arXiv subjects

Nishant Agarwal

Publications and source records attributed to Nishant Agarwal.

At least 19 recordsLinked to original sources

arXiv2026

Open system probes of renormalization group flow

Open system probes can provide an efficient means to characterize quantum many-body systems by employing them as engineered environments. The key idea is to map long-range spatial correlations of the environment onto dynamical correlations in the evolution of a simple quantum probe. Using the example of a qubit coupled to a transverse-field Ising model, we show how the non-Markovian rate or spectral flow can be used to identify stable and unstable fixed points, infer scaling dimensions of relevant fields, and deduce the renormalization group flow induced by deformations around any fixed point.

quant-ph↗

arXiv2026

Mutual information as a measure of renormalizability

Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been thoroughly refined for equilibrium systems, consistently extending it to out-of-equilibrium systems is an active area of research. In this paper, we identify a mutual information-based measure of renormalizability that applies to quantum field theories both in and out of equilibrium. Specifically, we use mutual information to characterize correlations between infinitesimal shells in momentum space and show that the logarithmic derivative of mutual information with mode separation, at large mode separation, is a measure of renormalizability. We first consider Minkowski spacetime, where we introduce dynamics by performing an interaction quench, initializing the field in the free theory vacuum and then turning on the interaction. We show that the late-time mutual information relaxes to that for the interacting vacuum and the logarithmic derivative at large mode separation is negative for super-renormalizable theories, zero for renormalizable (marginal) theories, and positive for non-renormalizable theories. We then consider a conformally-coupled scalar field on the Poincaré patch of de Sitter spacetime, initializing the field in the Bunch-Davies vacuum in the asymptotic past. For different self-interactions and at any finite time, we find that the resulting mutual information has the same qualitative behavior as a function of mode separation, demonstrating that it can be used as a reliable indicator of renormalizability.

hep-th↗

arXiv2026

Open system dynamics in interacting quantum field theories

A quantum system that interacts with an environment generally undergoes nonunitary evolution described by a non-Markovian or Markovian master equation. In this paper, we construct the non-Markovian Redfield master equation for a quantum scalar field that interacts with a second field through a bilinear or nonlinear interaction on a Minkowski background. We use the resulting master equation to set up coupled differential equations that can be solved to obtain the equal-time two-point function of the system field. We show how the equations simplify under various approximations including the Markovian limit and argue that the Redfield equation-based solution provides a perturbative resummation to the standard second-order Dyson series result. For the bilinear interaction, we explicitly show that the Redfield solution is closer to the exact solution compared to the perturbation theory-based one. Further, the environment correlation function is oscillatory and nondecaying in this case, making the Markovian master equation a poor approximation. For the nonlinear interaction, on the other hand, the environment correlation function is sharply peaked and the Redfield solution matches that obtained using a Markovian master equation in the late-time limit.

hep-th↗

arXiv2024

Initial value formulation of a quantum damped harmonic oscillator

The in-in formalism and its influence functional generalization are widely used to describe the out-of-equilibrium dynamics of unitary and open quantum systems, respectively. In this paper, we build on these techniques to develop an effective theory of a quantum damped harmonic oscillator and use it to study initial state-dependence, decoherence, and thermalization. We first consider a Gaussian initial state and quadratic influence functional and obtain general equations for the Green's functions of the oscillator. We solve the equations in the specific case of time-local dissipation and use the resulting Green's functions to obtain the purity and unequal-time two-point correlations of the oscillator. We find that the dynamics must include a non-vanishing noise term to yield physical results for the purity and that the oscillator decoheres in time such that the late-time density operator is thermal. We show that the frequency spectrum or unequal-time correlations can, however, distinguish between the damped oscillator and an isolated oscillator in thermal equilibrium, and obtain a generalized fluctuation-dissipation relation for the damped oscillator. We briefly consider time-nonlocal dissipation as well, to show that the fluctuation-dissipation relation is satisfied for a specific choice of dissipation kernels. Lastly, we develop a double in-out path integral approach to go beyond Gaussian initial states and show that our equal-time results for time-local dissipation are in fact non-perturbative in the initial state.

