arXiv subjects

L. Sriramkumar

Publications and source records attributed to L. Sriramkumar.

At least 73 records · Page 4Linked to original sources

arXiv2009

An introduction to inflation and cosmological perturbation theory

This article provides an introductory review of inflation and cosmological perturbation theory. I begin by motivating the need for an epoch of inflation during the early stages of the radiation dominated era, and describe how inflation is typically achieved using scalar fields. Then, after an overview of linear cosmological perturbation theory, I derive the equations governing the perturbations, and outline the generation of the scalar and the tensor perturbations during inflation. I illustrate that slow roll inflation naturally leads to an almost scale invariant spectrum of perturbations, a prediction that seems to be in remarkable agreement with the measurements of the anisotropies of the cosmic microwave background. I describe the constraints from the recent observations on some of the more popular models of inflation. I conclude with a brief discussion on the status and certain prospects of the inflationary paradigm.

astro-ph.CO↗

arXiv2009

Path integral duality modified propagators in spacetimes with constant curvature

The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length, $\lp$, in a {\it locally Lorentz invariant manner}. We use this prescription to evaluate the duality modified propagators in spacetimes with {\it constant curvature} (exactly in the case of one spacetime, and in the Gaussian approximation for another two), and show that: (i) the modified propagators are ultra violet finite, (ii) the modifications are {\it non-perturbative} in $\lp$, and (iii) $\lp$ seems to behave like a `zero point length' of spacetime intervals such that $ł< σ^2(x,x')\r> = ł[σ^{2}(x,x')+ {\cal O}(1) \lp^2 \r]$, where $σ(x,x')$ is the geodesic distance between the two spacetime points $x$ and $x'$, and the angular brackets denote (a suitable) average over the quantum gravitational fluctuations. We briefly discuss the implications of our results.

hep-th↗

arXiv2008

Punctuated inflation and the low CMB multipoles

We investigate inflationary scenarios driven by a class of potentials which are similar in form to those that arise in certain minimal supersymmetric extensions of the standard model. We find that these potentials allow a brief period of departure from inflation sandwiched between two stages of slow roll inflation. We show that such a background behavior leads to a step like feature in the scalar power spectrum. We set the scales such that the drop in the power spectrum occurs at a length scale that corresponds to the Hubble radius today--a feature that seems necessary to explain the lower power observed in the quadrupole moment of the Cosmic Microwave Background (CMB) anisotropies. We perform a Markov Chain Monte Carlo analysis to determine the values of the model parameters that provide the best fit to the recent WMAP 5-year data for the CMB angular power spectrum. We find that an inflationary spectrum with a suppression of power at large scales that we obtain leads to a much better fit (with just one extra parameter, $χ_{\rm eff}^{2}$ improves by 6.62) of the observed data when compared to the best fit reference $Λ$CDM model with a featureless, power law, primordial spectrum.

astro-ph↗

arXiv2008

Sub-leading contributions to the black hole entropy in the brick wall approach

[Abridged] We compute the canonical entropy of a quantum scalar field around static and spherically symmetric black holes through the brick wall approach at the higher orders (in fact, up to the sixth order in \hbar) in the WKB approximation. We explicitly show that the brick wall model generally predicts corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. In four dimensions, we find that the corrections to the Bekenstein-Hawking entropy are of the form (A^n \log A), while, in six dimensions, the corrections behave as (A^m + A^n \log A), where A denotes the area of the black hole event horizon, and (m, n) < 1. We compare our results with the corrections to the Bekenstein-Hawking entropy that have been obtained through the other approaches in the literature, and discuss the implications.

gr-qc↗

arXiv2008

Quantum gravitational corrections to the stress-energy tensor around the rotating BTZ black hole

