Searcharxiv⌕ Search

arXiv subjects

Sayantan Choudhury

Publications and source records attributed to Sayantan Choudhury.

At least 55 records · Page 3Linked to original sources
arXiv2024

Single field inflation in the light of Pulsar Timing Array Data: Quintessential interpretation of blue tilted tensor spectrum through Non-Bunch Davies initial condition

In this work, we present a quintessential interpretation of having a blue-tilted tensor power spectrum for canonical single-field slow-roll inflation to explain the recently observed Pulsar Timing Array (NANOGrav 15-year and EPTA) signal of Gravitational Waves (GW). We formulate the complete semi-classical description of cosmological perturbation theory in terms of scalar and tensor modes using the Non-Bunch Davies initial condition. We found that the existence of the blue tilt ($n_t$) within the favoured range $1.2<n_t<2.5$ can be explained in terms of a newly derived consistency relation. Further, we compute a new field excursion formula using the Non-Bunch Davies initial condition, that validates the requirement of Effective Field Theory in the sub-Planckian regime, $|Δϕ|\ll M_{\rm pl}$ for the allowed value of the tensor-to-scalar ratio, $r<0.06$ from CMB observations. In our study, we refer to this result as Anti Lyth bound as it violates the well-known Lyth bound originally derived for Bunch Davies initial condition. Further, we study the behaviour of the spectral density of GW and the associated abundance with the frequency, which shows that within the frequency domain $10^{-9}{\rm Hz}<f<10^{-7}{\rm Hz}$ the outcome obtained from our analysis is completely consistent with the Pulsar Timing Array (NANOGrav 15-year and EPTA) signal. Also, we found that the behaviour of GW spectra satisfies the CMB constraints at the low frequency, $f_*\sim 7.7\times 10^{-17}{\rm Hz}$ corresponding to the pivots scale wave number, $k_*\sim 0.05{\rm Mpc}^{-1}$. Finally, the sharp falling behaviour of the GW spectra within the frequency domain $10^{-7}{\rm Hz}<f<1{\rm Hz}$ validates our theory in the comparatively high-frequency regime as well.

astro-ph.CO↗
arXiv2024

Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum

In this work, we study the signatures of quantum entanglement by computing entanglement negativity between two causally unrelated regions in $3+1$ dimensional global de Sitter space. We investigate a bipartite quantum field theoretic setup for this purpose, driven by an axionic Bell pair resulting from Type IIB string compactification on a Calabi-Yau three fold. We take into account a spherical surface that divides the spatial slice of the global de Sitter space into exterior and interior causally unrelated sub regions. For the computational purpose we use the simplest possible initial choice of quantum vacuum, which is Bunch-Davies state. The quantitative quantum information theoretic measure for entanglement negativity turns out be consistent with the results obtained for entanglement entropy, even we have to say it is better than that from quantum information theoretic point of view. We design the problem in a hyperbolic open chart where one of the causally unrelated observers remains constrained and the scale dependence enters to the corresponding quantum information theoretic entanglement measure for axionic Bell pair.We find from our analysis that in the large scales initially maximally entangled Bunch-Davies state turns out to be strongly entangled or weakly entangled depending on the axionic decay constant and the supersymmetry breaking scale. We also find that at the small scales the initial entanglement can be perfectly recovered.We also discuss the possibility of having a biverse picture, which is a mini version of the multiverse in the present theoretical set up. Last but not the least, we provide the necessary criteria for generating non vanishing quantum entanglement measures within the framework of quantum field theory of global de Sitter space as well as well as in primordial cosmology due to the axion derived from string theory.

