arXiv subjects

Subodh P. Patil

Publications and source records attributed to Subodh P. Patil.

At least 19 recordsLinked to original sources

arXiv2026

On the Renormalization Group Flow of Active Flocks

In this paper, we study the statistical field-theoretic renormalization of active flocks via the MSRDJ action formulation for stochastic systems, focusing on the Toner-Tu theory of `Malthusian flocks', or polar-ordered, momentum non-conserving active fluids where relaxation times for density fluctuations are so short that they can be eliminated as a hydrodynamic variable. Working in the limit of isotropic diffusion in two spatial dimensions, we compute the renormalization of the couplings and their anomalous dimensions to all orders, facilitated by the Ward identities associated with the non-linear realization of a diagonal rotation/ shift symmetry, and a non-local field-dependent redundancy specific to the MSRDJ representation of this model. We find a range of behavior depending on the parameters of the theory. If $κ$ is the diffusion coefficient and $Δ$ is the variance of the noise, we find a line of fixed points and a marginal vertex instability at $Δ/κ= 2π$. This instability separates Gaussian, and symmetry-protected strongly interacting gapless phases, realizing non-equilibrium critical behavior beyond standard Wilson--Fisher criticality, and implies the persistence of long range order when $Δ/κ$ is below the critical value. We revisit and contextualize various claims and counter-claims in the literature in light of our findings, and discuss extensions of our analysis to flocks with anisotropic diffusion, and where density fluctuations are reintroduced.

cond-mat.soft↗

arXiv2026

Renormalization of Interacting Random Graph Models

Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical moments. In this investigation, we elaborate on a generalization of the former where link probabilities are conditioned on the appearance of other links, corresponding to the introduction of interactions in an effective generalized statistical mechanical formalism. When restricted to the simplest non-trivial case of pairwise interactions, one can derive a closed form renormalization group transformation for maximum coordination number two on the corresponding line graph. Higher coordination numbers do not admit exact closed form renormalization group transformations, a feature that paraphrases the usual absence of exact transformations in two or more dimensional lattice systems. We introduce disorder and study the induced renormalization group flow on its probability assignments, highlighting its formal equivalence to time reversed anisotropic drift-diffusion on the statistical manifold associated with the effective Hamiltonian. We discuss the implications of our findings, stressing the long wavelength irrelevance of certain classes of pair-wise conditioning on random graphs, and conclude with possible applications. These include modeling the scaling behavior of preferential effects on social networks, opinion dynamics, and reinforcement effects on neural networks, as well as how our findings offer a systematic framework to deal with data limitations in inference and reconstruction problems.

cond-mat.stat-mech↗

arXiv2025

Hydrodynamics without Boost-Invariance from Kinetic Theory: From Perfect Fluids to Active Flocks

We derive the hydrodynamic equations of perfect fluids without boost invariance [1] from kinetic theory. Our approach is to follow the standard derivation of the Vlasov hierarchy based on an a-priori unknown collision functional satisfying certain axiomatic properties consistent with the absence of boost invariance. The kinetic theory treatment allows us to identify various transport coefficients in the hydrodynamic regime. We identify a drift term that effects a relaxation to an equilibrium where detailed balance with the environment with respect to momentum transfer is obtained. We then show how the derivative expansion of the hydrodynamics of flocks can be recovered from boost non-invariant kinetic theory and hydrodynamics. We identify how various coefficients of the former relate to a parameterization of the so-called equation of kinetic state that yields relations between different coefficients, arriving at a symmetry-based understanding as to why certain coefficients in hydrodynamic descriptions of active flocks are naturally of order one, and others, naturally small. When inter-particle forces are expressed in terms of a kinetic theory influence kernel, a coarse-graining scale and resulting derivative expansion emerge in the hydrodynamic limit, allowing us to derive diffusion terms as infrared-relevant operators distilling different parameterizations of microscopic interactions. We conclude by highlighting possible applications.

hep-th↗

arXiv2025

Primordial Gravitational Wave Probes of Non-Standard Thermal Histories

Primordial gravitational waves propagate almost unimpeded from the moment they are generated to the present epoch. Nevertheless, they are subject to convolution with a non-trivial transfer function. Within the standard thermal history, shifts in the temperature-redshift relation combine with damping effects by free streaming neutrinos to non-trivially process different wavelengths during radiation domination, with subsequently negligible effects at later times. Presuming a nearly scale invariant primordial spectrum, one obtains a characteristic late time spectrum, deviations from which would indicate departures from the standard thermal history. Given the paucity of probes of the early universe physics before nucleosynthesis, it is useful to classify how deviations from the standard thermal history of the early universe can be constrained from observations of the late time stochastic background. The late time spectral density has a plateau at high frequencies that can in principle be significantly enhanced or suppressed relative to the standard thermal history depending on the equation of state of the epoch intervening reheating and the terminal phase of radiation domination, imprinting additional features from bursts of entropy production, and additional damping at intermediate scales via anisotropic stress production. In this paper, we survey phenomenologically motivated scenarios of early matter domination, kination, and late time decaying particles as representative non-standard thermal histories, elaborate on their late time stochastic background, and discuss constraints on different model scenarios.

