arXiv subjects

Sourav Bhattacharya

Publications and source records attributed to Sourav Bhattacharya.

At least 73 records · Page 4Linked to original sources

arXiv2019

Emergent $α$-like fermionic vacuum structure and entanglement in the hyperbolic de Sitter spacetime

We report a non-trivial feature of the vacuum structure of free massive or massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two causally disconnected regions, say $R$ and $L$ separated by another region, $C$. We are interested in the field theory in $R\cup L$ to understand the long range quantum correlations between $R$ and $L$. There are local modes of the Dirac field having supports individually either in $R$ or $L$, as well as global modes found via analytically continuing the $R$ modes to $L$ and vice versa. However, we show that unlike the case of a scalar field, the analytic continuation does not preserve the orthogonality of the resulting global modes. Accordingly, we need to orthonormalise them following the Gram-Schmidt prescription, prior to the field quantisation in order to preserve the canonical anti-commutation relations. We observe that this prescription naturally incorporates a spacetime independent continuous parameter, $θ_{\rm RL}$, into the picture. Thus interestingly, we obtain a naturally emerging one-parameter family of $α$-like de Sitter vacua. The values of $θ_{\rm RL}$ yielding the usual thermal spectra of massless created particles are pointed out. Next, using these vacua, we investigate both entanglement and Rényi entropies of either of the regions and demonstrate their dependence on $θ_{\rm RL}$.

hep-th↗

arXiv2019

MobiSR: Efficient On-Device Super-Resolution through Heterogeneous Mobile Processors

In recent years, convolutional networks have demonstrated unprecedented performance in the image restoration task of super-resolution (SR). SR entails the upscaling of a single low-resolution image in order to meet application-specific image quality demands and plays a key role in mobile devices. To comply with privacy regulations and reduce the overhead of cloud computing, executing SR models locally on-device constitutes a key alternative approach. Nevertheless, the excessive compute and memory requirements of SR workloads pose a challenge in mapping SR networks on resource-constrained mobile platforms. This work presents MobiSR, a novel framework for performing efficient super-resolution on-device. Given a target mobile platform, the proposed framework considers popular model compression techniques and traverses the design space to reach the highest performing trade-off between image quality and processing speed. At run time, a novel scheduler dispatches incoming image patches to the appropriate model-engine pair based on the patch's estimated upscaling difficulty in order to meet the required image quality with minimum processing latency. Quantitative evaluation shows that the proposed framework yields on-device SR designs that achieve an average speedup of 2.13x over highly-optimized parallel difficulty-unaware mappings and 4.79x over highly-optimized single compute engine implementations.

cs.CV↗

arXiv2019

Over-rotation intervals of bimodal interval maps

We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given bimodal map is. We then define a new class of polymodal interval maps called well behaved, and generalize the above results onto well behaved maps.

math.DS↗

arXiv2018

Particle creation by de Sitter black holes revisited

Creation of thermal distribution of particles by a black hole is independent of the detail of gravitational collapse, making the construction of the eternal horizons suffice to address the problem in asymptotically flat spacetimes. For eternal de Sitter black holes however, earlier studies have shown the existence of both thermal and non-thermal particle creation, originating from the non-trivial causal structure of these spacetimes. Keeping this in mind we consider this problem in the context of a quasistationary gravitational collapse occurring in a $(3+1)$-dimensional eternal de Sitter, settling down to a Schwarzschild- or Kerr-de Sitter spacetime and consider a massless minimally coupled scalar field. There is a unique choice of physically meaningful `in' vacuum here, defined with respect to the positive frequency cosmological Kruskal modes localised on the past cosmological horizon ${\cal C^-}$, at the onset of the collapse. We define our `out' vacuum at a fixed radial coordinate `close' to the future cosmological horizon, ${\cal C^+}$, with respect to positive frequency outgoing modes written in terms of the ordinary retarded null coordinate, $u$. We trace such modes back to ${\cal C^-}$ along past directed null geodesics through the collapsing body. Some part of the wave will be reflected back without entering it due to the greybody effect. We show that these two kind of traced back modes yield the two temperature spectra and fluxes subject to the aforementioned `in' vacuum. Since the coordinate $u$ used in the `out' modes is not well defined on a horizon, estimate on how `close' we might be to ${\cal C^+}$ is given by estimating backreaction. We argue no other reasonable choice of the `out' vacuum would give rise to any thermal spectra. Our conclusions remain valid for all non-Nariai class black holes, irrespective of the relative sizes of the two horizons.