hep-th↗
arXiv2023

Primordial non-Gaussianity from ultra slow-roll Galileon inflation

We present a detailed study of the generation of large primordial non-Gaussianities during the slow-roll (SR) to ultra-slow roll (USR) transitions in the framework of Galileon inflation. We found out that due to having sharp transitions in the USR phase, which persist with a duration of $Δ{\it N}_{\rm USR} \sim 2$ e-folds, we are able to generate the non-Gaussianity amplitude of the order: $|f_{\rm NL}| \sim {\it O}(10^{-2})$ in the SRI, $-5 < f_{\rm NL} < 5$ in the USR, and $-2 < f_{\rm NL} < 2$ in the SRII phases. As a result, we are able to achieve a cumulative average value of $|f_{\rm NL}| \sim {\it O}(1)$. This implies that our results strictly satisfy Maldacena's no-go theorem in the squeezed limit only for SRI, while they strictly violate the same condition in both the USR and SRII phases. The non-renormalization theorem in the Galileon theory helps to support our results regarding the generation of large mass primordial black holes along with large non-Gaussianities, which we show to be dependent on the specific positions of the transition wave numbers fixed at low scales.

astro-ph.CO↗
arXiv2023

Quantum loop effects on the power spectrum and constraints on primordial black holes

We present a detailed exposition on the prospects of the formation of Primordial Black Holes (PBHs) during Slow Roll (SR) to Ultra Slow Roll (USR) sharp transitions in the framework of single-field inflation. We use an effective field theory (EFT) approach in order to keep the analysis model-independent and applicable to both the canonical and non-canonical cases. We show in detail how renormalizing the power spectrum to one loop order in $P(X,ϕ)$ theories severely limits the prospects for PBH formation in a single-field inflationary framework. We demonstrate that for the allowed range of effective sound speed, $1<c_s<1.17$, the consistency of one-loop corrected power spectrum leaves a small window for black hole masses, $M_{\rm PBH}\sim \mathcal{O}(10^2-10^3)$gm to have sufficient e-foldings, $Δ{\cal N}_{\rm Total}\sim {\cal O}(54-59)$ for inflation. We confirm that adding an SR regime after USR before the end of inflation does not significantly alter our conclusions. Our findings for sharp transition strictly rule out the possibility of generating large masses of PBHs from all possible models of single-field inflation (canonical and non-canonical). Our results are at least valid for the situation where constraints from the loop effects are computed using either Late-Time (LT) or Adiabatic-Wave function (AF) scheme followed by Power Spectrum (PS) renormalization schemes.

astro-ph.CO↗
arXiv2023

Single-Call Stochastic Extragradient Methods for Structured Non-monotone Variational Inequalities: Improved Analysis under Weaker Conditions

Single-call stochastic extragradient methods, like stochastic past extragradient (SPEG) and stochastic optimistic gradient (SOG), have gained a lot of interest in recent years and are one of the most efficient algorithms for solving large-scale min-max optimization and variational inequalities problems (VIP) appearing in various machine learning tasks. However, despite their undoubted popularity, current convergence analyses of SPEG and SOG require a bounded variance assumption. In addition, several important questions regarding the convergence properties of these methods are still open, including mini-batching, efficient step-size selection, and convergence guarantees under different sampling strategies. In this work, we address these questions and provide convergence guarantees for two large classes of structured non-monotone VIPs: (i) quasi-strongly monotone problems (a generalization of strongly monotone problems) and (ii) weak Minty variational inequalities (a generalization of monotone and Minty VIPs). We introduce the expected residual condition, explain its benefits, and show how it can be used to obtain a strictly weaker bound than previously used growth conditions, expected co-coercivity, or bounded variance assumptions. Equipped with this condition, we provide theoretical guarantees for the convergence of single-call extragradient methods for different step-size selections, including constant, decreasing, and step-size-switching rules. Furthermore, our convergence analysis holds under the arbitrary sampling paradigm, which includes importance sampling and various mini-batching strategies as special cases.

