Spectrum Of Perturbations Research Articles

Probing the speed of scalar induced gravitational waves from observations

The propagation speed of gravitational waves is a fundamental issue in gravitational theory. According to general relativity, gravitational waves propagate at the speed of light. However, alternative theories of gravity propose modifications to general relativity, including variations in the speed of gravitational waves. In this paper, we investigate scalar-induced gravitational waves that propagate at speeds different from the speed of light. First, we analytically calculate the power spectrum of scalar induced gravitational waves based on the speed and spectrum of primordial curvature perturbations. We then explore several scalar power spectra, deriving corresponding fractional energy densities, including monochromatic spectrum, scale-invariant spectrum, and power-law spectrum. Finally, we constrain scalar-induced gravitational waves and evaluate the signatures of their speed from the combination of CMB+BAO and gravitational wave observations. Our numerical results clearly illustrate the influence of the speed of scalar-induced gravitational waves.

Shock-driven three-fluid mixing with various chevron interface configurations

When a shock wave crosses a density interface, the Richtmyer–Meshkov instability causes perturbations to grow. Richtmyer–Meshkov instabilities arise from the deposition of vorticity from the misaligned density and pressure gradients at the shock front. In many engineering applications, microscopic surface roughness will grow into multi-mode perturbations, inducing mixing between the fluid on either side of an initial interface. Applications often have multiple interfaces, some of which are close enough to interact in the later stages of instability growth. In this study, we numerically investigate the mixing of a three-layer system with periodic zigzag (or chevron) interfaces, calculating the dependence of the width and mass of mixed material on properties such as the shock timing, chevron amplitude, multi-mode perturbation spectrum, density ratio, and shock mach number. The multi-mode case is also compared with a single-mode perturbation. The Flash hydrodynamic code is used to solve the Euler equations in three dimensions with adaptive grid refinement. Key results include a significant increase in mixed mass when changing from a single-mode to a multi-mode perturbation on one of the interfaces. The mixed width is mainly sensitive to the density ratio and chevron amplitude, whereas the mixed mass also depends on the multi-mode spectrum. Steeper initial perturbation spectra have lower mixed mass at early times but a greater mixed mass after the reflected shock transits back across the layer.

Distinguishing bounce and inflation via quantum signatures from cosmic microwave background

Cosmological inflation is a popular paradigm for understanding Cosmic Microwave Background Radiation (CMBR); however, it faces many conceptual challenges. An alternative mechanism to inflation for generating an almost scale-invariant spectrum of perturbations is a bouncing cosmology with an initial matter-dominated contraction phase, during which the modes corresponding to currently observed scales exited the Hubble radius. Bouncing cosmology avoids the initial singularity but has fine-tuning problems. Taking an agnostic view of the two early-universe paradigms, we propose a quantum measure — Dynamical Fidelity Susceptibility (DFS) of CMBR — that distinguishes the two scenarios. Taking two simple models with the same power-spectrum, we explicitly show that DFS behaves differently for the two scenarios. We discuss the possibility of using DFS as a distinguisher in the upcoming space missions.

Dual inflation and bounce cosmologies interpretation of pulsar timing array data

We explore a dual scenario of generalized inflation and bounce cosmologies, producing a scale-invariant curvature perturbation spectrum. Bayesian analysis with pulsar timing array data identifies, for the first time, viable regions from inflation and bounce that simultaneously explain stochastic gravitational wave background (SGWB) signals and CMB anisotropies. Bayes factor calculations strongly favor this dual scenario over conventional sources and provide initial evidence of a duality between inflation and bounce regarding SGWB, offering new insights for early universe model-building and future observations.