gr-qc↗

arXiv2018

Comments on the entropic gravity proposal

Explicit tests are presented of the conjectured entropic origin of the gravitational force. The gravitational force on a test particle in the vicinity of the horizon of a large Schwarzschild black hole in arbitrary spacetime dimensions is obtained as entropic force. The same conclusion can be reached for the cases of a large electrically charged black hole and a large slowly rotating Kerr black hole. The generalization along the same lines to a test mass in the field of an arbitrary spherical star is also studied and found not to be possible. Our results thus reinforce the argument that the entropic gravity proposal cannot account for the gravitational force in generic situations.

gr-qc↗

arXiv2018

Cosmological screening and the phantom braneworld model

The scalar and vector cosmological perturbations at all length scales of our Universe are studied in the framework of the phantom braneworld model. The model is characterized by the parameter $Ω_M\equiv M^3/2m^2H_0$, with $M$ and $m$ the 5- and 4-dimensional Planck scales, respectively, and $H_0$ the Hubble parameter today, while $Ω_M\rightarrow 0$ recovers the $Λ\rm CDM$ model. Ignoring the backreaction due to the peculiar velocities and also the bulk cosmological constant, allows the explicit computation of the gravitational potentials, $Φ$ and $Ψ$. They exhibit exponentially decreasing screening behaviour characterized by a screening length which is a function of the quasidensity parameter $ Ω_M$.

gr-qc↗

arXiv2018

Kerr-de Sitter spacetime, Penrose process and the generalized area theorem

We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, $Λ$, always reduces the efficiency of this process. The Kerr-de Sitter spacetime has two ergospheres -- associated with the black hole and the cosmological event horizons. We prove by analysing turning points of the trajectory that the Penrose process in the cosmological ergoregion is never possible. We next show that in this process both black hole and cosmological event horizons' areas increase, the later becomes possible when the particle coming from the black hole ergoregion escapes through the cosmological event horizon. We identify a new, local mass function instead of the mass parameter, to prove this generalized area theorem. This mass function takes care of the local spacetime energy due to the cosmological constant as well, including that arises due to the frame dragging effect due to spacetime rotation. While the current observed value of $Λ$ is much tiny, its effect in this process could be considerable in the early universe scenario endowed with a rather high value of it, where the two horizons could have comparable sizes. In particular, the various results we obtain here are also evaluated in a triply degenerate limit of the Kerr-de Sitter spacetime we find, in which radial values of the inner, the black hole and the cosmological event horizons are nearly coincident.

gr-qc↗

arXiv2018

Light bending, static dark energy and related uniqueness of Schwarzschild-de Sitter spacetime

Since the Schwarzschild-de Sitter spacetime is static inside the cosmological event horizon, if the dark energy state parameter is sufficiently close to $-1$, apparently one could still expect an effectively static geometry, in the attraction dominated region inside the maximum turn around radius, $R_{\rm TA, max}$, of a cosmic structure. We take the first order metric derived recently assuming a static and ideal dark energy fluid with equation of state $P(r)=αρ(r)$ as a source in Ref. [1], which reproduced the expression for $R_{\rm TA, max}$ found earlier in the cosmological McVittie spacetime. Here we show that the equality originates from the equivalence of geodesic motion in these two backgrounds, in the non-relativistic regime. We extend this metric up to the third order and compute the bending of light using the Rindler-Ishak method. For $ α\neq -1$, a dark energy dependent term appears in the bending equation, unlike the case of the cosmological constant, $α=-1$. Due to this new term in particular, existing data for the light bending at galactic scales yields, $(1+α)\lesssim {\cal O}(10^{-14})$, thereby practically ruling out any such static and inhomogeneous dark energy fluid we started with. Implication of this result pertaining the uniqueness of the Schwarzschild-de Sitter spacetime in such inhomogeneous dark energy background is discussed.

gr-qc↗

arXiv2017

Cross-modal Recurrent Models for Weight Objective Prediction from Multimodal Time-series Data

