arXiv subjects

Tarun Souradeep

Publications and source records attributed to Tarun Souradeep.

124 records · Page 7Linked to original sources

arXiv2001

Relic Gravity Waves from Braneworld Inflation

We discuss a scenario in which extra dimensional effects allow a scalar field with a steep potential to play the dual role of the inflaton as well as dark energy (quintessence). The post-inflationary evolution of the universe in this scenario is generically characterised by a `kinetic regime' during which the kinetic energy of the scalar field greatly exceeds its potential energy resulting in a `stiff' equation of state for scalar field matter $P_ϕ\simeq ρ_ϕ$. The kinetic regime precedes the radiation dominated epoch and introduces an important new feature into the spectrum of relic gravity waves created quantum mechanically during inflation. The gravity wave spectrum increases with wavenumber for wavelengths shorter than the comoving horizon scale at the commencement of the radiative regime. This `blue tilt' is a generic feature of models with steep potentials and imposes strong constraints on a class of inflationary braneworld models. Prospects for detection of the gravity wave background by terrestrial and space-borne gravity wave observatories such as LIGO II and LISA are discussed.

gr-qc↗

arXiv2001

Window Function for Non-Circular Beam CMB Anisotropy Experiment

We develop computationally rapid methods to compute the window function for a cosmic microwave background anisotropy experiment with a non-circular beam which scans over large angles on the sky. To concretely illustrate these methods we compute the window function for the Python V experiment which scans over large angles on the sky with an elliptical Gaussian beam.

astro-ph↗

arXiv2001

Binned Cosmic Microwave Background Anisotropy Power Spectra: Peak Location

We use weighted mean and median statistics techniques to combine individual cosmic microwave background (CMB) anisotropy detections and determine binned, multipole-space, CMB anisotropy power spectra. The resultant power spectra are peaked. The derived weighted-mean CMB anisotropy power spectrum is not a good representation of the individual measurements in a number of multipole-space bins, if the CMB anisotropy is Gaussian and correlations between individual measurements are small. This could mean that some observational error bars are underestimated, possibly as a consequence of undetected systematic effects. Discarding the most discrepant 5% of the measurements alleviates but does not completely resolve this problem. The median-statistics power spectrum of this culled data set is not as constraining as the weighted-mean power spectrum. Nevertheless it indicates that there is more power at multipoles $\ell \sim 150-250$ than is expected in an open cold dark matter (CDM) model, and it is more consistent with a flat CDM model. Unlike the weighted-mean power spectrum, the median-statistics power spectrum at $\ell \sim 400-500$ does not exclude a second peak in the flat CDM model.

astro-ph↗

arXiv2000

Tree structure of the percolating Universe

We present a numerical study of topological descriptors of initially Gaussian and scale-free density perturbations evolving via gravitational instability in an expanding universe. We carefully evaluate and avoid numerical contamination in making accurate measurements on simulated fields on a grid in a finite box. Independent of extent of non linearity, the measured Euler number of the excursion set at the percolation threshold, $δ_c$, is positive and nearly equal to the number of isolated components, suggesting that these structures are trees. Our study of critical point counts reconciles the clumpy appearance of the density field at $δ_c$ with measured filamentary local curvature. In the Gaussian limit, we measure $|δ_c|> σ$ in contrast to widely held belief that $|δ_c| \sim σ$, where $σ^2$ is the variance of the density field.

astro-ph↗

arXiv1999

CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions

CMB anisotropy measurements have brought the issue of global topology of the universe from the realm of theoretical possibility to within the grasp of observations. The global topology of the universe modifies the correlation properties of cosmic fields. In particular, strong correlations are predicted in CMB anisotropy patterns on the largest observable scales if the size of the Universe is comparable to the distance to the CMB last scattering surface. We describe in detail our completely general scheme using a regularized method of images for calculating such correlation functions in models with nontrivial topology, and apply it to the computationally challenging compact hyperbolic spaces. Our procedure directly sums over images within a specified radius, ideally many times the diameter of the space, effectively treats more distant images in a continuous approximation, and uses Cesaro resummation to further sharpen the results. At all levels of approximation the symmetries of the space are preserved in the correlation function. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. Although the eigenspectrum can be obtained by this method if desired, at a given level of approximation the correlation functions are more accurately determined. We use the 3-torus example to demonstrate that the method works very well. We apply it to power spectrum as well as correlation function evaluations in a number of compact hyperbolic (CH) spaces. Application to the computation of CMB anisotropy correlations on CH spaces, and the observational constraints following from them, are given in a companion paper.

