arXiv subjects

Dipayan Mukherjee

Publications and source records attributed to Dipayan Mukherjee.

12 recordsLinked to original sources

arXiv2026

Cosmic variance and ergodicity in finite systems with correlations

We consider the difference between ensemble and volume average in cosmology. It is known that for sufficiently weak long-range correlations the root mean square of the difference, which we call ergodicity bias, decays like $R^{-3/2}$ in the limit of large volume $R^3$. We calculate the condition this imposes on the power spectrum of a Gaussian random field. We quantify the bias for finite $R$, and show that the $R\to\infty$ limit is of little relevance for cosmological observations when the measured scales and correlations extend to the size of the observable universe. We consider curvature, density, and velocity perturbations. On large scales the bias is important in all three cases. For the density perturbations, which are observationally the most relevant, the relative bias first exceeds 100% at the separation $r=177$ Mpc, and is larger than 100% for all $r>560$ Mpc. It should be taken into account when comparing ensemble and volume averages for large-scale structure. The bias is also large for the cosmic microwave background temperature perturbations on large angular scales, but this is not relevant for observations, as their analysis does not involve volume averaging.

astro-ph.CO↗

arXiv2026

Capturing statistical isotropy violation with rotational averages

Recent high precision cosmological observations have revealed several anomalies in the Cosmic Microwave Background (CMB), indicating possible violations of statistical isotropy (nSI). Typically, nSI in the CMB sky is studied in the harmonic space, such as, using the Bipolar Spherical Harmonics (BipoSH) formalism, where the BipoSH coefficients capture the general structure of the angular correlation function. In this work, we present a geometric real space framework to quantify violations of statistical isotropy complementing the BipoSH approach. This geometric approach involves averaging the angular correlation function over all rotated configurations, weighted by Wigner matrices. These rotational averages systematically isolate the nSI components of the CMB sky. They also provide a physical space based route to interpretation of how the BipoSH formalism captures breaking of rotational symmetry. As a demonstration, we consider an analytical dipole modulation model. We numerically implement the rotational average measures and show their agreement with their harmonic space counterparts. The real space approach to quantify nSI could be advantageous in certain scenarios: rotational averages can directly extract nSI information from the correlation function at the level of a given multipole, bypassing the need to compute BipoSH coefficients up to arbitrarily high internal ranks. Importantly, analyzing the temperature map in real space can circumvent the unavoidable partial-sky effects present in CMB observations, which typically complicate harmonic space approaches. We envisage broader applications of this formalism to studies of primordial non-Gaussianity, CMB polarization, and weak gravitational lensing, as well as to the characterization of general random fields on a sphere.

astro-ph.CO↗

arXiv2026

Quantum Cosmology as a Hydrogen atom: Discrete $\Lambda$ and cyclic Universes from Wheeler-DeWitt quantization

Building upon our recently established correspondence between quantum cosmology and the hydrogen atom [1], we investigate the specific sector of a negative cosmological constant ($\Lambda < 0$) in a flat FLRW universe with dust. While the positive $\Lambda$ sector [1] yields a continuous spectrum and a single bounce, we show here that the negative $\Lambda$ sector leads to a discrete spectrum of energy eigenvalues, effectively quantizing the cosmological constant. Within this dual description, the operator-ordering ambiguity parameter appears as the azimuthal quantum number of the hydrogen atom. A skewed Bohr correspondence emerges for the bound states, matching classical evolution at large volumes but deviating near the bounce. By constructing wave packets from these bound states, we demonstrate that the classical Big Bang and Big Crunch singularities are resolved, and the universe oscillates between quantum bounces and classical turnaround points. The expectation values of the observables indicate a cyclic universe -- with vanishing Hubble parameter at turnarounds -- undergoing quantum bounces. This exactly solvable model offers a tractable setting to explore quantum gravitational effects in cosmology. We analyze the properties of this cyclic universe, contrasting its bound-state dynamics with the scattering states of the de Sitter case.

gr-qc↗

arXiv2025

A dynamical systems perspective on the thermodynamics of late-time cosmology

A thermodynamic description of cosmological spacetimes may provide insights into the fundamentals of the cosmic evolution that remain otherwise obscure, similar to `black hole thermodynamics'. We investigate the thermodynamic properties of late-time cosmological evolution using the dynamical systems approach, focusing on $\Lambda${}CDM model and scalar field models with exponential potentials. Thermodynamic quantities obtained through the Hayward-Kodama formalism are mapped onto the phase-space of these models. Specifically, we express the thermodynamic quantities as functions of the phase-space variables, allowing us to study the thermodynamic behavior across the phase space, particularly at the critical points. We focus on thermodynamic stability and phase transitions, analyzed in an initial condition-independent manner. In these models, the universe inevitably undergoes a thermodynamic phase transition, marked by diverging specific heats, irrespective of its initial configuration. We further demonstrate that the thermodynamic stability can occur only during an accelerating phase of the universe. For $\Lambda$CDM and quintessence models, the necessary stability conditions are never satisfied anywhere in the phase space, rendering both models thermodynamically unstable within the Hayward-Kodama framework and the canonical ensemble based stability criteria. Interestingly, the phantom models, although dynamically unstable, allow for the universe to attain thermodynamic stability in its asymptotic future. This can indicate the limitations of applying canonical ensemble based thermodynamic stability criteria to cosmological horizons. Through these archetypal descriptions of late-time cosmology, we show that the dynamical system approach is a robust framework to probe the thermodynamic aspects of cosmological evolution.