Improved model of large-field inflation with primordial black hole production in Starobinsky-like supergravity

Abstract A viable model of large-field (chaotic) inflation with efficient production of primordial black holes is proposed in Starobinsky-like (modified) supergravity leading to the ‘no-scale-type’ Kähler potential and the Wess-Zumino-type (‘renormalizable’) superpotential. The cosmological tilts are in good (within 1σ) agreement with Planck measurements of the cosmic microwave background radiation. In addition, the power spectrum of scalar perturbations has a large peak at smaller scales, which leads to a production of primordial black holes from gravitational collapse of large perturbations with the masses about 1017 g. The masses are beyond the Hawking (black hole) evaporation limit of 1015 g, so that those primordial black holes may be viewed as viable candidates for a significant part or the whole of the current dark matter. The parameters of the superpotential were fine-tuned for those purposes, while the cubic term in the superpotential is essential whereas the quadratic term should vanish. The vacuum after inflation (relevant to reheating) is Minkowskian. The energy density fraction of the gravitational waves induced by the production of primordial black holes and their frequency were also calculated in the second order with respect to perturbations.

Application of High-Speed Self-Aligned Focusing Schlieren System for Supersonic Flow Velocimetry

A self-aligned focusing schlieren (SAFS) system combines the field of view of a conventional schlieren system with the defocus blur of a focusing schlieren system away from the object plane. It can be assembled in a compact form, measuring 1.2 m (4 ft) in length in the described case. The depth of field is sufficiently shallow to distinguish specific spanwise features in a supersonic flow field within a 76.2 mm (3 in) wide test section. As a result, the boundary-layer perturbations on windows and window-material defects and surface imperfections are blurred. Analytical forms are derived for depth of field and vignetting of the SAFS system. A laser spark velocity measurement in Mach 2 flow is performed by tracking the blast wave of a laser spark using 500 kHz SAFS imaging with a 200 ns optical pulse width. The flow Mach number and stagnation temperature are measured by comparing the blast-wave dynamics to an analytical solution. Additionally, schlieren image velocimetry is performed by analyzing natural flow perturbations in 500 kHz SAFS images using a self-correlation method. Comparing the spectra of gas density perturbations from the core flow and a near-wall region reveals a significant difference, with high-frequency prevalence at the boundary-layer location.

Constant-roll inflation with non-minimally derivative coupling

We investigate the constant-roll inflation with non-minimally kinetic coupling to the Einstein tensor. With the slow-roll parameter ηϕ=−ϕ̈/(Hϕ̇) being a constant, we calculate the power spectra for scalar and tensor perturbations, and derive the expressions for the scalar spectral tilt n s , the tensor spectral tilt n T , and the tensor-to-scalar ratio r. We find that the expressions for n s are different with different ordering of taking the derivative of the scalar power spectrum with respect to the scale k and the horizon crossing condition c s k = aH in the constant-roll inflation, the consistency relation r = − 8n T does not hold if ∣η ϕ ∣ is not small, and the duality of the tensor-to-scalar ratio between the slow-roll inflation and ultra-slow-roll inflation does not exist in inflationary models with non-minimally derivative coupling. The result offers a fresh perspective on the understanding of the inflationary models with non-minimally derivative coupling and is helpful for the production of scalar induced gravitational waves in the framework of ultra-slow-roll inflation with non-minimally derivative coupling.

Properties of Central Regions of the Dark Matter Halos in the Model with a Bump in the Power Spectrum of Density Perturbations

A surprisingly large number of galaxies with masses of ~109–1010\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{M}_{ \\odot }}$$\\end{document} at redshifts of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z \\geqslant 9$$\\end{document} are discovered with the James Webb Space Telescope. A possible explanation for the increase in the mass function can be the presence of a local maximum (bump) in the power spectrum of density perturbations on the corresponding scale. In this paper, it is shown that simultaneously with the growth of the mass function, galaxies from the bump region must have a higher density (compactness) compared to cosmological models without a bump. These more compact galaxies have been partially included in larger galaxies and have been subjected to tidal gravitational disruption. They have been less destructed than “ordinary” galaxies of the same mass, and some of them could survive to z = 0 and persist on the periphery of some galaxies. The formation and evolution of compact halos in a cube with a volume of (47 Mpc)3 with (1024)3 dark matter particles in the redshift range from 120 to 0 have been numerically simulated and observational implications of the presence of such galaxies in the current Universe have been discussed.