astro-ph↗

arXiv1999

CMB Anisotropy in Compact Hyperbolic Universes II: COBE Maps and Limits

We calculate the CMB anisotropy in compact hyperbolic universe models using the regularized method of images described in paper-I, including the 'line-of-sight `integrated Sachs-Wolfe' effect, as well as the last-scattering surface terms. We calculate the Bayesian probabilities for a selection of models by confronting our theoretical pixel-pixel temperature correlation functions with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. This conclusion is qualitatively insensitive to the matter content of the universe, in particular, the presence of a cosmological constant. If the universe is of comparable size to the 'horizon', the likelihood function is very dependent upon orientation of the manifold wrt the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over those for the conventional infinite models. The full Bayesian analysis we use is the most complete statistical test that can be done on the COBE maps, taking into account all possible signals and their variances in the theoretical skies, in particular the high degree of anisotropic correlation that can exist. We show that standard visual measures for comparing theoretical predictions with the data such as the isotropized power spectrum $C_\ell$ are not so useful in small compact spaces because of enhanced cosmic variance associated with the breakdown of statistical isotropy.

astro-ph↗

arXiv1998

Computing CMB Anisotropy in Compact Hyperbolic Spaces

The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. For compact topologies, the two main effects on the CMB are: (1) the breaking of statistical isotropy in characteristic patterns determined by the photon geodesic structure of the manifold and (2) an infrared cutoff in the power spectrum of perturbations imposed by the finite spatial extent. We present a completely general scheme using the regularized method of images for calculating CMB anisotropy in models with nontrivial topology, and apply it to the computationally challenging compact hyperbolic topologies. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. We estimate a Bayesian probability for a selection of models by confronting the theoretical pixel-pixel temperature correlation function with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. If the universe is of comparable size, the likelihood function is very dependent upon orientation of the manifold wrt the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over the conventional infinite models.

astro-ph↗

arXiv1998

Probing Cosmic topology using CMB anisotropy

The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. We have developed a new method for calculating the CMB anisotropy in models with nontrivial topology and apply it to open universe models with compact spatial topology. We conduct a Bayesian probability analysis for a selection of models which confronts the theoretical pixel-pixel temperature correlation function with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations.

astro-ph↗

arXiv1998

Prospects for measuring Inflation parameters with the CMB

We present the status of our study into the feasibility of estimating the parameters of inflation from planned satellite observations of the anisotropy of the cosmic microwave background (CMB).We describe a perturbative procedure for studying inflation models with soft departures from scale free spectra and find that in this case the parameters of inflation are likely to be well determined. We also demonstrate that radical departures from scale free initial perturbations with broad features in $k$-space can be be measured by Planck. However, allowing for very fine features in $k$-space can very strongly compromise the ability to measure cosmological parameters.

astro-ph↗

arXiv1997

Skewness in the Cosmic Microwave Background Anisotropy from Inflationary Gravity Wave Background

In the context of inflationary scenarios, the observed large angle anisotropy of the Cosmic Microwave Background (CMB) temperature is believed to probe the primordial metric perturbations from inflation. Although the perturbations from inflation are expected to be gaussian random fields, there remains the possibility that nonlinear processes at later epochs induce ``secondary'' non-gaussian features in the corresponding CMB anisotropy maps. The non-gaussianity induced by nonlinear gravitational instability of scalar (density) perturbations has been investigated in existing literature. In this paper, we highlight another source of non-gaussianity arising out of higher order scattering of CMB photons off the metric perturbations. We provide a simple and elegant formalism for deriving the CMB temperature fluctuations arising due to the Sachs-Wolfe effect beyond the linear order. In particular, we derive the expression for the second order CMB temperature fluctuations. The multiple scattering effect pointed out in this paper leads to the possibility that tensor metric perturbation, i.e., gravity waves (GW) which do not exhibit gravitational instability can still contribute to the skewness in the CMB anisotropy maps. We find that in a flat $Ω=1$ universe, the skewness in CMB contributed by gravity waves via multiple scattering effect is comparable to that from the gravitational instability of scalar perturbations for equal contribution of the gravity waves and scalar perturbations to the total rms CMB anisotropy. The secondary skewness is found to be smaller than the cosmic variance leading to the conclusion that inflationary scenarios do predict that the observed CMB anisotropy should be statistically consistent with a gaussian random distribution.

astro-ph↗

arXiv1997

Constraints on Compact Hyperbolic Spaces from COBE

The (large angle) COBE DMR data can be used to probe the global topology of our universe on scales comparable to and just beyond the present ``horizon''. For compact topologies, the two main effects on the CMB are: [1] the breaking of statistical isotropy in characteristic patterns determined by the photon geodesic structure of the manifold and [2] an infrared cutoff in the power spectrum of perturbations imposed by the finite spatial extent. To make a detailed confrontation of these effects with the COBE maps requires the computation of the pixel-pixel temperature correlation function for each topology and for each orientation of it relative to the sky. We present a general technique using the method of images for doing this in compact hyperbolic (CH) topologies which does not require spatial eigenmode decomposition. We demonstrate that strong constraints on compactness follow from [2] and that these limits can be improved by exploiting the details of the geodesic structure for each individual topology ([1]), as we show for the flat 3-torus and selected CH models.

astro-ph↗

arXiv1995

Skewness of Cosmic Microwave Background Temperature Fluctuations Due to Non-linear Gravitational Instability