Modes emerging out of a collapsing black hole are red-shifted to such an extent that Hawking radiation at future null infinity consists of modes that have energies beyond the Planck scale at past null infinity. This indicates that physics at the Planck scale may modify the spectrum of Hawking radiation and the associated stress-energy tensor of the quantum field. Recently, it has been shown that, the T-duality symmetry of string fluctuations along compact extra dimensions leads to a modification of the standard propagator of point particles in quantum field theory. At low energies (when compared to the string scale), the modified propagator is found to behave as though the spacetime possesses a minimal length, say, $\lp$, which we shall assume to be of the order of the Planck length. We utilize the duality approach to evaluate the modified propagator around the rotating Banados-Teitelboim-Zanelli black hole and show that the propagator is finite in the coincident limit. We compute the stress-energy tensor associated with the modified Green's function and illustrate graphically that the quantum gravitational corrections turn out to be negligibly small. We conclude by briefly commenting on the results we have obtained.

hep-th↗

arXiv2007

On the evolution of tachyonic perturbations at super-Hubble scales

In the slow-roll inflationary scenario, the amplitude of the curvature perturbations approaches a constant value soon after the modes leave the Hubble radius. However, relatively recently, it was shown that the amplitude of the curvature perturbations induced by the canonical scalar field can grow at super-Hubble scales if there is either a transition to fast roll inflation or if inflation is interrupted for some period of time. In this work, we extend the earlier analysis to the case of a non-canonical scalar field described by the Dirac-Born-Infeld action. With the help of a specific example, we show that the amplitude of the tachyonic perturbations can be enhanced or suppressed at super-Hubble scales if there is a transition from slow roll to fast roll inflation. We also illustrate as to how the growth of the entropy perturbations during the fast roll regime proves to be responsible for the change in the amplitude of the curvature perturbations at super-Hubble scales. Furthermore, following the earlier analysis for the canonical scalar field, we show that the power spectrum evaluated in the long wavelength approximation matches the exact power spectrum obtained numerically very well. Finally, we briefly comment on an application of this phenomenon.

astro-ph↗

arXiv2007

Entropy of BTZ black strings in the brick wall approach

During the last few years, exact solutions that describe black holes that are bound to a two-brane in a four dimensional anti-de Sitter bulk have been constructed. In situations wherein there is a negative cosmological constant on the brane, for large masses, these solutions are exactly the rotating BTZ black holes on the brane and, in fact, describe rotating BTZ black strings in the bulk. We evaluate the canonical entropy of a free and massless scalar field (at the Hawking temperature) around the rotating BTZ black string using the brick wall model. We explicitly show that the Bekenstein-Hawking `area' law is satisfied both on the brane as well as in the bulk.

gr-qc↗

arXiv2006

Path integral duality and Planck scale corrections to the primordial spectrum in exponential inflation

The enormous red-shifting of the modes during the inflationary epoch suggests that physics at the Planck scale may modify the standard, nearly, scale-invariant, primordial, density perturbation spectrum. Under the principle of path-integral duality, the space-time behaves as though it has a minimal length $L_{_{\rm P}}$ (which we shall assume to be of the order of the Planck length), a feature that is expected to arise when the quantum gravitational effects on the matter fields have been taken into account. Using the method of path integral duality, in this work, we evaluate the Planck scale corrections to the spectrum of density perturbations in the case of exponential inflation. We find that the amplitude of the corrections is of the order of $({\cal H}/M_{_{\rm P}})$, where ${\cal H}$ and $M_{_{\rm P}}$ denote the inflationary and the Planck energy scales, respectively. We also find that the corrections turn out to be completely independent of scale. We briefly discuss the implications of our result, and also comment on how it compares with an earlier result.

hep-th↗

arXiv2004

Trans-Planckian corrections to the primordial spectrum in the infra-red and the ultra-violet