gr-qc↗

arXiv2025

V(is)owel: An Interactive Vowel Chart to Understand What Makes Visual Pronunciation Effective in Second Language Learning

Visual feedback speeds up learners' improvement of pronunciation in a second language. The visual combined with audio allows speakers to see sounds and differences in pronunciation that they are unable to hear. Prior studies have tested different visual methods for improving pronunciation, however, we do not have conclusive understanding of what aspects of the visualizations contributed to improvements. Based on previous work, we created V(is)owel, an interactive vowel chart. Vowel charts provide actionable feedback by directly mapping physical tongue movement onto a chart. We compared V(is)owel with an auditory-only method to explore how learners parse visual and auditory feedback to understand how and why visual feedback is effective for pronunciation improvement. The findings suggest that designers should include explicit anatomical feedback that directly maps onto physical movement for phonetically untrained learners. Furthermore, visual feedback has the potential to motivate more practice since all eight of the participants cited using the visuals as a goal with V(is)owel versus relying on their own judgment with audio alone. Their statements are backed up by all participants practicing words with V(is)owel more than with audio-only. Our results indicate that V(is)owel is effective at providing actionable feedback, demonstrating the potential of visual feedback methods in second language learning.

cs.HC↗

arXiv2025

Scalar-induced gravitational waves from coherent initial states

We investigate the impact of statistical inhomogeneity and anisotropy in primordial scalar perturbations on the scalar-induced gravitational waves (SIGW). Assuming inflationary quantum fluctuations originate from a coherent state, the resulting primordial scalar perturbations acquire a non-zero space-dependent mean, violating statistical homogeneity, statistical isotropy, and parity. As a consequence of statistical inhomogeneities, SIGW acquires distinct scale-dependent features in its correlation function. Statistical anisotropies further lead to possible parity violation and correlation between different polarization modes in the tensor perturbations. Therefore, detection of these signatures in the stochastic gravitational wave background would offer probes to the statistical nature of primordial scalar perturbations beyond the scales accessible to CMB observations.

astro-ph.CO↗

arXiv2025

Unitary quantum matter-bounce in a universe with a positive cosmological constant

We analyze the Wheeler-DeWitt quantization of a spatially flat Friedmann-Lema\^itre-Robertson-Walker universe containing pressureless dust and a positive cosmological constant ($\Lambda > 0$). Following relational time framework, we establish a direct mathematical correspondence between the cosmological Hamiltonian and the radial Schr\"odinger equation for the scattering states of the non-relativistic hydrogen atom. This exact solvability allows us to rigorously construct the physical Hilbert space and ensure the self-adjointness of the Hamiltonian. As a concrete result, we show that the wave packets unitarily evolve depicting a non-singular quantum bounce, systematically replacing the classical Big Bang singularity. Finally, we discuss the physical relevance of this exact solution within the matter-bounce scenario. We demonstrate that this framework provides a robust quantum origin for a bounce during a dust-dominated contracting phase -- a necessary prerequisite for generating a scale-invariant spectrum of primordial perturbations -- derived from the unitary dynamics of the quantized background.

gr-qc↗

arXiv2024

Cosmological consequences of statistical inhomogeneity

A space-dependent mean for cosmological perturbations negates the ansatz of statistical homogeneity and isotropy, and hence ergodicity. In this work, we construct such a primordial mean of scalar perturbations from an alternative quantum initial state (coherent state) and examine the associated power and bi-spectra. A multitude of cosmological tests based on these spectra are discussed. We find that current cosmological data doesn't favor a primordial mean over large scales and strong constraints arise from the limit on bispectrum from Planck data. At small scales, this hypothesis can be tested by future observables such as $\mu$-distortion of CMB.

astro-ph.CO↗

arXiv2024

eScope: A Fine-Grained Power Prediction Mechanism for Mobile Applications

Managing the limited energy on mobile platforms executing long-running, resource intensive streaming applications requires adapting an application's operators in response to their power consumption. For example, the frame refresh rate may be reduced if the rendering operation is consuming too much power. Currently, predicting an application's power consumption requires (1) building a device-specific power model for each hardware component, and (2) analyzing the application's code. This approach can be complicated and error-prone given the complexity of an application's logic and the hardware platforms with heterogeneous components that it may execute on. We propose eScope, an alternative method to directly estimate power consumption by each operator in an application. Specifically, eScope correlates an application's execution traces with its device-level energy draw. We implement eScope as a tool for Android platforms and evaluate it using workloads on several synthetic applications as well as two video stream analytics applications. Our evaluation suggests that eScope predicts an application's power use with 97% or better accuracy while incurring a compute time overhead of less than 3%.