Skewness of temperature fluctuations of the cosmic microwave background (CMB) produced by initially Gaussian adiabatic perturbations with the flat (Harrison-Zeldovich) spectrum, which arises due to non-linear corrections to a gravitational potential at the matter-dominated stage, is calculated quantitatively. For the standard CDM model, the effect appears to be smaller than expected previously and lies below the cosmic variance limit even for small angles. The sign of the skewness is opposite to that of the skewness of density perturbations.

astro-ph↗

arXiv1993

Post-COBE predictions for Inflationary Gravity Wave and Density Perturbation spectra

We assess the relative contribution to the COBE - measured microwave anisotropy arising both from relic gravity waves as well as primordial density perturbations originating during inflation. We show that the gravity wave contribution to the CMBR anisotropy depends sensitively upon $n$ -- the primordial spectral index ($\dk^2 \propto k^n$), increasing as $n$ deviates from a Harrison - Zeldovich spectrum (n = 1). As a result, for $n < 0.84$ the contribution from gravity waves towards $δT/ T $ is greater than the corresponding contribution from density perturbations, whereas for $n > 0.84$ the reverse is true. ($ n = 0.84$ corresponds to an expansion index $p = 13.5$ in models with power-law inflation $a \propto t^p$. ) Our results show that for a scale-invariant Harrison-Zeldovich spectrum generated by chaotic inflation, gravity waves contribute approximately $24\%$ to the CMBR anisotropy measured by COBE. Applying our results to the cold dark matter scenario for galaxy formation, we find that in general CDM models with tilted power spectra ($n < 1$), require the biasing parameter to be greater than unity, on scales of $16h_{50}^{-1} Mpc$. We also obtain an expression for the COBE - normalised amplitude and spectrum of the stochastic gravity wave background and compare it with the sensitivity of planned laser-interferometer gravity wave detectors.

hep-ph↗

arXiv1992

Generation of seed perturbations from Quantum Cosmology

The origin of seed perturbations in the Universe is studied within the framework of a specific minisuperspace model. It is shown that the `creation' of the Universe as a result of a quantum transition from a flat empty spacetime would lead to a flat FLRW (Friedmann Lema\^ıtre Robertson-Walker) Universe with weak inhomogeneous perturbations at large wavelengths. The power spectrum of these perturbations is found to be scale invariant at horizon crossing (i.e., the Harrison-Zeldovich spectrum). It is also recognised that the seed perturbations generated in our model would be generically of the isocurvature kind.

gr-qc↗

arXiv1992

Quantum effects near a point mass in 2+1 dimensional gravity

We investigate the behaviour of classical and quantum fields in the conical space-time associated with a point mass in 2+1 dimensions. We show that the presence of conical boundary conditions alters the electrostatic field of a point charge leading to the presence of a finite self-force on the charge from the direction of the point mass exactly as if the point mass itself were charged. The conical space-time geometry also affects the zero point fluctuations of a quantum scalar field leading to the existence of a vacuum polarisation --- $\langle T_\mn \rangle$, in the 2+1 dimensional analog of the Schwarzschild metric. The resulting linearised semi-classical Einstein equations --- $G_\mn = 8 πG \langle T_\mn \rangle$, possess a well defined Newtonian limit, in marked contrast to the classical case for which no Newtonian limit is known to exist. An elegant reformulation of our results in terms of the method of images is also presented. Our analysis also covers the non-static de Sitter--Schwarzschild metric in 2+1 dimensions, in which in addition to the vacuum polarisation, a non-zero vacuum flux ofenergy -- $\langle T_{rt} \rangle $ is also found to exist.As part of this analysis, we evaluate the scalar field propagator in an $n$-dimensional de Sitter space,

hep-ph↗

arXiv1992

Density Perturbations,Gravity Waves and the Cosmic Microwave Background

We asses the contribution to the observed large scale anisotropy of the cosmic microwave background radiation, arising from both gravity waves as well as adiabatic density perturbations, generated by a common inflationary mechanism in the early Universe. We find that for inflationary models predicting power law primordial spectra %$a(t) \propto t^p, p > 1$, $\dk^2 \propto k^n$, the relative contribution to the quadrupole anisotropy from gravity waves and scalar density perturbations, depends crucially upon $n$. For $n < 0.87$, gravity waves perturb the CMBR by a larger amount than density perturbations, whereas for $n > 0.87$ the reverse is true. %For nearly exponential inflation, on the other hand, the contribution to the %microwave anisotropy from scalar density perturbations always exceeds %that due to gravity waves. Normalising the amplitude of the density perturbation spectrum at large scales, using the observed value of the COBE quadrupole, we determine $(δM /M)_{16}$ -- the rms density contrast on scales $\sim 16 h_{50}^{-1}$ Mpc, for cosmological models with cold dark matter. We find that for $n < 0.75$, a large amount of biasing is required in order to reconcile theory with observations.

hep-ph↗