Scale Invariant Research Articles

A Survey of Dynamical and Gravitational Lensing Tests in Scale Invariance: The Fall of Dark Matter?

We first briefly review the adventure of scale invariance in physics, from Galileo Galilei, Weyl, Einstein, and Feynman to the revival by Dirac (1973) and Canuto et al. (1977). In the way that the geometry of space–time can be described by the coefficients gμν, a gauging condition given by a scale factor λ(xμ) is needed to express the scaling. In general relativity (GR), λ=1. The “Large Number Hypothesis” was taken by Dirac and by Canuto et al. to fix λ. The condition that the macroscopic empty space is scale-invariant was further preferred (Maeder 2017a), the resulting gauge is also supported by an action principle. Cosmological equations and a modified Newton equation were then derived. In short, except in extremely low density regions, the scale-invariant effects are largely dominated by Newtonian effects. However, their cumulative effects may still play a significant role in cosmic evolution. The theory contains no “adjustment parameter”. In this work, we gather concrete observational evidence that scale-invariant effects are present and measurable in astronomical objects spanning a vast range of masses (0.5 M⊙< M <1014M⊙) and an equally impressive range of spatial scales (0.01 pc < r < 1 Gpc). Scale invariance accounts for the observed excess in velocity in galaxy clusters with respect to the visible mass, the relatively flat/small slope of rotation curves in local galaxies, the observed steep rotation curves of high-redshift galaxies, and the excess of velocity in wide binary stars with separations above 3000 kau found in Gaia DR3. Last but not least, we investigate the effect of scale invariance on gravitational lensing. We show that scale invariance does not affect the geodesics of light rays as they pass in the vicinity of a massive galaxy. However, scale-invariant effects do change the inferred mass-to-light ratio of lens galaxies as compared to GR. As a result, the discrepancies seen in GR between the total lensing mass of galaxies and their stellar mass from photometry may be accounted for. This holds true both for lenses at high redshift like JWST-ER1 and at low redshift like in the SLACS sample. Of note is that none of the above observational tests require dark matter or any adjustable parameter to tweak the theory at any given mass or spatial scale.

Rotating AdS3× S3 and dyonic strings from 3-dimensions

We make a general Killing spinor analysis of a particular D = 3, N = 4 gauged supergravity that comes from a consistent S3 reduction of D = 6, N = (1, 0) supergravity coupled to a single chiral tensor multiplet. We then focus on its supersymmetric solutions with a null Killing vector and find three new ones. Two of these, namely the null warped AdS3 (also known as the Schrödinger spacetime) and the charged domain wall solutions, admit non-trivial gauge fields which give rise to rotating solutions in 6-dimensions. The uplift of the first one produces an interesting AdS3 × S3 background with a non-trivial rotation in the U(1) fiber direction of the S3 which retains the Schrödinger scale invariance that the seed solution has. The second one leads to the well-known rotating dyonic string solution. Finally, the uplift of the third one, which is a domain wall solution with no gauge fields, results in a distribution of dyonic strings.

An Uncertain Perspective on Consciousness

This should be considered as an addendum to Fundamental Cosmology and Physics Beyond the Standard Model [1] and ideas from pilot/wave theory [2]. It is more accurate to say that this is a philosophical perspective that comes from common basic observations and we can give a simple demonstration of this Pilot Wave theory by showing several examples of scale invariance [3]. It is not only just at the smallest levels of quantum mechanics we can observe these properties. Consider large flocks of birds or schools of fish moving together at the human scales of perception. We may show each bird is a particle being piloted by the wave of birds in the flock. But, each bird is also a small part of the wave and has the freedom to change the waveform simultaneously, dynamically. As some might say, “That’s all there is folks.” A living fish or bird, with simpleconsciousness, can change the waveform based on internal freewill. There is something happening internally that sets life apart from that which can only be influenced externally. Life has internal dynamics. Particles interacting at the sub-atomic level have no choice in their interaction with the waveform, as this is solely influenced by its own (external) properties. Indeed there is a Markov blanket separating internal and external states. There is a repeating pattern of scale invariance when comparing brain holography theory and ADS-CFT correspondence [4], as black hole holography, as we will show.