hep-th↗

arXiv2023

Thermalization and localization in a discretized quantum field theory

Localization marks the breakdown of thermalization in subregions of quantum many-body systems in the presence of sufficiently large disorder. In this paper, we use numerical techniques to study thermalization and localization in a many-body system of coupled quantum harmonic oscillators obtained by discretizing a scalar quantum field theory in Minkowski spacetime. We consider a Gaussian initial state, constructed through a global mass quench, with a quadratic Hamiltonian, and solve for the system's exact dynamics without and with disorder in one and two spatial dimensions. We find that finite-size systems localize for sufficiently large disorder in both cases, such that the entanglement entropy of subregions retains its initial area-law behavior, and the system no longer develops long-range correlations. To probe the thermalization-to-localization transition further, we define a frequency gap ratio that measures adjacent gaps in the phase space eigenvalues of the Hamiltonian and study how it varies with disorder strength and system size. We find signatures of a chaotic regime at intermediate disorder in two spatial dimensions and argue that it is a finite-size effect, such that the system would localize for arbitrarily small disorder in the continuum in both one and two spatial dimensions, consistent with Anderson localization. Lastly, we use the frequency gap ratio to argue that in three spatial dimensions, on the other hand, the system would only localize for disorder strengths above a critical value in the continuum, again consistent with Anderson localization.

cond-mat.stat-mech↗

arXiv2023

Loop corrections in Minkowski spacetime away from equilibrium. Part I. Late-time resummations

Loop corrections to unequal-time correlation functions in Minkowski spacetime exhibit secular growth due to a breakdown of time-dependent perturbation theory. This is analogous to secular growth in equal-time correlators on time-dependent backgrounds, except that in Minkowski the divergences must not signal a real IR issue. In this paper, we calculate the late-time limit of the two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background. We first use a late-time version of the in-in path integral starting in the vacuum of the free theory; in this limit, the calculation, including UV renormalization, reduces to that in in-out. We find linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. We next develop the Weisskopf-Wigner resummation method, that proceeds by demanding unitarity within a truncated Hilbert space, to calculate the resummed correlator and find that it gives an exact exponentiation of the late-time perturbative result. The resummed (unequal-time) correlator thus decays with an exponential or polynomial time-dependence, which is suggestive of `universal' behavior that depends on the dimensions of the interaction strength.

hep-th↗

arXiv2023

Loop corrections in Minkowski spacetime away from equilibrium. Part II. Finite-time results

Loop corrections to finite-time correlation functions in quantum field theories away from equilibrium can be calculated using the in-in path integral approach. In this paper, we calculate the unequal-time two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background, starting the field evolution at an arbitrary initial time. We find the counterterms that need to be added to UV-renormalize the result, including usual in-out counterterms in the dynamics and additional initial state counterterms that are required to cancel all UV divergences. We find that the late-time limit of the renormalized correlation function exhibits a linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. The late-time correlations match those obtained in our companion paper and, as shown there, the divergences do not indicate a real IR issue, consistent with what one would expect in Minkowski.

hep-th↗

arXiv2022

Linear growth of structure in massive gravity

We study background dynamics and the growth of matter perturbations in the extended quasidilaton setup of massive gravity. For the analysis of perturbations, we first choose a scalar field matter component and obtain the conditions under which all scalar perturbations are stable. We work in unitary gauge for the matter field, which allows us to directly map to known results in the limit of general relativity. By performing a parameter search, we find that the perturbations are unstable in general, while a particular choice of potential, where the scalar field effectively behaves like pressureless matter, allows for stable perturbations. We next consider the growth of matter perturbations in a cold dark matter-dominated Universe. Working in conformal Newtonian gauge, we obtain evolution equations for various observables including the growth factor and growth rate, and find scale-independent growth in the quasistatic and subhorizon approximations. We finally show how the Hubble parameter and matter perturbations evolve in massive gravity for a specific choice of parameter values, and how this evolution compares to the standard cosmological model consisting of a cosmological constant and cold dark matter.

gr-qc↗

arXiv2021

Information content in the redshift-space galaxy power spectrum and bispectrum

We present a Fisher information study of the statistical impact of galaxy bias and selection effects on the estimation of key cosmological parameters from galaxy redshift surveys; in particular, the angular diameter distance, Hubble parameter, and linear growth rate at a given redshift, the cold dark matter density, and the tilt and running of the primordial power spectrum. The line-of-sight-dependent selection contributions we include here are known to exist in real galaxy samples. We determine the maximum wavenumber included in the analysis by requiring that the next-order corrections to the galaxy power spectrum or bispectrum, treated here at next-to-leading and leading order, respectively, produce shifts of $\lesssim 0.25σ$ on each of the six cosmological parameters. With the galaxy power spectrum alone, selection effects can deteriorate the constraints severely, especially on the linear growth rate. Adding the galaxy bispectrum helps break parameter degeneracies significantly. We find that a joint power spectrum-bispectrum analysis of a Euclid-like survey can still measure the linear growth rate to 10% precision after complete marginalization over selection bias. We also discuss systematic parameter shifts arising from ignoring selection effects and/or other bias parameters, and emphasize that it is necessary to either control selection effects at the percent level or marginalize over them. We obtain similar results for the Roman Space Telescope and HETDEX.