Due to the tremendous red-shift that occurs during the inflationary epoch in the early universe, it has been realized that trans-Planckian physics may manifest itself at energies much lower than the Planck energy. The presence of a fundamental scale suggests that local Lorentz invariance may be violated at sufficiently high energies. Motivated by this possibility, recently, different models that violate Lorentz invariance locally have been used to evaluate the trans-Planckian corrections to the inflationary density perturbation spectrum. However, certain astrophysical observations seem to indicate that local Lorentz invariance may be preserved to extremely high energies. In such a situation, to study the trans-Planckian effects, it becomes imperative to consider models that preserve local Lorentz invariance even as they contain a fundamental scale. In this work, we construct one such model and evaluate the resulting spectrum of density perturbations in the power-law inflationary scenario. While our model reproduces the standard spectrum on small scales, it naturally predicts a suppression of power on large scales. In fact, the spectrum we obtain has some features which are similar to the one that has recently been obtained from non-commutative inflation. However, we find that the amount of suppression predicted by our model is far less than that is required to fit the observations. We comment on the fact that, with a suitable choice of initial conditions, our approach can lead to corrections at the infra-red as well as at the ultra-violet ends of the spectrum.

hep-th↗

arXiv2004

Planck scale effects and the suppression of power on the large scales in the primordial spectrum

The enormous red-shifting of the modes during the inflationary epoch suggests that physics at the very high energy scales may modify the primordial perturbation spectrum. Therefore, the measurements of the anisotropies in the Cosmic Microwave Background (CMB) could provide us with clues to understanding physics beyond the Planck scale. In this proceeding, we study the Planck scale effects on the primordial spectrum in the power-law inflation using a model which preserves local Lorentz invariance. While our model reproduces the standard spectrum on small scales, it naturally predicts a suppression of power on the large scales -- a feature that seems to be necessary to explain deficit of power in the lower multipoles of the CMB.

hep-th↗

arXiv2004

Initial state of matter fields and trans-Planckian physics: Can CMB observations disentangle the two?

The standard, scale-invariant, inflationary perturbation spectrum will be modified if the effects of trans-Planckian physics are incorporated into the dynamics of the matter field in a phenomenological manner, say, by the modification of the dispersion relation. The spectrum also changes if we retain the standard dynamics but modify the initial quantum state of the matter field. We show that, given {\it any} spectrum of perturbations, it is possible to choose a class of initial quantum states which can exactly reproduce this spectrum with the standard dynamics. We provide an explicit construction of the quantum state which will produce the given spectrum. We find that the various modified spectra that have been recently obtained from `trans-Planckian considerations' can be constructed from suitable squeezed states above the Bunch-Davies vacuum in the standard theory. Hence, the CMB observations can, at most, be useful in determining the initial state of the matter field in the standard theory, but it can {\it not} help us to discriminate between the various Planck scale models of matter fields. We study the problem in the Schrodinger picture, clarify various conceptual issues and determine the criterion for negligible back reaction due to modified initial conditions.

gr-qc↗

arXiv2002

Interpolating between the Bose-Einstein and the Fermi-Dirac distributions in odd dimensions

We consider the response of a uniformly accelerated monopole detector that is coupled to a superposition of an odd and an even power of a quantized, massless scalar field in flat spacetime in arbitrary dimensions. We show that, when the field is assumed to be in the Minkowski vacuum, the response of the detector is characterized by a Bose-Einstein factor in even spacetime dimensions, whereas a Bose-Einstein as well as a Fermi-Dirac factor appear in the detector response when the dimension of spacetime is odd. Moreover, we find that, it is possible to interpolate between the Bose-Einstein and the Fermi-Dirac distributions in odd spacetime dimensions by suitably adjusting the relative strengths of the detector's coupling to the odd and the even powers of the scalar field. We point out that the response of the detector is always thermal and we, finally, close by stressing the apparent nature of the appearance of the Fermi-Dirac factor in the detector response.

gr-qc↗

arXiv2002

Odd statistics in odd dimensions for odd couplings

We consider the response of a uniformly accelerated monopole detector that is coupled non-linearly to the nth power of a quantum scalar field in (D+1)-dimensional flat spacetime. We show that, when (D+1) is even, the response of the detector in the Minkowski vacuum is characterized by a Bose-Einstein factor for all n. Whereas, when (D+1) is odd, we find that a Fermi-Dirac factor appears in the detector response when n is odd, but a Bose-Einstein factor arises when n is even. We emphasize the point that, since, along the accelerated trajectory, the Wightman function and, as a result, the (2n)-point function satisfy the Kubo-Martin-Schwinger condition (as required for a scalar field) in all dimensions, the appearance of a Fermi-Dirac factor (instead of the expected Bose-Einstein distribution) for odd (D+1) and n reflects a peculiar feature of the detector rather than imply a fundamental change in field theory.