Fractional Brownian motion in confining potentials: non-equilibrium distribution tails and optimal fluctuations

Abstract At long times, a fractional Brownian particle in a confining external potential reaches a non-equilibrium (non-Boltzmann)
steady state. Here we consider scale-invariant power-law potentials $V(x)\sim |x|^m$, where $m>0$, and employ the optimal fluctuation method (OFM) to determine the large-$|x|$ tails of the steady-state probability distribution $\mathcal{P}(x)$ of the particle position. The calculations involve finding the optimal (that is, the most likely) path of the particle, which determines these tails, via a minimization of the exact action functional for this system, which has recently become available. Exploiting dynamical scale invariance of the model in conjunction with the OFM ansatz, we establish the large-$|x|$ tails of $\ln \mathcal{P}(x)$ up to a dimensionless factor $\alpha(H,m)$, where $0<H<1$ is the Hurst exponent. We determine $\alpha(H,m)$ analytically (i) in the limits of $H\to 0$ and $H\to 1$, and (ii) for $m=2$ and arbitrary $H$, corresponding to the fractional Ornstein-Uhlenbeck (fOU) process. Our results for the fOU process are in agreement with the previously known exact $\mathcal{P}(x)$ and autocovariance. The form of the tails of $\mathcal{P}(x)$ yields exact conditions, in terms of $H$ and $m$, for the particle confinement in the potential.
For $H\neq 1/2$, the tails encode the non-equilibrium character of the steady state distribution, and we observe violation of time reversibility of the system except for $m=2$. To compute the optimal paths and the factor $\alpha(H,m)$ for arbitrary permissible $H$ and $m$, one needs to solve an (in general nonlinear) integro-differential equation. To this end we develop a specialized numerical iteration algorithm which
accounts analytically for an intrinsic cusp singularity of the optimal paths for $H<1/2$.


Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio B w 2 / B w 1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

Odd Viscosity Suppresses Intermittency in Direct Turbulent Cascades.

Intermittency refers to the broken self-similarity of turbulent flows caused by anomalous spatiotemporal fluctuations. In this Letter, we ask how intermittency is affected by a nondissipative viscosity, known as odd viscosity (also Hall viscosity or gyroviscosity), which appears in parity-breaking fluids such as magnetized polyatomic gases, electron fluids under magnetic field, and spinning colloids or grains. Using a combination of Navier-Stokes simulations and theory, we show that intermittency is suppressed by odd viscosity at small scales. This effect is caused by parity-breaking waves, induced by odd viscosity, that break the multiple scale invariances of the Navier-Stokes equations. Building on this insight, we construct a two-channel helical shell model that reproduces the basic phenomenology of turbulent odd-viscous fluids including the suppression of anomalous scaling. Our findings illustrate how a fully developed direct cascade that is entirely self-similar can emerge below a tunable length scale, paving the way for designing turbulent flows with adjustable levels of intermittency.

Ladder top-quark condensation imprints in supercooled electroweak phase transition

The electroweak (EW) phase transition in the early Universe might be supercooled due to the presence of the classical scale invariance involving Beyond the Standard Model (BSM) sectors and the supercooling could persist down till a later epoch around which the QCD chiral phase transition is supposed to take place. Since this supercooling period keeps masslessness for all the six SM quarks, it has simply been argued that the QCD phase transition is the first order, and so is the EW one. However, not only the QCD coupling but also the top Yukawa and the Higgs quartic couplings get strong at around the QCD scale due to the renormalization group running, hence this scenario is potentially subject to a rigorous nonperturbative analysis. In this work, we employ the ladder Schwinger-Dyson (LSD) analysis based on the Cornwall-Jackiw-Tomboulis formalism at the two-loop level in such a gauge-Higgs-Yukawa system. We show that the chiral broken QCD vacuum emerges with the nonperturbative top condensate and the lightness of all six quarks is guaranteed due to the accidental U(1) axial symmetry presented in the top-Higgs sector. We employ a quark-meson model-like description in the mean field approximation to address the impact on the EW phase transition arising due to the top quark condensation at the QCD phase transition epoch. In the model, the LSD results are encoded to constrain the model parameter space. We then observe the cosmological phase transition of the first-order type and discuss the induced gravitational wave (GW) productions. We find that in addition to the conventional GW signals sourced from an expected BSM at around or over the TeV scale, the dynamical topponium-Higgs system can yield another power spectrum sensitive to the BBO, LISA, and DECIGO, etc.

