the abundance of voids using the excursion set formalism in the presence of primordial NG is subject to the same technical issues as the one for halos, which were discussed e.g. in arXiv:1005.1203. However, unlike the excursion set problem for halos which involved random walks in the presence of one barrier $δ_c$, the void excursion set problem involves two barriers $δ_v$ and $δ_c$. This leads to a new complication introduced by what is called the "void-in-cloud" effect discussed in the literature, which is unique to the case of voids. We explore a path integral approach which allows us to carefully account for all these issues, leading to a rigorous derivation of the effects of primordial NG on void abundances. The void-in-cloud issue in particular makes the calculation conceptually rather different from the one for halos. However, we show that its final effect can be described by a simple yet accurate approximation. Our final void abundance function is valid on larger scales than the expressions of other authors, while being broadly in agreement with those expressions on smaller scales.

astro-ph.CO↗
arXiv2009

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 \emph{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.

gr-qc↗
arXiv2009

The Averaging Problem in Cosmology

This thesis deals with the averaging problem in cosmology, which has gained considerable interest in recent years, and is concerned with correction terms (after averaging inhomogeneities) that appear in the Einstein equations when working on the large scales appropriate for cosmology. It has been claimed in the literature that these terms may account for the phenomenon of dark energy which causes the late time universe to accelerate. We investigate the nature of these terms by using averaging schemes available in the literature and further developed to be applicable to the problem at hand. We show that the effect of these terms when calculated carefully, remains negligible and cannot explain the late time acceleration.

astro-ph.CO↗
arXiv2009

Radiation from collapsing shells, semiclassical backreaction and black hole formation

We provide a detailed analysis of quantum field theory around a collapsing shell and discuss several conceptual issues related to the emission of radiation flux and formation of black holes. Explicit calculations are performed using a model for a collapsing shell which turns out to be analytically solvable. We use the insights gained in this model to draw reliable conclusions regarding more realistic models. We first show that any shell of mass $M$ which collapses to a radius close to $r=2M$ will emit approximately thermal radiation for a period of time. In particular, a shell which collapses from some initial radius to a final radius $2M(1-ε^2)^{-1}$ (where $ε\ll 1$) without forming a black hole, will emit thermal radiation during the period $M\lesssim t \lesssim M\ln (1/ε^2)$. Later on ($t\gg M \ln(1/ε^2)$), the flux from such a shell will decay to zero exponentially. We next study the effect of backreaction computed using the vacuum expectation value of the stress tensor on the collapse. We find that, in any realistic collapse scenario, the backreaction effects do \emph{not} prevent the formation of the event horizon. The time at which the event horizon is formed is, of course, delayed due to the radiated flux -- which decreases the mass of the shell -- but this effect is not sufficient to prevent horizon formation. We also clarify several conceptual issues and provide pedagogical details of the calculations in the Appendices to the paper.

gr-qc↗
arXiv2008

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.

astro-ph↗
arXiv2008

Cosmic Inhomogeneities and the Average Cosmological Dynamics

If general relativity (GR) describes the expansion of the Universe, the observed cosmic acceleration implies the existence of a `dark energy'. However, while the Universe is on average homogeneous on large scales, it is inhomogeneous on smaller scales. While GR governs the dynamics of the \emph{in}homogeneous Universe, the averaged \emph{homogeneous} Universe obeys modified Einstein equations. Can such modifications alone explain the acceleration? For a simple generic model with realistic initial conditions, we show the answer to be `no'. Averaging effects negligibly influence the cosmological dynamics.

astro-ph↗
arXiv2008

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 analysing 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 \emph{any} situation (not necessarily restricted to the linear perturbations considered here) where the \emph{metric} can be brought to the perturbed FLRW 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.

astro-ph↗
arXiv2008

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 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 nonlinear. 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.

astro-ph↗
arXiv2007

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-Lemaitre-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 [7, 8] 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.

astro-ph↗
arXiv2007

The 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 behaviour 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-Lemaitre-Robertson-Walker (FLRW) equations. We find that whereas one cannot escape the problem of dependence on \emph{one} gauge choice -- which is inherent in the assumption of large scale homogeneity and isotropy -- it is however possible to construct \emph{spacetime scalar} corrections to the standard FLRW equations. This partially addresses 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.

gr-qc↗
arXiv2007

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 \emph{spacetime scalar} corrections which are therefore observable in principle, and further, that the broad structure of these corrections is \emph{identical} to those derived by Buchert.

gr-qc↗
arXiv2007

Entropy of Null Surfaces and Dynamics of Spacetime

The null surfaces of a spacetime act as one-way membranes and can block information for a corresponding family of observers (time-like curves). Since lack of information can be related to entropy, this suggests the possibility of assigning an entropy to the null surfaces of a spacetime. We motivate and introduce such an entropy functional for any vector field in terms of a fourth-rank divergence free tensor P_{ab}^{cd} with the symmetries of the curvature tensor. Extremising this entropy for all the null surfaces then leads to equations for the background metric of the spacetime. When P_{ab}^{cd} is constructed from the metric alone, these equations are identical to Einstein's equations with an undetermined cosmological constant (which arises as an integration constant). More generally, if P_{ab}^{cd} is allowed to depend on both metric and curvature in a polynomial form, one recovers the Lanczos-Lovelock gravity. In all these cases: (a) We only need to extremise the entropy associated with the null surfaces; the metric is not a dynamical variable in this approach. (b) The extremal value of the entropy agrees with standard results, when evaluated on-shell for a solution admitting a horizon. The role of full quantum theory of gravity will be to provide the specific form of P_{ab}^{cd} which should be used in the entropy functional. With such an interpretation, it seems reasonable to interpret the Lanczos-Lovelock type terms as quantum corrections to classical gravity.

gr-qc↗
arXiv2006

Thermodynamic route to Field equations in Lanczos-Lovelock Gravity

Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate the notions of temperature and entropy with them. In the case of Einstein-Hilbert gravity, it is possible to interpret Einstein's equations as the thermodynamic identity TdS = dE + PdV for a spherically symmetric spacetime and thus provide a thermodynamic route to understand the dynamics of gravity. We study this approach further and show that the field equations for Lanczos-Lovelock action in a spherically symmetric spacetime can also be expressed as TdS = dE + PdV with S and E being given by expressions previously derived in the literature by other approaches. The Lanczos-Lovelock Lagrangians are of the form L=Q_a^{bcd}R^a_{bcd} with \nabla_b Q^{abcd}=0. In such models, the expansion of Q^{abcd} in terms of the derivatives of the metric tensor determines the structure of the theory and higher order terms can be interpreted quantum corrections to Einstein gravity. Our result indicates a deep connection between the thermodynamics of horizons and the allowed quantum corrections to standard Einstein gravity, and shows that the relation TdS = dE + PdV has a greater domain of validity that Einstein's field equations.

hep-th↗
arXiv2003

Embedding Diagrams for the Reissner-Nordström spacetime

We consider embedding diagrams for the Reissner-Nordström spacetime. We embed the $(r-t)$ and $(r-ϕ)$ planes into 3-Minkowski/Euclidean space and discuss the relation between the diagrams and the corresponding curvature scalar of the 2-metrics

gr-qc↗