astro-ph.CO↗

arXiv2024

Network Renormalization

The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling constants, across different levels of resolution. It also provides a way to identify critical points of phase transitions and study the system's behaviour around them by distinguishing between relevant and irrelevant details, the latter being unnecessary to describe the emergent macroscopic properties. In traditional physical applications, the RG largely builds on the notions of homogeneity, symmetry, geometry and locality to define metric distances, scale transformations and self-similar coarse-graining schemes. More recently, various approaches have tried to extend RG concepts to the ubiquitous realm of complex networks where explicit geometric coordinates do not necessarily exist, nodes and subgraphs can have very different properties, and homogeneous lattice-like symmetries are absent. The strong heterogeneity of real-world networks significantly complicates the definition of consistent renormalization procedures. In this review, we discuss the main attempts, the most important advances, and the remaining open challenges on the road to network renormalization.

cond-mat.stat-mech↗

arXiv2024

An Étude on the Regularization and Renormalization of Divergences in Primordial Observables

Many cosmological observables of interest derive from primordial vacuum fluctuations evolved to late times. These observables represent statistical draws from some underlying quantum or statistical field theoretic framework where infinities arise and require regularization. After subtracting divergences, renormalization conditions must be imposed by measurements or observations at some scale, mindful of scheme and background dependence. We review this process on backgrounds that transition from finite duration inflation to radiation domination, and show how in spite of the ubiquity of scaleless integrals, UV divergences can still be meaningfully extracted from quantities that nominally vanish when dimensionally regularized. In this way, one can contextualize calculations with hard cutoffs, distinguishing between UV and IR scales corresponding to the beginning and end of inflation from UV and IR scales corresponding the unknown completion of the theory and its observables. This distinction has significance as observable quantities cannot depend on the latter although they will certainly depend on the former. One can also explicitly show the scheme independence of the coefficients of UV divergent logarithms. Furthermore, certain IR divergences can be shown to be an artifact of the de Sitter limit and are cured for finite duration inflation. For gravitational wave observables, we stress the need to regularize stress tensors that do not presume a prior scale separation in their construction (as with the standard Isaacson form), deriving an improved stress tensor fit to purpose. We conclude by highlighting the inextricable connection between inferring $N_{\rm eff}$ bounds from vacuum tensor perturbations and the process of background renormalization.

hep-th↗

arXiv2024

Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes

Primordial black holes (PBHs) can be produced by a range of mechanisms in the early universe. A particular formation channel that connects PBHs with inflationary phenomenology invokes enhanced primordial curvature perturbations at small scales. In this paper, we examine how rapidly the background can transition between different values of the parameters of the Hubble hierarchy in the context of single-clock inflation, which must ultimately derive from a consistent derivative expansion for the background inflaton field. We discuss artefacts associated with instant or very rapid transitions, and consider the impact on the steepest power spectrum growth and the formation of PBHs. In particular, we highlight the robustness of the $k^4$ steepest growth previously found for single-field inflation with conservatively smoothed transitions and limits on how much the amplitude of the power spectrum can grow, and demonstrate that the PBH mass distribution is sensitive to the artefacts, which go away when the transitions are smoothed. We also show that the mass distribution is relatively insensitive to the steepness of the growth and subsequent decay of the power spectrum, depending primarily on the peak amplitude and the presence of any plateaus that last more than an e-fold. The shape of the power spectrum can of course be constrained by other tracers, and so understanding the physical limitations on its shape remains a pertinent question.

astro-ph.CO↗

arXiv2024

Hadamard Regularization of the Graviton Stress Tensor

We present the details for the covariant renormalization of the stress tensor for vacuum tensor perturbations at the level of the effective action, adopting Hadamard regularization techniques to isolate short distance divergences and gauge fixing via the Faddeev-Popov procedure. The subsequently derived renormalized stress tensor can be related to more familiar forms reliant upon an averaging prescription, such as the Isaacson or Misner-Thorne-Wheeler forms. The latter, however, are premised on a prior scale separation (beyond which the averaging is invoked) and therefore unsuited for the purposes of renormalization. This can lead to potentially unphysical conclusions when taken as a starting point for the computation of any observable that needs regularization, such as the energy density associated to a stochastic background. Any averaging prescription, if needed, should only be invoked at the end of the renormalization procedure. The latter necessarily involves the imposition of renormalization conditions via a physical measurement at some fixed scale, which we retrace for primordial gravitational waves sourced from vacuum fluctuations through direct or indirect observation.