math.OC↗
arXiv2023

Thermalization in Quenched Open Quantum Cosmology

In this article, we study the quantum field theoretic generalization of the Caldeira-Leggett model in general curved space-time considering interactions between two scalar fields in a classical gravitational background. The thermalization phenomena is then studied from the obtained de Sitter solution using quantum quench from one scalar field model obtained from path integrated effective action. We consider an instantaneous quench in the time-dependent mass protocol of the field of our interest. We find that the dynamics of the field post-quench can be described in terms of the state of the generalized Calabrese-Cardy (gCC) form and computed the different types of two-point correlation functions in this context. We explicitly found the conserved charges of $W_{\infty}$ algebra that represents the gCC state after a quench in de Sitter space and found it to be significantly different from the flat space-time results. We extend our study for the different two-point correlation functions not only considering the pre-quench state as the ground state, but also a squeezed state. We found that irrespective of the pre-quench state, the post quench state can be written in terms of the gCC state showing that the subsystem of our interest thermalizes in de Sitter space. Furthermore, we provide a general expression for the two-point correlators and explicitly show the thermalization process by considering a thermal Generalized Gibbs ensemble (GGE). Finally, from the equal time momentum dependent counterpart of the obtained results for the two-point correlators, we have studied the hidden features of the power spectra and studied its consequences for different choices of the quantum initial conditions.

hep-th↗
arXiv2023

Galileon inflation evades the no-go for PBH formation in the single-field framework

We consider Galileon inflation in the Effective Field Theory (EFT) framework and examine the possibility for PBH formation during slow roll (SR) to ultra slow roll (USR) transitions. We show that loop corrections to the power spectrum, in this case, do not impose additional constraints on the masses of PBHs produced. We indicate that the remarkable non-renormalization property of Galileans due to generalized shift symmetry dubbed as Galilean symmetry is responsible for protecting PBH formation from quantum loop corrections.

astro-ph.CO↗
arXiv2023

PBH formation in EFT of single field inflation with sharp transition

Using the Effective Field Theory (EFT) framework of single field inflation, we investigate the possibility of the formation of Primordial Black Holes (PBHs) in the Slow Roll (SR) to Ultra Slow Roll (USR) sharp transition. We demonstrate that, due to one-loop correction to the power spectrum, causality is violated ($c_s>1$) for the mass range of PBHs, $M_{\rm PBH}>10^{2}{\rm gm}$ created during the said transition. We find that non-canonical features with $c_s<1$ worsen the predictions of the canonical framework of single-field inflation.

astro-ph.CO↗
arXiv2023

Krylov Complexity in Quantum Field Theory

In this paper, we study the Krylov complexity in quantum field theory and make a connection with the holographic "Complexity equals Volume" conjecture. When Krylov basis matches with Fock basis, for several interesting settings, we observe that the Krylov complexity equals the average particle number showing that complexity scales with volume. Using similar formalism, we compute the Krylov complexity for free scalar field theory and find surprising similarities with holography. We also extend this framework for field theory where an inverted oscillator appears naturally and explore its chaotic behavior.

hep-th↗
arXiv2023

Cosmological Krylov Complexity

In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we obtain the explicit behavior of Krylov complexity ($K$) and lancoz coefficients ($b_n$) with respect to the conformal time scale and scale factor in the presence of effective sound speed $c_s$. Since lancoz coefficients ($b_n$) grow linearly with integer $n$, this suggests that universe acts like a chaotic system during this period. We also obtain the corresponding Lyapunov exponent $λ$ in presence of effective sound speed $c_s$. We show that the Krylov complexity ($K$) for this system is equal to average particle numbers suggesting it's relation to the volume. Finally, we give a comparison of Krylov complexity ($K$) with entanglement entropy (Von-Neumann) where we found that there is a large difference between Krylov complexity ($K$) and entanglement entropy for large values of squeezing amplitude. This suggests that Krylov complexity ($K$) can be a significant probe for studying the dynamics of the cosmological system even after the saturation of entanglement entropy.