One-loop power spectrum in ultra slow-roll inflation and implications for primordial black hole dark matter

We apply the in-in formalism to address the question of whether the size of the one-loop spectrum of curvature fluctuations in ultra-slow-roll inflation models designed for producing a large population of primordial black holes implies a breakdown of perturbation theory. We consider a simplified piece-wise description of inflation, in which the ultra-slow-roll phase is preceded and followed by slow-roll phases linked by transitional periods. We work in the δϕ-gauge, including all relevant cubic and quartic interactions and the necessary counterterms to renormalize the ultraviolet divergences, regularized by a cutoff. The ratio of the one-loop to the tree-level contributions to the spectrum of curvature perturbations is controlled by the duration of the ultra-slow-roll phase and of the transitions. Our results indicate that perturbation theory does not necessarily break in well-known models proposed to account for all the dark matter in the form of primordial black holes.

Enhanced curvature perturbation and primordial black hole formation in two-stage inflation with a break

We investigate a model of R2-gravity with a non-minimally coupled scalar field that gives rise to two-stage inflation with a break, that is, with an intermediate stage where inflation momentarily halts. We find that the power spectrum of the primordial curvature perturbation is significantly enhanced at the break scale, which can account for the primordial black hole (PBH) formation, without affecting the CMB constraint on large scales. The behavior of the curvature perturbation is carefully analyzed and we find a few notable new features in the spectrum. In particular, we find that the k3 growth of the spectrum of toward the end of the first stage of inflation. We argue that this is a universal feature common to all two-stage models where the field dominating the second stage is heavy during the first stage. By appropriately tuning the model parameters, we find that our model can realize the scenario of PBHs as the cold dark matter of the Universe. We also find that we can choose the parameters so that the spectrum of the induced gravitational waves from the enhanced curvature perturbation fits the NANOGrav-15yr data of pulsar timing array observation.

Measuring the substructure mass power spectrum of 23 SLACS strong galaxy–galaxy lenses with convolutional neural networks

ABSTRACT Strong gravitational lensing can be used as a tool for constraining the substructure in the mass distribution of galaxies. In this study we investigate the power spectrum of dark matter perturbations in a population of 23 Hubble Space Telescope images of strong galaxy–galaxy lenses selected from The Sloan Lens ACS (SLACS) survey. We model the dark matter substructure as a Gaussian random field perturbation on a smooth lens mass potential, characterized by power-law statistics. We expand upon the previously developed machine learning framework to predict the power-law statistics by using a convolutional neural network (CNN) that accounts for both epistemic and aleatoric uncertainties. For the training sets, we use the smooth lens mass potentials and reconstructed source galaxies that have been previously modelled through traditional fits of analytical and shapelet profiles as a starting point. We train three CNNs with different training set: the first using standard data augmentation on the best-fitting reconstructed sources, the second using different reconstructed sources spaced throughout the posterior distribution, and the third using a combination of the two data sets. We apply the trained CNNs to the SLACS data and find agreement in their predictions. Our results suggest a significant substructure perturbation favouring a high frequency power spectrum across our lens population.

Requiem to “proof of inflation” or sourced fluctuations in a non-singular bounce

Popular wisdom suggests that measuring the tensor to scalar ratio r on CMB scales is a “proof of inflation” since one generic prediction is a scale-invariant tensor spectrum while alternatives predict r that is many orders of magnitude below the sensitivity of future experiments. A bouncing Universe with sourced fluctuations allows for nearly scale-invariant spectra of both scalar and tensor perturbations challenging this point of view. Past works have analyzed the model until the bounce, under the assumption that the bounce will not change the final predictions. In this work, we discard this assumption. We explicitly follow the evolution of the Universe and fluctuations across the bounce until reheating. The evolution is stable, and the existence of the sourced fluctuations does not destroy the bounce. The bounce enhances the scalar spectrum while leaving the tensor spectrum unchanged. The enhancement depends on the duration of the bounce — a shorter bounce implies a larger enhancement. The model matches current observations and predicts any viable tensor-to-scalar ratio r ≲ 10-2, which may be observed in upcoming CMB experiments. Hence, a measurement of r will no longer be a “proof of inflation”, and a Sourced Bounce is a viable paradigm with distinct predictions.