hep-th↗

arXiv2023

Disentangling the primordial nature of stochastic gravitational wave backgrounds with CMB spectral distortions

The recent detection of a stochastic gravitational wave background (SGWB) at nanohertz frequencies by pulsar timing arrays (PTAs) has sparked a flurry of interest. Beyond the standard interpretation that the progenitor is a network of supermassive black hole binaries, many exotic models have also been proposed, some of which can potentially offer a better fit to the data. We explore how the various connections between gravitational waves and CMB spectral distortions can be leveraged to help determine whether a SGWB was generated primordially or astrophysically. To this end, we present updated $k$-space window functions which can be used for distortion parameter estimation on enhancements to the primordial scalar power spectrum. These same enhancements can also source gravitational waves (GWs) directly at second order in perturbation theory, so-called scalar-induced GWs (SIGWs), and indirectly through the formation of primordial black holes (PBHs). We perform a mapping of scalar power spectrum constraints into limits on the GW parameter space of SIGWs for $δ$-function features. We highlight that broader features in the scalar spectrum can explain the PTA results while simultaneously producing a spectral distortion (SD) within reach of future experiments. We additionally update PBH constraints from $μ$- and $y$-type spectral distortions. Refined treatments of the distortion window functions widen existing SD constraints, and we find that a future CMB spectrometer could play a pivotal role in unraveling the origin of GWs imprinted at or below CMB anisotropy scales.

astro-ph.CO↗

arXiv2023

Primordial black holes from single-field inflation: a fine-tuning audit

All single-field inflationary models invoke varying degrees of tuning in order to account for cosmological observations. Mechanisms that generate primordial black holes (PBHs) from enhancement of primordial power at small scales posit inflationary potentials that transiently break scale invariance and possibly adiabaticity over a range of modes. This requires additional tuning on top of that required to account for observations at scales probed by cosmic microwave background (CMB) anisotropies. In this paper we study the parametric dependence of various single-field models of inflation that enhance power at small scales and quantify the degree to which coefficients in the model construction have to be tuned in order for certain observables to lie within specified ranges. We find significant tuning: changing the parameters of the potentials by between one part in a hundred and one part in $10^8$ (depending on the model) is enough to change the power spectrum peak amplitude by an order one factor. The fine-tuning of the PBH abundance is larger still by 1-2 orders of magnitude. We highlight the challenges imposed by this tuning on any given model construction. Furthermore, polynomial potentials appear to require significant additional fine-tuning to also match the CMB observations.

astro-ph.CO↗

arXiv2022

Phases of Small Worlds: A Mean Field Formulation

A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the small-world property for Gilbert-Erdös-Renyi random networks. We employ a mean field approximation that permits the analytic derivation of the distribution of shortest paths that exhibits logarithmic scaling away from the phase transition, inferable via a suitably interpreted order parameter. We begin by framing the problem in generality with a formal generating functional for undirected weighted random graphs with arbitrary disorder, recovering the result that the free energy associated with an ensemble of Gilbert graphs corresponds to a system of non-interacting fermions identified with the edge states. We then present a mean field solution for this model and extend it to more general realizations of network randomness. For a two family class of stochastic block models that we refer to as dimorphic networks, which allow for links within the different families to be drawn from two independent discrete probability distributions, we find the mean field approximation maps onto a spin chain combinatorial problem and again yields useful approximate analytic expressions for mean path lengths. Dimorophic networks exhibit a richer phase structure, where distinct small world regimes separate in analogy to the spinodal decomposition of a fluid. We find that is it possible to induce small world behavior in sub-networks that by themselves would not be in the small-world regime.

cond-mat.stat-mech↗

arXiv2022

Galaxy number-count dipole and superhorizon fluctuations

In view of the growing tension between the dipole anisotropy of number counts of cosmologically distant sources and of the cosmic microwave background (CMB), we investigate the number count dipole induced by primordial perturbations with wavelength comparable to or exceeding the Hubble radius today. First, we find that neither adiabatic nor isocurvature superhorizon modes can generate an intrinsic number count dipole. However a superhorizon isocurvature mode does induce a relative velocity between the CMB and the (dark) matter rest frames and thereby affects the CMB dipole. We revisit the possibility that it has an intrinsic component due to such a mode, thus enabling consistency with the galaxy number count dipole if the latter is actually kinematic in origin. Although this scenario is not particularly natural, there are possible links with other anomalies and it predicts a concommitant galaxy number count quadrupole which may be measurable in future surveys. We also investigate the number count dipole induced by modes smaller than the Hubble radius, finding that subject to CMB constraints this is too small to reconcile the dipole tension.