A note on Weyl gauge symmetry in gravity

Abstract A scale invariant theory of gravity, containing at most two derivatives, requires, in addition to the Riemannian metric, a scalar field and (or) a gauge field. The gauge field is usually used to construct the affine connection of Weyl geometry. In this note, we incorporate both the gauge field and the scalar field to build a generalised scale invariant Weyl affine connection. The Ricci tensor and the Ricci scalar made out of this generalised Weyl affine connection contain, naturally, kinetic terms for the scalar field and the gauge field. This provides a geometric interpretation for these terms. It is also shown that scale invariance in the presence of a cosmological constant and mass terms is not completely lost. It becomes a duality transformation relating various fields.

About Jordan and Einstein Frames: A Study in Inflationary Magnetogenesis

In this paper, we make a detailed side-by-side comparison between Jordan and Einstein frames in the context of cosmic magnetogenesis. We have computed the evolution of the vector potential in each frame along with some observables such as the spectral index and the magnetic field amplitude. We found that contrary to the Einstein frame, the electric and magnetic energy densities in the Jordan Frame do not depend on any parameter associated with the scalar field. Furthermore, in the Einstein frame, and assuming scale invariance for the magnetic field, most of the total energy density contribution comes from the electric and magnetic densities. Finally, we show the ratio between magnetic field signals in both frames printed in the CMB.

Highly robust thermal infrared and visible image registration with canny and phase congruence detection

When a dual-optical vehicle-mounted camera is photographed, visible and thermal infrared (VI-T) images cannot be registered, and realising fine matching of the images to solve for the optimal affine parameters is thus key to this research. Visible and thermal image matching is of great interest owing to the presence of challenging scale transformations, nonlinear radial aberrations, and robustness under illumination conditions. Thus, this paper presents a novel algorithm, namely, Highly Robust Thermal Infrared and Visible Image Registration with Canny and Phase Congruence Detection (HRCP). Firstly, the image is pre-processed, and feature point detection is performed by combining adaptive thresholding GW-Canny edge detection and phase coherence (PC), which increases the edge information. Secondly, SURF and FAST feature detection at the maximum distance of PC maps can obtain stable and reliable feature points, which are robust to scale invariance and rotation invariance. Finally, the optimal affine parameter is solved using the least square method with several iterations. Compared to existing matching methods, we find that VI-T image matching is particularly sensitive to both lighting factors and scale-transformed nonlinear radial distortion and that HRCP is robust in performing matching. For the randomly selected dataset, the average image matching time is reduced by 3.265 s, the number of correct image matches increases by 44 pairs on average, the root mean square error improves to 1.830, and the average error improves to 2.815. The proposed method not only improves the inaccuracy of radiation-insensitive feature transform matching in both low and high light, but also achieves a higher accuracy and an increase in the number of feature matching points, which facilitates robust VI-T image registration.

Mean-field dynamics of the non-consensus opinion model

In 2009, Shao et al. (Phys Rev Lett 103(1):018701, 2009) introduced the Non-consensus opinion (NCO) model, which allows different opinions to coexist in the steady state. We propose a mean-field-based dynamical model for the NCO model on networks with low degree correlation, which reveals the mechanism of opinion formation in the NCO model. This mean-field model provides a new way of estimating important system properties such as the fraction of a certain opinion F, the critical threshold fc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_c$$\\end{document}, and the size of the largest connected cluster for a given opinion s1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_1$$\\end{document}. It offers an accurate estimation in less time than the Monte Carlo simulations. The scale invariance of the NCO model is discussed. The variation in the degree of nodes holding different opinions in the dynamics of the NCO model is investigated. The trends in the dynamics of the NCO model are also revealed. This approach can be applied to real-world social networks, providing a method of analyzing opinion dynamics in human society.

Exploring the conformal transition from above and below

We consider conformal transitions arising from the merging of IR and UV fixed points, expected to occur in QCD with a large enough number of flavors. We study the smoothness of physical quantities across this transition, being mostly determined by the logarithmic breaking of conformal invariance. We investigate this explicitly using holography where approaching the conformal transition either from outside or inside the conformal window (perturbed by a mass term) is characterized by the same dynamics. The mass of spin-1 mesons and Fπ are shown to be continuous across the transition, as well as the dilaton mass. This implies that the lightness of the dilaton cannot be a consequence of the spontaneous breaking of scale invariance when leaving the conformal window. Our analysis suggests that the light scalar observed in QCD lattice simulations is a qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} meson that becomes light since the qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document}-operator dimension reaches its minimal value.