hep-th↗
arXiv2023

Primordial Gravitational Wave Circuit Complexity

In this article, we investigate various physical implications of quantum circuit complexity using squeezed state formalism of Primordial Gravitational Waves (PGW). Recently quantum information theoretic concepts, such as entanglement entropy, and complexity are playing a pivotal role to understand the dynamics of quantum system even in the diverse fields such as, high energy physics and cosmology. This paper is devoted in studying quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas model etc. We compute complexity measure using both Covariance and Nielsen's wave function method for three different choices of quantum initial vacua: Motta-Allen, $α$ and Bunch-Davies. Besides computing circuit complexity, we have also computed Von-Neumann entanglement entropy. By making the comparison of complexity with entanglement entropy, we are able to probe various features regarding the dynamics of evolution for different cosmological models. Because entanglement entropy is independent of the squeezing angle, we are able to understand more details of the system using Nielsen's measure of complexity which is dependent on both squeezing parameter and angle. This implies that quantum complexity could indeed be a useful probe to study quantum features in cosmological scale. Quantum complexity is also becoming a powerful technique to understand the chaotic behaviour and random fluctuations of quantum fields. Using the growth of complexity, we are able to compute quantum Lyapunov exponent for various cosmological models and comment on it's chaotic nature.

gr-qc↗
arXiv2023

Circuit Complexity in an interacting quenched Quantum Field Theory

In this work, we explore the effects of a quantum quench on the circuit complexity for a quenched quantum field theory having weakly coupled quartic interaction. We use the invariant operator method, under a perturbative framework, for computing the ground state of this system}. We give the analytical expressions for specific reference and target states using the ground state of the system. Using a particular cost functional, we show the analytical computation of circuit complexity for the quenched and interacting field theory. Further, we give a numerical estimate of circuit complexity with respect to the quench rate, $δt$ for two coupled oscillators. The parametric variation of the unambiguous contribution of the circuit complexity for an arbitrary number of oscillators has been studied with respect to the dimensionless parameter $(t/δt$). We comment on the variation of circuit complexity for different values of coupling strength, different number of oscillators, and even in different dimensions.

hep-th↗
arXiv2023

Causality Constraint on Circuit Complexity from $COSMOEFT$

In this article, we investigate the physical implications of the causality constraint via effective sound speed $c_s(\leq 1)$ on Quantum Circuit Complexity(QCC) in the framework of Cosmological Effective Field Theory (COSMOEFT) using the two-mode squeezed quantum states. This COSMOEFT setup is constructed using the St$\ddot{\text{u}}$ckelberg trick with the help of the lowest dimensional operators, which are broken under time diffeomorphism. In this setup, we consider only the contribution from two derivative terms in the background quasi de Sitter metric. Next, we compute the relevant measures of circuit complexity and their cosmological evolution for different $c_s$ by following two different approaches, Nielsen's and Covariance matrix method. Using this setup, we also compute the Von-Neumann and Rényi entropy, which finally establishes an underlying connecting relationship between the entanglement entropy and circuit complexity. Essentially, we study the behaviour of the circuit complexity measures and entanglement entropy with respect to the scale factor and $c_s$ and find various interesting unexplored features within the window, $0.024\leq c_s\leq 1$, which is supported by both causality and cosmological observation. Finally, we also comment on the connection between the circuit complexity, entanglement entropy and equilibrium temperature for different $c_s$ lying within the mentioned window.

hep-th↗
arXiv2022

Circuit Complexity in $\mathcal{Z}_{2}$ ${\cal EEFT}$

Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in $\mathcal{Z}_2$ Even Effective Field Theories ($\mathcal{Z}_2$ EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as $ϕ^{4}$, $ϕ^{6}$ and $ϕ^8.$ To facilitate our computation we regularize the theory by putting it on a lattice. First, we consider a simple case of two oscillators and later generalize the results to $N$ oscillators. The study has been carried out for nearly Gaussian states. In our computation, the reference state is an approximately Gaussian unentangled state, and the corresponding target state, calculated from our theory, is an approximately Gaussian entangled state. We compute the complexity using the geometric approach developed by Nielsen, parameterizing the path ordered unitary transformation and minimizing the geodesic in the space of unitaries. The contribution of higher-order operators, to the circuit complexity, in our theory has been discussed. We also explore the dependency of complexity with other parameters in our theory for various cases.