gr-qc↗

arXiv2001

On the response of non-linearly coupled, accelerated detectors in odd-dimensional flat spacetimes

In this note, we consider the response of a uniformly accelerated monopole detector that is coupled non-linearly to the nth power of a quantum scalar field in (D+1)-dimensional flat spacetime. We show that, when (D+1) is even, the response of the detector in the Minkowski vacuum is characterized by a Bose-Einstein factor for all n. Whereas, when (D+1) is odd, we find that a Fermi-Dirac factor appears in the detector response when n is odd, but a Bose-Einstein factor arises when n is even.

gr-qc↗

arXiv2001

Probes of the vacuum structure of quantum fields in classical backgrounds

We compare the different approaches presently available in literature to probe the vacuum structure of quantum fields in classical electromagnetic and gravitational backgrounds. We compare the results from the Bogolubov transformations and the effective Lagrangian approach with the response of monopole detectors (of the Unruh-DeWitt type) in non-inertial frames in flat spacetime and in inertial frames in different types of classical electromagnetic backgrounds. We also carry out such a comparison in inertial and rotating frames when boundaries are present in flat spacetime. We find that the results from these different approaches do not, in general, agree with each other. We attempt to identify the origin of these differences and then go on to discuss its implications for classical gravitational backgrounds.

gr-qc↗

arXiv2000

Fluctuations in the current and energy densities around a magnetic flux carrying cosmic string

We calculate the fluctuations in the current and energy densities for the case of a quantized, minimally coupled, massless, complex scalar field around a straight and infinitesimally thin cosmic string carrying magnetic flux. At zero temperature, we evaluate the fluctuations in the current and energy densities for arbitrary flux and deficit angle. At a finite temperature, we evaluate the fluctuations in the energy density for the special case wherein the flux is absent and the deficit angle equals $π$. We find that, quite generically, the dimensionless ratio of the variance to the mean-squared values of the current and energy densities are of order unity which suggests that the fluctuations around cosmic strings can be considered to be large.

gr-qc↗

arXiv1999

Will small particles exhibit Brownian motion in the quantum vacuum?

The Brownian motion of small particles interacting with a field at a finite temperature is a well-known and well-understood phenomenon. At zero temperature, even though the thermal fluctuations are absent, quantum fields still possess vacuum fluctuations. It is then interesting to ask whether a small particle that is interacting with a quantum field will exhibit Brownian motion when the quantum field is assumed to be in the vacuum state. In this paper, we study the cases of a small charge and an imperfect mirror interacting with a quantum scalar field in (1+1) dimensions. Treating the quantum field as a classical stochastic variable, we write down a Langevin equation for the particles. We show that the results we obtain from such an approach agree with the results obtained from the fluctuation-dissipation theorem. Unlike the finite temperature case, there exists no special frame of reference at zero temperature and hence it is essential that the particles do not break Lorentz invariance. We find that that the scalar charge breaks Lorentz invariance, whereas the imperfect mirror does not. We conclude that small particles such as the imperfect mirror {\it will} exhibit Brownian motion even in the quantum vacuum, but this effect can be so small that it may prove to be difficult to observe it experimentally.

quant-ph↗

arXiv1999

On the response of detectors in classical electromagnetic backgrounds

I study the response of a detector that is coupled non-linearly to a quantized complex scalar field in different types of classical electromagnetic backgrounds. Assuming that the quantum field is in the vacuum state, I show that, when in {\it inertial} motion, the detector responds {\it only} when the electromagnetic background produces particles. However, I find that the response of the detector is {\it not} proportional to the number of particles produced by the background.

hep-th↗