We analyse multimodal time-series data corresponding to weight, sleep and steps measurements. We focus on predicting whether a user will successfully achieve his/her weight objective. For this, we design several deep long short-term memory (LSTM) architectures, including a novel cross-modal LSTM (X-LSTM), and demonstrate their superiority over baseline approaches. The X-LSTM improves parameter efficiency by processing each modality separately and allowing for information flow between them by way of recurrent cross-connections. We present a general hyperparameter optimisation technique for X-LSTMs, which allows us to significantly improve on the LSTM and a prior state-of-the-art cross-modal approach, using a comparable number of parameters. Finally, we visualise the model's predictions, revealing implications about latent variables in this task.

stat.ML↗

arXiv2017

Constraining phantom braneworld model from cosmic structure sizes

We consider the phantom braneworld model in the context of the maximum turn around radius, $R_{\rm TA,max}$, of a stable, spherical cosmic structure with a given mass. The maximum turn around radius is the point where the attraction due to the central inhomogeneity gets balanced with the repulsion of the ambient dark energy, beyond which a structure cannot hold any mass, thereby giving the maximum upper bound on the size of a stable structure. In this work we derive an analytical expression of $R_{\rm TA,max}$ for this model using cosmological scalar perturbation theory. Using this we numerically constrain the parameter space, including a bulk cosmological constant and the Weyl fluid, from the mass versus observed size data for some nearby, non-virial cosmic structures. We use different values of the matter density parameter $Ω_m$, both larger and smaller than that of the $Λ{\rm CDM}$, as the input in our analysis. We show in particular, that a) with a vanishing bulk cosmological constant the predicted upper bound is always greater than what is actually observed; similar conclusion holds if the bulk cosmological constant is negative b) if it is positive, the predicted maximum size can go considerably below than what is actually observed and owing to the involved nature of the field equations, it leads to interesting constraints on not only the bulk cosmological constant itself but on the whole parameter space of the theory.

gr-qc↗

arXiv2017

Entropy of a box of gas in an external gravitational field $-$ revisited

Earlier it was shown that the entropy of an ideal gas, contained in a box and moving in a gravitational field, develops an area dependence when it approaches the horizon of a static, spherically symmetric spacetime. Here we extend the above result in two directions; viz., to (a) the stationary axisymmteric spacetimes and (b) time dependent cosmological spacetimes evolving asymptotically to the de Sitter or the Schwarzschild de Sitter spacetimes. While our calculations are exact for the stationary axisymmetric spacetimes, for the cosmological case we present an analytical expression of the entropy when the spacetime is close to the de Sitter or the Schwarzschild de Sitter spacetime. Unlike the static spacetimes, there is no hypersurface orthogonal timelike Killing vector field in these cases. Nevertheless, the results hold and the entropy develops an area dependence in the appropriate limit.

gr-qc↗

arXiv2017

Cosmic structure sizes in generic dark energy models

The maximum allowable size of a spherical cosmic structure as a function of its mass is determined by the maximum turn around radius $R_{\rm TA,max}$, the distance from its centre where the attraction on a radial test particle due to the spherical mass is balanced with the repulsion due to the ambient dark energy. In this work, we extend the existing results in several directions. (a) We first show that for $w\neq -1$, the expression for $R_{\rm TA, max}$ found earlier using the cosmological perturbation theory, can be derived using a static geometry as well. (b) In the generic dark energy model with arbitrary time dependent state parameter $w(t)$, taking into account the effect of inhomogeneities upon the dark energy as well, where it is shown that the data constrain $w(t={\rm today})>-2.3$, and (c) in the quintessence and the generalized Chaplygin gas models, both of which are shown to predict structure sizes consistent with observations.

gr-qc↗

arXiv2017

The maximum sizes of large scale structures in alternative theories of gravity

The maximum size of a cosmic structure is given by the maximum turnaround radius -- the scale where the attraction due to its mass is balanced by the repulsion due to dark energy. We derive generic formulae for the estimation of the maximum turnaround radius in any theory of gravity obeying the Einstein equivalence principle, in two situations: on a spherically symmetric spacetime and on a perturbed Friedman-Robertson-Walker spacetime. We show that the two formulae agree. As an application of our formula, we calculate the maximum turnaround radius in the case of the Brans-Dicke theory of gravity. We find that for this theory, such maximum sizes always lie above the \LCDM value, by a factor $1 + \frac{1}{3ω}$, where $ω\gg 1$ is the Brans-Dicke parameter, implying consistency of the theory with current data.