astro-ph.CO↗

arXiv2022

Primordial tensor bispectra in $μ$-CMB cross-correlations

Cross-correlations between Cosmic Microwave Background (CMB) temperature and polarization anisotropies and $μ$-spectral distortions have been considered to measure (squeezed) primordial scalar bispectra in a range of scales inaccessible to primary CMB bispectra. In this work we address whether it is possible to constrain tensor non-Gaussianities with these cross-correlations. We find that only primordial tensor bispectra with statistical anisotropies leave distinct signatures, while isotropic tensor bispectra leave either vanishing or highly suppressed signatures. We discuss how the angular dependence of squeezed bispectra in terms of the short and long momenta determine the non-zero cross-correlations. We also discuss how these non-vanishing configurations are affected by the way in which primordial bispectra transform under parity. By employing the so-called BipoSH formalism to capture the observational effects of statistical anisotropies, we make Fisher-forecasts to assess the detection prospects from $μT$, $μE$ and $μB$ cross-correlations. Observing statistical anisotropies in squeezed $\langle γγγ\rangle$ and $\langle γγζ\rangle$ bispectra is going to be challenging as the imprint of tensor perturbations on $μ$-distortions is subdominant to scalar perturbations, therefore requiring a large, independent amplification of the effect of tensor perturbations in the $μ$-epoch. In absence of such a mechanism, statistical anisotropies in squeezed $\langle ζζγ\rangle$ bispectrum are the most relevant sources of $μT$, $μE$ and $μB$ cross-correlations. In particular, we point out that in anisotropic inflationary models where $\langle ζζζ\rangle$ leaves potentially observable signatures in $μT$ and $μE$, the detection prospects of $\langle ζζγ\rangle$ from $μB$ are enhanced.

astro-ph.CO↗

arXiv2021

Backreaction of Schwinger pair creation in massive QED$_2$

Particle-antiparticle pairs can be produced by background electric fields via the Schwinger mechanism provided they are unconfined. If, as in QED in (3+1)-$d$ these particles are massive, the particle production rate is exponentially suppressed below a threshold field strength. Above this threshold, the energy for pair creation must come from the electric field itself which ought to eventually relax to the threshold strength. Calculating this relaxation in a self-consistent manner, however, is difficult. Chu and Vachaspati addressed this problem in the context of capacitor discharge in massless QED$_2$ [1] by utilizing bosonization in two-dimensions. When the bare fermions are massless, the dual bosonized theory is free and capacitor discharge can be analyzed exactly [1], however, special care is required in its interpretation given that the theory exhibits confinement. In this paper we reinterpret the findings of [1], where the capacitors Schwinger-discharge via electrically neutral dipolar meson-production, and generalize this to the case where the fermions have bare masses. Crucially, we note that when the initial charge of the capacitor is large compared to the charge of the fermions, $Q \gg e$, the classical equation of motion for the bosonized model accurately characterizes the dynamics of discharge. For massless QED$_2$, we find that the discharge is suppressed below a critical plate separation that is commensurate with the length scale associated with the meson dipole moment. For massive QED$_2$, we find in addition, a mass threshold familiar from (3+1)-$d$, and show the electric field relaxes to a final steady state with a magnitude proportional to the initial charge. We discuss the wider implications of our findings and identify challenges in extending this treatment to higher dimensions.

hep-th↗

arXiv2021

Bridging the gap: spectral distortions meet gravitational waves

Gravitational waves (GWs) have the potential to probe the entirety of cosmological history due to their nearly perfect decoupling from the thermal bath and any intervening matter after emission. In recent years, GW cosmology has evolved from merely being an exciting prospect to an actively pursued avenue for discovery, and the early results are very promising. As we highlight in this paper, spectral distortions (SDs) of the cosmic microwave background (CMB) uniquely probe GWs over six decades in frequency, bridging the gap between astrophysical high- and cosmological low-frequency measurements. This means SDs will not only complement other GW observations, but will be the sole probe of physical processes at certain scales. To illustrate this point, we explore the constraining power of various proposed SD missions on a number of phenomenological scenarios: early-universe phase transitions (PTs), GW production via the dynamics of SU(2) and ultra-light U(1) axions, and cosmic string (CS) network collapse. We highlight how some regions of parameter space were already excluded with data from COBE/FIRAS, taken over two decades ago. To facilitate the implementation of SD constraints in arbitrary models we provide GW2SD. This tool calculates the window function, which easily maps a GW spectrum to a SD amplitude, thus opening another portal for GW cosmology with SDs, with wide reaching implications for particle physics phenomenology.