Thermal curvature perturbations in thermal inflation

We compute the power spectrum of super-horizon curvature perturbations generated during a late period of thermal inflation, taking into account fluctuation-dissipation effects resulting from the scalar flaton field's interactions with the ambient radiation bath. We find that, at the onset of thermal inflation, the flaton field may reach an equilibrium with the radiation bath even for relatively small coupling constants, maintaining a spectrum of thermal fluctuations until the critical temperature T c, below which thermal effects stop holding the field at the false potential minimum. This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations. In particular, we find that this inhibits the later formation of primordial black holes, at least on scales that leave the horizon for T > T c. The larger thermal field variance also reduces the duration of a period of fast-roll inflation below T c, as the field rolls to the true potential minimum, which should also affect the generation of (large) curvature perturbations on even smaller scales.

Gravitational waves in a cyclic Universe: resilience through cycles and vacuum state

We present a generalised calculation for the spectrum of primordial tensor perturbations in a cyclic Universe, making no assumptions about the vacuum state of the theory and accounting for the contribution of tensor modes produced in the dark energy phase of the previous cycle. We show that these modes have minimal impact on the spectrum observed in the current cycle, except for corrections on scales as large as the comoving Hubble radius today. These corrections are due to sub-horizon modes produced towards the end of the dark energy phase, persisting into the ekpyrotic phase of the next cycle as additional quanta. In relation to the vacuum state, we argue that non-Bunch-Davies quanta can easily overwhelm the energy density driving the dark energy phase, potentially compromising the model. Therefore, avoiding backreaction effects sets restrictive constraints on deviations away from the Bunch-Davies vacuum during this phase, limiting the overall freedom to consider alternative vacua in the cyclic Universe.

Freeze out of multi-mode Richtmyer–Meshkov instability using particles

Richtmyer–Meshkov instability (RMI) occurs when a shock wave traverses an interface separated by two fluids with different densities. Achieving “freeze out” (i.e., “killing” of RMI), a critical objective in RMI research for engineering applications, remains an open problem in the context of multi-mode RMI. Here, we introduce particles into the flow field to achieve freeze out, which is attributed to the momentum non-equilibrium effect inherent in the gas–particle phases. This effect facilitates the transfer of momentum and energy from the fluid to the particles, thereby mitigating the amplification of initial perturbations within the mixing zone. We developed a one-dimensional model to predict the velocities of the mixing zone boundaries in multiphase RMI. The growth of RMI was suppressed by controlling the velocities of the mixing zone boundaries through particle effects. A non-dimensional freeze out criterion was derived, incorporating the gas–particle coupling along with the particle volume fraction effect. The condition for freezing a multi-mode RMI was specially designed to estimate the required particle volume fraction to achieve the freeze out. A series of simulations were conducted using a well-verified compressible multiphase particle-in-cell method to validate the realization of freeze out. Further analysis reveals that the designed condition exhibits applicability across a spectrum of multi-mode perturbations, including both broadband and narrowband perturbations, as well as various initial Mach numbers.

Bare mass effects on the reheating process after inflation

We consider the effects of a bare mass term for the inflaton, when the inflationary potential takes the form V(ϕ)=λϕk about its minimum with k≥4. We concentrate on k=4, but discuss general cases as well. Further, we assume λϕend2≫mϕ2, where ϕend is the inflaton field value when the inflationary expansion ends. We show that the presence of a mass term (which may be present due to radiative corrections or supersymmetry breaking) can significantly alter the reheating process, as the equation of state of the inflaton condensate changes from wϕ=13 to wϕ=0 when λϕ2 drops below mϕ2. We show that, for a mass mϕ≳3λ14TRH, the mass term will dominate at reheating. The value of λ is relatively model independent as it is normalized by the cosmic microwave background perturbation spectrum. For T models of inflation, this leads to mϕ≳TRH/250. We compute the effects on the reheating temperature for cases where reheating is due to inflaton decay (to fermions, scalars, or vectors) or to inflaton scattering (to scalars or vectors). For scattering to scalars and in the absence of a decay, there is always a residual inflaton background that acts as cold dark matter. In this case, we derive a strong upper limit to the inflaton bare mass which for T models is mϕ<350 MeV(TRH/1010 GeV)3/5. We also consider the effect of the bare mass term on the fragmentation of the inflaton condensate. Published by the American Physical Society 2024