Logarithmic correlation functions in 2D critical percolation

It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities and to find an explanation and a physical interpretation, in terms of lattice observables, for their appearance. We show that certain percolation correlation functions receive independent contributions from a large number of similar connectivity events happening at different scales. Combined with scale invariance, this leads to logarithmic divergences. We study several logarithmic correlation functions for critical percolation in the bulk and in the presence of a boundary, including the four-point function of the density (spin) field. Our analysis confirms previous findings, provides new explicit calculations and explains, in terms of lattice observables, the physical mechanism that leads to the logarithmic singularities we discover. Although we adopt conformal field theory (CFT) terminology to present our results, the core of our analysis relies on probabilistic arguments and recent rigorous results on the scaling limit of critical percolation and does not assume a priori the existence of a percolation CFT. As a consequence, our results provide strong support for the validity of a CFT description of critical percolation and a step in the direction of a mathematically rigorous formulation of a logarithmic CFT of two-dimensional critical percolation.

Physics and chemistry from parsimonious representations: image analysis via invariant variational autoencoders

Electron, optical, and scanning probe microscopy methods are generating ever increasing volume of image data containing information on atomic and mesoscale structures and functionalities. This necessitates the development of the machine learning methods for discovery of physical and chemical phenomena from the data, such as manifestations of symmetry breaking phenomena in electron and scanning tunneling microscopy images, or variability of the nanoparticles. Variational autoencoders (VAEs) are emerging as a powerful paradigm for the unsupervised data analysis, allowing to disentangle the factors of variability and discover optimal parsimonious representation. Here, we summarize recent developments in VAEs, covering the basic principles and intuition behind the VAEs. The invariant VAEs are introduced as an approach to accommodate scale and translation invariances present in imaging data and separate known factors of variations from the ones to be discovered. We further describe the opportunities enabled by the control over VAE architecture, including conditional, semi-supervised, and joint VAEs. Several case studies of VAE applications for toy models and experimental datasets in Scanning Transmission Electron Microscopy are discussed, emphasizing the deep connection between VAE and basic physical principles. Python codes and datasets discussed in this article are available at https://github.com/saimani5/VAE-tutorials and can be used by researchers as an application guide when applying these to their own datasets.

Self-similar blow-up solutions in the generalised Korteweg-de Vries equation: spectral analysis, normal form and asymptotics

In the present work we revisit the problem of the generalised Korteweg–de Vries equation parametrically, as a function of the relevant nonlinearity exponent, to examine the emergence of blow-up solutions, as traveling waveforms lose their stability past a critical point of the relevant parameter p, here at p = 5. We provide a normal form of the associated collapse dynamics, and illustrate how this captures the collapsing branch bifurcating from the unstable traveling branch. We also systematically characterise the linearisation spectrum of not only the traveling states, but importantly of the emergent collapsing waveforms in the so-called co-exploding frame where these waveforms are identified as stationary states. This spectrum, in addition to two positive real eigenvalues which are shown to be associated with the symmetries of translation and scaling invariance of the original (non-exploding) frame features complex patterns of negative eigenvalues that we also fully characterise. We show that the phenomenology of the latter is significantly affected by the boundary conditions and is far more complicated than in the corresponding symmetric Laplacian case of the nonlinear Schrödinger problem that has recently been explored. In addition, we explore the dynamics of the unstable solitary waves for p > 5 in the co-exploding frame.

Automated cell lineage reconstruction using label-free 4D microscopy.

Patterns of lineal descent play a critical role in the development of metazoan embryos. In eutelic organisms that generate a fixed number of somatic cells, invariance in the topology of their cell lineage provides a powerful opportunity to interrogate developmental events with empirical repeatability across individuals. Studies of embryonic development using the nematode Caenorhabditis elegans have been drivers of discovery. These studies have depended heavily on high-throughput lineage tracing enabled by 4D fluorescence microscopy and robust computer vision pipelines. For a range of applications, computer-aided yet manual lineage tracing using 4D label-free microscopy remains an essential tool. Deep learning approaches to cell detection and tracking in fluorescence microscopy have advanced significantly in recent years, yet solutions for automating cell detection and tracking in 3D label-free imaging of dense tissues and embryos remain inaccessible. Here, we describe embGAN, a deep learning pipeline that addresses the challenge of automated cell detection and tracking in label-free 3D time-lapse imaging. embGAN requires no manual data annotation for training, learns robust detections that exhibits a high degree of scale invariance, and generalizes well to images acquired in multiple labs on multiple instruments. We characterize embGAN's performance using lineage tracing in the C. elegans embryo as a benchmark. embGAN achieves near-state-of-the-art performance in cell detection and tracking, enabling high-throughput studies of cell lineage without the need for fluorescent reporters or transgenics.