astro-ph.CO↗

arXiv2021

Clarifying transfer function approximations for the large-scale gravitational wave background in $Λ$CDM

The primordial gravitational wave background (GWB) offers an exciting future avenue of discovery for new physics. Its information content encodes multiple eras in the early Universe's history, corresponding to many orders of magnitude in frequency and physical scale to be measured today. By numerically solving for the GW transfer functions we provide simple yet accurate formulas describing the average power of the large-scale energy spectrum of the GWB for arbitrary primordial tensor power spectra. In doing so we can pedagogically explain and clarify previous GWB literature, highlight the important cosmological parameters of various GWB features, and reveal multiple ways in which cancelling conceptual errors can give deceptively accurate results. The scales considered here are particularly important for CMB probes of the GWB, via $B$-modes and spectral distortions. In particular, we carefully study the effects of both neutrino damping, and the precise nature of the transition between the radiation-dominated (RD) and matter-dominated (MD) eras. A byproduct of numerically solving the problem is the ability to study the robustness of common approximations in the literature. Specifically, we show that a numerical treatment is especially important around the RD--MD transition, and for a brief moment of history where neutrino damping occurs during MD. In passing we also discuss the effects of late acceleration caused by dark energy -- showing that this can be neglected in most practical GWB applications -- and the effects of changing relativistic degrees of freedom on the GWB at very small-scales.

astro-ph.CO↗

arXiv2021

Multi-messenger Probes of Inflationary Fluctuations and Primordial Black Holes

Next generation cosmic microwave background spectral distortion and pulsar timing array experiments have the potential to probe primordial fluctuations at small scales with remarkable sensitivity. We demonstrate the potential of these probes to either detect signatures of primordial black holes (PBHs) sourced from primordial overdensities within the standard thermal history of the universe over a 13-decade mass range ${\cal O}(0.1-10^{12})M_\odot$, or constrain their existence to a negligible abundance. Our conclusions are based only on global cosmological signals, and are robust under changes in i) the statistical properties of the primordial density fluctuations (whether Gaussian or non-Gaussian), ii) the merger and accretion history of the PBHs and assumptions about associated astrophysical processes, and iii) clustering statistics. Any positive detection of enhanced primordial fluctuations at small scales would have far-reaching implications from the content of dark matter to origin of BHs in the centers of galaxies, and to the field content of the inflation. On the other hand, their non-detection would also have important corollaries. For example, non-detection up to forecast sensitivities would tell us that PBHs larger than a fraction of a solar mass can constitute no more than a negligible fraction of dark matter. Moreover, non-detection will also rule out the scenario that PBHs generated by primordial overdensities could be the progenitors of super-massive black holes (SMBHs), of topical interest as there are only a few widely accepted proposals for the formation of SMBHs, an even more pressing question after the detection of active galactic nuclei over a billion solar masses at redshifts $z \geq 7$. Finally, non-detection sets the strongest bounds on the amplitude of small scale inflationary fluctuations for over 6 decades.

astro-ph.CO↗

arXiv2019

Microwave Spectro-Polarimetry of Matter and Radiation across Space and Time

This paper discusses the science case for a sensitive spectro-polarimetric survey of the microwave sky. Such a survey would provide a tomographic and dynamic census of the three-dimensional distribution of hot gas, velocity flows, early metals, dust, and mass distribution in the entire Hubble volume, exploit CMB temperature and polarisation anisotropies down to fundamental limits, and track energy injection and absorption into the radiation background across cosmic times by measuring spectral distortions of the CMB blackbody emission. In addition to its exceptional capability for cosmology and fundamental physics, such a survey would provide an unprecedented view of microwave emissions at sub-arcminute to few-arcminute angular resolution in hundreds of frequency channels, a data set that would be of immense legacy value for many branches of astrophysics. We propose that this survey be carried-out with a large space mission featuring a broad-band polarised imager and a moderate resolution spectro-imager at the focus of a 3.5m aperture telescope actively cooled to about 8K, complemented with absolutely-calibrated Fourier Transform Spectrometer modules observing at degree-scale angular resolution in the 10-2000 GHz frequency range. We propose two observing modes: a survey mode to map the entire sky as well as a few selected wide fields, and an observatory mode for deeper observations of regions of specific interest.

astro-ph.CO↗