arXiv subjects

V. Sreenath

Publications and source records attributed to V. Sreenath.

23 records · Page 2Linked to original sources

arXiv2015

The tensor bi-spectrum in a matter bounce

Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of tensor perturbations just as de Sitter inflation does. In this work, we examine if the tensor bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the tensor bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter $h_{_{\rm NL}}$ that characterizes the amplitude of the tensor bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the tensor perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the tensor bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the tensor perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce. We discuss the implications of the results.

astro-ph.CO↗

arXiv2015

On the scalar consistency relation away from slow roll

As is well known, the non-Gaussianity parameter $f_{_{\rm NL}}$, which is often used to characterize the amplitude of the scalar bi-spectrum, can be expressed completely in terms of the scalar spectral index $n_{\rm s}$ in the squeezed limit, a relation that is referred to as the consistency condition. This relation, while it is largely discussed in the context of slow roll inflation, is actually expected to hold in any single field model of inflation, irrespective of the dynamics of the underlying model, provided inflation occurs on the attractor at late times. In this work, we explicitly examine the validity of the consistency relation, analytically as well as numerically, away from slow roll. Analytically, we first arrive at the relation in the simple case of power law inflation. We also consider the non-trivial example of the Starobinsky model involving a linear potential with a sudden change in its slope (which leads to a brief period of fast roll), and establish the condition completely analytically. We then numerically examine the validity of the consistency relation in three inflationary models that lead to the following features in the scalar power spectrum due to departures from slow roll: (i) a sharp cut off at large scales, (ii) a burst of oscillations over an intermediate range of scales, and (iii) small, but repeated, modulations extending over a wide range of scales. It is important to note that it is exactly such spectra that have been found to lead to an improved fit to the CMB data, when compared to the more standard power law primordial spectra, by the Planck team. We evaluate the scalar bi-spectrum for an arbitrary triangular configuration of the wavenumbers in these inflationary models and explicitly illustrate that, in the squeezed limit, the consistency condition is indeed satisfied even in situations consisting of strong deviations from slow roll.

astro-ph.CO↗

arXiv2014

Examining the consistency relations describing the three-point functions involving tensors

It is well known that the non-Gaussianity parameter $f_{_{\rm NL}}$ characterizing the scalar bi-spectrum can be expressed in terms of the scalar spectral index in the squeezed limit, a property that is referred to as the consistency relation. In this work, we consider the consistency relations associated with the three-point cross-correlations involving scalars and tensors as well as the tensor bi-spectrum in inflationary models driven by a single, canonical, scalar field. Characterizing the cross-correlations in terms of the dimensionless non-Gaussianity parameters $C_{_{\rm NL}}^{\mathcal R}$ and $C_{_{\rm NL}}^{\mathcal γ}$ that we had introduced earlier, we express the consistency relations governing the cross-correlations as relations between these non-Gaussianity parameters and the scalar or tensor spectral indices, in a fashion similar to that of the purely scalar case. We also discuss the corresponding relation for the non-Gaussianity parameter $h_{_{\rm NL}}$ used to describe the tensor bi-spectrum. We analytically establish these consistency relations explicitly in the following two situations: a simple example involving a specific case of power law inflation and a non-trivial scenario in the so-called Starobinsky model that is governed by a linear potential with a sharp change in its slope. We also numerically verify the consistency relations in three types of inflationary models that permit deviations from slow roll and lead to scalar power spectra with features which typically result in an improved fit to the data than the more conventional, nearly scale invariant, spectra. We close with a summary of the results we have obtained. (Abridged)

astro-ph.CO↗

arXiv2013

Numerical evaluation of the three-point scalar-tensor cross-correlations and the tensor bi-spectrum

Utilizing the Maldacena formalism and extending the earlier efforts to compute the scalar bi-spectrum, we construct a numerical procedure to evaluate the three-point scalar-tensor cross-correlations as well as the tensor bi-spectrum in single field inflationary models involving the canonical scalar field. We illustrate the accuracy of the adopted procedure by comparing the numerical results with the analytical results that can be obtained in the simpler cases of power law and slow roll inflation. We also carry out such a comparison in the case of the Starobinsky model described by a linear potential with a sudden change in the slope, which provides a non-trivial and interesting (but, nevertheless, analytically tractable) scenario involving a brief period of deviation from slow roll. We then utilize the code we have developed to evaluate the three-point correlation functions of interest (and the corresponding non-Gaussianity parameters that we introduce) for an arbitrary triangular configuration of the wavenumbers in three different classes of inflationary models which lead to features in the scalar power spectrum, as have been recently considered by the Planck team. We also discuss the contributions to the three-point functions during preheating in inflationary models with a quadratic minimum. We conclude with a summary of the main results we have obtained.

astro-ph.CO↗

arXiv2011

Localised zero-energy modes in the Kitaev model with vacancy-disorder

We study the effects of vacancy disorder on the Kitaev model defined on a hexagonal lattice. We show that the vacancy disorder induces a zero-mode that is localized at the defect site. We derive analytical forms for these localized wave functions in both the gapped and gapless phases of the Kitaev model. We conjecture that the vacancy disorder can be utilized as a probe of the quantum phase transition (from the gapped to gapless phases) in this model. The behavior of the Inverse Participation Ratio (IPR) in the gapless phase and across the transition is also studied numerically. Comments are made about the behavior of site-site entanglement in the single particle states for the case of a single vacancy.

cond-mat.str-el↗