Testing for Markovian character of transfer of fluctuations in solar wind turbulence on kinetic scales.

We apply statistical analysis to search for processes responsible for turbulence in physical systems. In our previous studies, we have shown that solar wind turbulence in the inertial range of large magnetohydrodynamic scales exhibits Markov properties. We have recently extended this approach on much smaller kinetic scales. Here we are testing for the Markovian character of stochastic processes in a kinetic regime based on magnetic field and velocity fluctuations in the solar wind, measured onboard the Magnetospheric Multiscale (MMS) mission: behind the bow shock, inside the magnetosheath, and near the magnetopause. We have verified that the Chapman-Kolmogorov necessary conditions for Markov processes is satisfied for local transfer of energy between the magnetic and velocity fields also on kinetic scales. We have confirmed that for magnetic fluctuations, the first Kramers-Moyal coefficient is linear, while the second term is quadratic, corresponding to drift and diffusion processes in the resulting Fokker-Planck equation. It means that magnetic self-similar turbulence is described by generalized Ornstein-Uhlenbeck processes. We show that for the magnetic case, the Fokker-Planck equationleads to the probability density functions of the kappa distributions, which exhibit global universal scale invariance with a linear scaling and lack of intermittency. On the contrary, for velocity fluctuations, higher order Kramers-Moyal coefficients should be taken into account and hence scale invariance is not observed. However, the nonextensity parameter in Tsallis entropy provides a robust measure of the departure of the system from equilibrium. The obtained results are important for a better understanding of the physical mechanism governing turbulent systems in space and laboratory.

Dilaton forbidden dark matter

Dilaton effective field theory (dEFT) describes the long distance behavior of certain confining, near-conformal gauge theories that have been studied via lattice computation. Pseudo-Nambu- Goldstone bosons (pNGBs), emerging from the breaking of approximate, continuous, internal symmetries, are coupled to an additional scalar particle, the dilaton, arising from the spontaneous breaking of approximate scale invariance. This effective theory has been employed to study possible extensions of the standard model. In this paper, we propose a complementary role for dEFT, as a description of the dark matter of the Universe, with the pNGBs identified as the dark matter particles. We show that this theory provides a natural implementation of the “forbidden” dark matter mechanism, and we identify regions of parameter space for which the thermal history of dEFT yields the measured dark matter relic density. Published by the American Physical Society 2024

Scale and conformal invariance on (A)dS spacetimes

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general two-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension D>4, these conformal theories can be diagonalized into standard massive fields in which unbroken conformal symmetry nontrivially mixes components of different spins. In D=4, the tensor case becomes a conformal theory mixing a partially massless spin-2 field with a massless spin-1 field. For massless linearized gravity in D=4, we confirm through direct calculation that correlation functions of gauge-invariant operators take the conformally invariant form, despite the absence of standard conformal symmetry at the level of the action. Published by the American Physical Society 2024

Scale invariance beyond criticality within the mean-field analysis of tensorial field theories

We continue the series of articles on the application of Landau-Ginzburg mean-field theory to unveil the basic phase structure of tensorial field theories which are characterized by combinatorially non-local interactions. Among others, this class covers tensor field theories (TFT) which lead to a new class of conformal field theories highly relevant for investigations on the AdS/CFT conjecture. Moreover, it also encompasses models within the tensorial group field theory (TGFT) approach to quantum gravity. Crucially, in the infrared we find that the effective mass of the modes relevant for the critical behavior vanishes not only at criticality but also throughout the entire phase of non-vanishing vacuum expectation value due to the non-locality of the interactions. As a consequence, one encounters there the emergence of scale invariance on configuration space which is potentially enhanced to conformal invariance thereon.