astro-ph.CO↗

arXiv2019

Cosmic Expansion in Extended Quasidilaton Massive Gravity

Quasidilaton massive gravity offers a physically well-defined gravitational theory with non-zero graviton mass. We present the full set of dynamical equations governing the expansion history of the universe, valid during radiation domination, matter domination, and a late-time self-accelerating epoch related to the graviton mass. The existence of self-consistent solutions constrains the amplitude of the quasi-dilaton field and the graviton mass, as well as other model parameters. We point out that the effective mass of gravitational waves can be significantly larger than the graviton mass, opening the possibility that a single theory can explain both the late-time acceleration of the cosmic expansion and modifications of structure growth leading to the suppression of large-angle correlations observed in the cosmic microwave background.

astro-ph.CO↗

arXiv2018

A cosmological open quantum system

We derive the evolution equation for the density matrix of a UV- and IR- limited band of comoving momentum modes of the canonically normalized scalar degree of freedom in two examples of nearly de Sitter universes. Including the effects of a cubic interaction term from the gravitational action and tracing out a set of longer wavelength modes, we find that the evolution of the system is non-Hamiltonian and non-Markovian. We find linear dissipation terms for a few modes with wavelength near the boundary between system and bath and nonlinear dissipation terms for all modes. The non-Hamiltonian terms persist to late times when the scalar field dynamics is such that the curvature perturbation continues to evolve on super-Hubble scales.

hep-th↗

arXiv2015

Looking for non-Gaussianity in all the right places: A new basis for non-separable bispectra

Non-Gaussianity in the distribution of inflationary perturbations, measurable in statistics of the cosmic microwave background (CMB) and large scale structure fluctuations, can be used to probe non-trivial initial quantum states for these perturbations. The bispectrum shapes predicted for generic non-Bunch-Davies initial states are non-factorizable ("non-separable") and are highly oscillatory functions of the three constituent wavenumbers. This can make the computation of CMB bispectra, in particular, computationally intractable. To efficiently compare with CMB data one needs to construct a separable template that has a significant similarity with the actual shape in momentum space. In this paper we consider a variety of inflationary scenarios, with different non-standard initial conditions, and how best to construct viable template matches. In addition to implementing commonly used separable polynomial and Fourier bases, we introduce a basis of localized piecewise spline functions. The spline basis is naturally nearly orthogonal, making it easy to implement and to extend to many modes. We show that, in comparison to existing techniques, the spline basis can provide better fits to the true bispectrum, as measured by the cosine between shapes, for sectors of the theory space of general initial states. As such, it offers a useful approach to investigate non-trivial features generated by fundamental properties of the inflationary Universe.

astro-ph.CO↗

arXiv2015

Sloan Digital Sky Survey III Photometric Quasar Clustering: Probing the Initial Conditions of the Universe using the Largest Volume

The Sloan Digital Sky Survey has surveyed 14,555 square degrees of the sky, and delivered over a trillion pixels of imaging data. We present the large-scale clustering of 1.6 million quasars between z = 0.5 and z = 2.5 that have been classified from this imaging, representing the highest density of quasars ever studied for clustering measurements. This data set spans ~11,000 square degrees and probes a volume of 80(Gpc/h)^3. In principle, such a large volume and medium density of tracers should facilitate high-precision cosmological constraints. We measure the angular clustering of photometrically classified quasars using an optimal quadratic estimator in four redshift slices with an accuracy of ~25% over a bin width of l ~10 - 15 on scales corresponding to matter-radiation equality and larger (l ~ 2 - 30). Observational systematics can strongly bias clustering measurements on large scales, which can mimic cosmologically relevant signals such as deviations from Gaussianity in the spectrum of primordial perturbations. We account for systematics by employing a new method recently proposed by Agarwal et al. (2014) to the clustering of photometrically classified quasars. We carefully apply our methodology to mitigate known observational systematics and further remove angular bins that are contaminated by unknown systematics. Combining quasar data with the photometric luminous red galaxy (LRG) sample of Ross et al. (2011) and Ho et al. (2012), and marginalizing over all bias and shot noise-like parameters, we obtain a constraint on local primordial non-Gaussianity of fNL = -113+/-154 (1σerror). [Abridged]

astro-ph.CO↗

arXiv2014

Why does the effective field theory of inflation work?