astro-ph.CO↗

arXiv2017

Constraining some Horndeski gravity theories

We discuss two spherically symmetric solutions admitted by the Horndeski (or scalar tensor) theory in the context of solar system and astrophysical scenarios. One of these solutions is derived for Einstein-Gauss-Bonnet gravity, while the other originates from the coupling of the Gauss-Bonnet invariant with a scalar field. Specifically, we discuss the perihelion precession and the bending angle of light for these two different spherically symmetric spacetimes derived in references \cite{Maeda:2006hj} and \cite{Sotiriou:2014pfa} respectively. The later in particular, applies only to the black hole spacetimes. We further delineate on the numerical bounds of relevant parameters of these theories from such computations.

gr-qc↗

arXiv2016

Entropy of a generic null surface from its associated Virasoro algebra

Null surfaces act as one-way membranes, blocking information from those observers who do not cross them (e.g., in the black hole and the Rindler spacetimes) and these observers associate an entropy (and temperature) with the null surface. The black hole entropy can be computed from the central charge of an appropriately defined, local, Virasoro algebra on the horizon. We show that one can extend these ideas to a general class of null surfaces, all of which possess a Virasoro algebra and a central charge, leading to an entropy density (i.e., per unit area) which is just $(1/4)$. All the previously known results of associating entropy with horizons arise as special cases of this very general property of null surfaces demonstrated here and we believe this work represents the derivation of the entropy-area law in the most general context. The implications are discussed.

gr-qc↗

arXiv2016

Perturbation of mass accretion rate, associated acoustic geometry and stability analysis

We investigate the stability of stationary integral solutions of an ideal irrotational fluid in a general static and spherically symmetric background, by studying the profile of the perturbation of the mass accretion rate. We consider low angular momentum axisymmetric accretion flows for three different accretion disk models and consider time dependent and radial linear perturbation of the mass accretion rate. First we show that the propagation of such perturbation can be determined by an effective $2\times2$ matrix, which has qualitatively similar acoustic causal properties as one obtains via the perturbation of the velocity potential. Next, using this matrix we analytically address the stability issues, for both standing and travelling wave configurations generated by the perturbation. Finally, based on this general formalism we briefly discuss the explicit example of the Schwarzschild spacetime and compare our results of stability with the existing literature, which instead address this problem via the perturbation of the velocity potential.

astro-ph.HE↗

arXiv2016

Rotating Killing horizons in generic $F(R)$ gravity theories

We discuss various properties of rotating Killing horizons in generic $F(R)$ theories of gravity in dimension four for spacetimes endowed with two commuting Killing vector fields. Assuming there is no curvature singularity anywhere on or outside the horizon, we construct a suitable $(3+1)$-foliation. We show that similar to Einstein's gravity, we must have $T_{ab}k^ak^b=0$ on the Killing horizon, where $k^a$ is a null geodesic tangent to the horizon. For axisymmetric spacetimes, the effective gravitational coupling $\sim\,F'^{-1}(R)$ should usually depend upon the polar coordinate and hence need not necessarily be a constant on the Killing horizon. We prove that the surface gravity of such a Killing horizon must be a constant, irrespective of whether $F'(R)$ is a constant there or not. We next apply these results to investigate some further basic features. In particular, we show that any hairy solution for the real massive vector field in such theories is clearly ruled out, as long as the potential of the scalar field generated in the corresponding Einstein's frame is a positive definite quantity.

gr-qc↗

arXiv2016

Large scale structures and the cubic galileon model

The maximum size of a bound cosmic structure is computed perturbatively as a function of its mass in the framework of the cubic galileon, proposed recently to model the dark energy of our Universe. Comparison of our results with observations constrains the matter-galileon coupling of the model to $0.033\lesssim α\lesssim 0.17$, thus improving previous bounds based solely on solar system physics.

gr-qc↗