hep-th↗
arXiv2022

Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation

In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations,(1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region ($-kτ\gg 1$), super Hubble region ($-kτ\ll 1$) and at the horizon crossing point ($-kτ= 1$) for massless field ($m/{\cal H}\ll 1$), partially massless field ($m/{\cal H}\sim 1$) and massive/heavy field ($m/{\cal H}\gg 1$), in the background of quantum field theory of spatially flat quasi De Sitter geometry. The prime motivation for this work is to investigate the various unknown quantum mechanical features of primordial universe. To give the realistic interpretation of the derived theoretical results we express everything initially in terms of slowly varying conformal time dependent parameters, and then to connect with cosmological observation we further express the results in terms of cosmological observables, which are spectral index/tilt of scalar mode power spectrum ($n_ζ$) and tensor-to-scalar ratio ($r$). Finally, this identification helps us to provide the stringent numerical constraints on the Pancharatnam Berry phase, which confronts well with recent cosmological observation.

gr-qc↗
arXiv2022

Four-mode squeezed states in de Sitter space: A study with two field interacting quantum system

In this paper we study the application of four-mode squeezed states in the cosmological context, studying two weakly coupled scalar fields in the planar patch of the de Sitter space. We construct the four-mode squeezed state formalism and connect this concept with the Hamiltonian of the two coupled inverted harmonic oscillators having a time-dependent effective frequency in the planar patch of the de Sitter space. Further, the corresponding evolution operator for the quantum Euclidean vacuum state has been constructed, which captures its dynamics. Using the Heisenberg picture coupled differential equations describing the time evolution for all squeezing parameters (amplitude, phase and angle) have been obtained, for the weakly coupled two scalar field model. With the help of these evolutions for the coupled system, we simulate the dynamics of the squeezing parameters in terms of conformal time. From our analysis, we observe interesting dynamics, which helps us to explore various underlying physical implications of the weakly coupled two scalar field system in the planar patch of the de Sitter cosmological background.

gr-qc↗
arXiv2022

Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function

Computation of circuit complexity has gained much attention in the Theoretical Physics community in recent times to gain insights into the chaotic features and random fluctuations of fields in the quantum regime. Recent studies of circuit complexity take inspiration from Nielsen's geometric approach, which is based on the idea of optimal quantum control in which a cost function is introduced for the various possible path to determine the optimum circuit. In this paper, we study the relationship between the circuit complexity and Morse theory within the framework of algebraic topology, which will then help us study circuit complexity in supersymmetric quantum field theory describing both simple and inverted harmonic oscillators up to higher orders of quantum corrections. We will restrict ourselves to $\mathcal{N} = 1$ supersymmetry with one fermionic generator $Q_α$. The expression of circuit complexity in quantum regime would then be given by the Hessian of the Morse function in supersymmetric quantum field theory. We also provide technical proof of the well known universal connecting relation between quantum chaos and circuit complexity of the supersymmetric quantum field theories, using the general description of Morse theory.

hep-th↗
arXiv2022

Entanglement in interacting quenched two-body coupled oscillator system

In this work, we explore the effects of a quantum quench on the entanglement measures of a two-body coupled oscillator system having quartic interaction. We use the invariant operator method, under a perturbative framework, for computing the ground state of this system. We give the analytical expressions for the total and reduced density matrix of the system having non-Gaussian, quartic interaction terms. Using this reduced density matrix, we show the analytical calculation of two entanglement measures viz., Von Neumann entanglement entropy using replica trick and Renyi entanglement entropy. Further, we give a numerical estimate of these entanglement measures with respect to the dimensionless parameter $(t/δt$) and show its behaviour in the three regimes, i.e; late time behaviour, around the quench point and the early time behaviour. We comment on the variation of these entanglement measures for different orders of coupling strength. The variation of Renyi entropy of different orders has also been discussed.

hep-th↗