cs.DC↗

arXiv2023

Einstein and Jordan frame correspondence in quantum cosmology: Expansion-collapse duality

The conformal correspondence between FLRW universes in the Einstein and Jordan frames allows for an expansion-collapse duality -- an always expanding Einstein frame universe can have a dual Jordan frame description that is contracting forever. The scenario eventually runs into an apparent paradox. When a collapsing universe approaches singularity, the classical description of the spacetime becomes inadequate. The contracting Jordan frame universe is expected to develop quantum characteristics when its scale factor becomes sufficiently small. However, at the same time, the corresponding Einstein frame universe is expected to behave classically, due to the arbitrarily large size it has grown to. In this case, the conformal map appears to be providing a duality between a quantum effect-dominated universe and a universe behaving classically. We investigate the status of the conformal map at the quantum level in such a scenario, focusing on addressing this paradox. The Einstein and Jordan frame universes are quantized individually using the Wheeler-DeWitt prescription. We show that the classical conformal map holds true at the quantum level when compared through the expectation values of the scale factor operators in the two frames. The relative quantum fluctuation in the scale factor is found to be conformally invariant, and it increases in both the past and future directions according to the internal clock. Expectedly, the quantum fluctuations in the collapsing Jordan frame keep on increasing as it shrinks towards singularity. More surprisingly, the quantum fluctuations in the expanding Einstein frame keep on increasing as well, even as its classical scale factor becomes larger. Despite having drastically different cosmological evolutions, the rise in quantum characteristics in a collapsing frame implies the same in its expanding counterpart, thereby resolving the apparent paradox.

gr-qc↗

arXiv2022

Bouncing and collapsing universes dual to late-time cosmological models

We use the Jordan frame-Einstein frame correspondence to explore dual universes with contrasting cosmological evolutions. We study the mapping between Einstein and Jordan frames where the Einstein frame universe describes the late-time evolution of the physical universe, which is driven by dark energy and non-relativistic matter. The Brans-Dicke theory of gravity is considered to be the dual scalar-tensor theory in the Jordan frame. We show that an Einstein frame universe, with cosmological evolution of the $\Lambda$CDM model, always corresponds to a bouncing Jordan frame universe governed by a Brans-Dicke theory. On the other hand, quintessence models of dark energy with non-relativistic matter component are shown to be always dual to a Brans-Dicke Jordan frame with a turn-around, i.e., a bounce or a collapse. The evolution of the equation of state of the quintessence field determines whether the turn-around is a bounce or a collapse. The point of the Jordan frame turn-around for all the cases can be tuned anywhere by choosing an appropriate Brans-Dicke parameter. This essentially leads to alternative descriptions of the late-time evolution of the physical universe, in terms of bouncing or collapsing Brans-Dicke universes in the Jordan frame. Therefore,the effect of dark energy can equivalently be seen as collapse of space in a conformally connected universe. We further study the stability of such conformal maps against linear perturbations. The effective bouncing and collapsing descriptions of the current accelerating universe may have interesting implications for the evolutions of perturbations and quantum fluctuations in the cosmological background.

gr-qc↗

arXiv2021

$f(R)$ Dual Theories of Quintessence : Expansion-Collapse Duality

The accelerated expansion of the universe demands presence of an exotic matter, namely the dark energy. Though the cosmological constant fits this role very well, a scalar field minimally coupled to gravity, or quintessence, can also be considered as a viable alternative for the cosmological constant. We study $f(R)$ gravity models which can lead to an effective description of dark energy implemented by quintessence fields in Einstein gravity, using the Einstein frame-Jordan frame duality. For a family of viable quintessence models, the reconstruction of the $f(R)$ function in the Jordan frame consists of two parts. We first obtain a perturbative solution of $f(R)$ in the Jordan frame, applicable near the present epoch. Second, we obtain an asymptotic solution for $f(R)$, consistent with the late time limit of the Einstein frame if the quintessence field drives the universe. We show that for certain class of viable quintessence models, the Jordan frame universe grows to a maximum finite size, after which it begins to collapse back. Thus, there is a possibility that in the late time limit where the Einstein frame universe continues to expand, the Jordan frame universe collapses. The condition for this expansion-collapse duality is then generalized to time varying equations of state models, taking into account the presence of non-relativistic matter or any other component in the Einstein frame universe. This mapping between an expanding geometry and a collapsing geometry at the field equation level may have interesting potential implications on the growth of perturbations therein at late times.

gr-qc↗