Species Scale and Primordial Gravitational Waves

AbstractThe species scale is a field‐dependent UV cut‐off for any effective field theory weakly coupled to gravity. In this letter, it is shown that in the context of inflationary cosmology, a detection of primordial gravitational waves will set an upper bound on the decay rate of the species scale. Specifically, this is derived in terms of the tensor‐to‐scalar ratio of power spectra of primordial perturbations. Given the targets of current and next generation experiments, it is shown that any successful detection would signify that this upper limit is of the order of unity, which is consistent with recent discussions in the literature.

Analytical insights into constant-roll condition: extending the paradigm to non-canonical models

In this work, we explore the prospect of generalizing the constant-roll condition in canonical inflationary model to non-canonical models. To find a natural generalization, we focus on three manifestations of this condition and construct constant-roll models corresponding to each manifestation. These models are not equivalent but reduce to the familiar constant-roll model in canonical limit. To showcase the applicability of our generalized mechanism, we examine a specific class of non-canonical models, which can be viewed as extensions of k/G inflation. In these models sound speed is constant. We conduct a comparative study, and with an analytical examination of the model, specify instances when our constant-roll conditions yield dissimilar outcomes and when they exhibit analogies. We also apply our findings to scrutinize another kinetically driven inflationary model with varying sound speed. We demonstrate that each of our constant-roll conditions leads to a unique set of solutions. Afterward, we construct a four-stage constant-roll kinetically driven inflation that complies with CMB constraints, it sustains for a sufficiently long period of time, and finally gracefully exits. In this model the spectrum of curvature perturbations is enhanced in a brief phase of non-slow-roll inflationary evolution. Employing numerical methods, we analyse this scenario to elucidate how altering the constant-roll condition impacts the power spectrum and the model's dynamics.

The second data release from the European Pulsar Timing Array

The European Pulsar Timing Array (EPTA) and Indian Pulsar Timing Array (InPTA) collaborations have measured a low-frequency common signal in the combination of their second and first data releases, respectively, with the correlation properties of a gravitational wave background (GWB). Such a signal may have its origin in a number of physical processes including a cosmic population of inspiralling supermassive black hole binaries (SMBHBs); inflation, phase transitions, cosmic strings, and tensor mode generation by the non-linear evolution of scalar perturbations in the early Universe; and oscillations of the Galactic potential in the presence of ultra-light dark matter (ULDM). At the current stage of emerging evidence, it is impossible to discriminate among the different origins. Therefore, for this paper, we consider each process separately, and investigated the implications of the signal under the hypothesis that it is generated by that specific process. We find that the signal is consistent with a cosmic population of inspiralling SMBHBs, and its relatively high amplitude can be used to place constraints on binary merger timescales and the SMBH-host galaxy scaling relations. If this origin is confirmed, this would be the first direct evidence that SMBHBs merge in nature, adding an important observational piece to the puzzle of structure formation and galaxy evolution. As for early Universe processes, the measurement would place tight constraints on the cosmic string tension and on the level of turbulence developed by first-order phase transitions. Other processes would require non-standard scenarios, such as a blue-tilted inflationary spectrum or an excess in the primordial spectrum of scalar perturbations at large wavenumbers. Finally, a ULDM origin of the detected signal is disfavoured, which leads to direct constraints on the abundance of ULDM in our Galaxy.

Quasinormal Spectrum of (2+1)$(2+1)$‐Dimensional Asymptotically Flat, dS and AdS Black Holes

AbstractWhile ‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher resembles that in four‐dimensional spacetime with the corresponding asymptotic.