The effective field theory (EFT) of inflation has become the preferred method for computing cosmological correlation functions of the curvature fluctuation, $ζ$. It makes explicit use of the soft breaking of time diffeomorphisms by the inflationary background to organize the operators expansion in the action of the Goldstone mode $π$ associated with this breaking. Despite its ascendancy, there is another method for calculating $ζ$ correlators, involving the direct calculation of the so-called Horndeski action order by order in powers of $ζ$ and its derivatives. The question we address in this work is whether or not the $ζ$ correlators calculated in these seemingly different ways are in fact the same. The answer is that the actions to cubic order in either set of variables do indeed give rise to the same $ζ$ bispectra, but that to make this equivalence manifest requires a careful understanding of the non-linear transformations relating $π$ to $ζ$ and how boundary terms in the actions are affected by imposing this relation. As a by product of our study we find that the calculations in the $π$ language can be simplified considerably in a way that allows us to use only the linear part of the $π-ζ$ relation simply by changing the coefficients of some of the operators in the EFT. We also note that a proper accounting of the boundary terms will be of the greatest importance when computing the bispectrum for more general initial states than the Bunch-Davies one.

hep-th↗

arXiv2014

Characterizing unknown systematics in large scale structure surveys

Photometric large scale structure (LSS) surveys probe the largest volumes in the Universe, but are inevitably limited by systematic uncertainties. Imperfect photometric calibration leads to biases in our measurements of the density fields of LSS tracers such as galaxies and quasars, and as a result in cosmological parameter estimation. Earlier studies have proposed using cross-correlations between different redshift slices or cross-correlations between different surveys to reduce the effects of such systematics. In this paper we develop a method to characterize unknown systematics. We demonstrate that while we do not have sufficient information to correct for unknown systematics in the data, we can obtain an estimate of their magnitude. We define a parameter to estimate contamination from unknown systematics using cross-correlations between different redshift slices and propose discarding bins in the angular power spectrum that lie outside a certain contamination tolerance level. We show that this method improves estimates of the bias using simulated data and further apply it to photometric luminous red galaxies in the Sloan Digital Sky Survey as a case study.

astro-ph.CO↗

arXiv2014

Constraining the initial conditions of the Universe using large scale structure

Primordial non-Gaussianity induces a scale-dependent bias in large scale structure (LSS) data, proportional to $f_{\rm NL}/k^2$ for the exact local ansatz. Recent work has shown that models of inflation that predict a large squeezed limit bispectrum, such as multi-field models and single field inflation with a modified initial state, typically give rise to a generalized local ansatz, with the scale-dependent bias now proportional to ${\cal A}_{\rm NL}/k^α$. We use photometric measurements of the angular power spectrum of luminous red galaxies and quasars in the Sloan Digital Sky Survey Data Release Eight (SDSS DR8) with the above parameterization to constrain the amplitude ${\cal A}_{\rm NL}$ and scale-dependence $α$. We find that the marginalized upper limit on $α$ is 2.0 at the $95\%$ confidence level, consistent with the local ansatz. We also present Fisher forecasts for a survey of the same size as DR8 to assess the role of systematics in current photometric LSS data. Moreover, we present analytic results on the expected mass dependence of ${\cal A}_{\rm NL}$ for different inflationary models, which can be an important observable for future surveys, if primordial non-Gaussianity is non-zero.

astro-ph.CO↗

arXiv2013

What is the shape of the initial state?

We argue that a plausible operational definition for an initial state of the Universe is the initial quantum state of the curvature perturbations generated during inflation. We provide a parameterization of this state and generalize the standard in-in formalism to incorporate the structures in this state into the computation of correlators of the perturbations. Measurements of these correlators using both the CMB as well as large scale structure probe different structures in the initial state, as they give rise to bi- and tri-spectra peaked on different shapes of triangles and quadrilaterals in momentum space. In essence, the shapes implied by the correlators feed directly into information about the shape of the initial state and what physics could have preceded inflation to set this state up.

hep-th↗

arXiv2013

Effective field theory and non-Gaussianity from general inflationary states

We study the effects of non-trivial initial quantum states for inflationary fluctuations within the context of the effective field theory for inflation constructed by Cheung et al. which allows us to discriminate between different initial states in a model-independent way. We develop a Green's function/path integral based formulation that incorporates initial state effects and use it to address questions such as how state-dependent is the consistency relation for the bispectrum, how many e-folds beyond the minimum required to solve the cosmological fine tunings of the big bang are we allowed so that some information from the initial state survives until late times, among others. We find that the so-called consistency condition relating the local limit of the bispectrum and the slow-roll parameter is a state-dependent statement that can be avoided for physically consistent initial states either with or without initial non-Gaussianities.

hep-th↗