Growth Of Linear Perturbations Research Articles

A comprehensive data-driven odyssey to explore the equation of state of dark energy

For the first time, we reconstruct the dark energy equation of the state parameter w from the combination of background and perturbation observations, specifically combining the Hubble parameter data from cosmic chronometer observations and the logarithmic growth rate data from the growth rate observations. We do this analysis using posterior Gaussian process regression without considering any specific cosmological model or parametrization. However there are three main assumptions: (I) a flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric is considered for the cosmological background, (II) there is no interaction between dark energy and matter sectors, and (III) for the growth of inhomogeneity, sub-Hubble approximation and linear perturbations are considered. This study is unique in the sense that the reconstruction of w is independent of any derived parameters such as the present values of the matter-energy density parameter and Hubble parameter. From the reconstruction, we look at how the dark energy equation of state evolves between redshifts 0 and 1.5, finding a slight hint of dynamical behavior in dark energy. However, the evidence is not significant. We also find a leaning towards non-phantom behavior over phantom behavior. We observe that the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model (w=-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(w=-1)$$\\end{document} nearly touches the lower boundary of the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence region in the redshift range 0.6≲z≲0.85.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.6 \\lesssim z \\lesssim 0.85.$$\\end{document} However, it comfortably resides within the 2σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence region in the whole redshift range under investigation, 0≤z≤1.5.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\\le z \\le 1.5.$$\\end{document} Consequently, the non-parametric, model-independent reconstruction of dark energy provides no compelling evidence to deviate from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model when considering cosmic chronometer and growth rate observations.

Control of linear instabilities in two-dimensional airfoil boundary layers

The present study deals with the control of linear, modal and non-modal growth of perturbations in a trapezoidal wing boundary layer. The asymmetric NACA 2515 airfoil is chosen for the analysis. The boundary layer velocity profiles, at different locations on the airfoil, are obtained using the Falkner–Skan equations. The non-modal linear stability theory is used to obtain the amplification of the initial perturbations, for which the state-space approach is adopted. The control is brought about using a Linear Quadratic Regulator (LQR) controller by the means of addition of fluid momentum in the wall-normal direction from the wing surface. Maximum transient energy growth is calculated across a range of wavenumber pairs, and control is applied to the pair with the highest energy growth. In this numerical analysis, we show that the transient growth is higher towards the trailing edge because of the adverse pressure gradient of the flow. Upon control actuation, the reduction in the transient energy growth of perturbations is achieved up to a maximum of 54.6%.

Exploring the growth index γL : Insights from different CMB dataset combinations and approaches

In this study we investigate the growth index γL, which characterizes the growth of linear matter perturbations, while analysing different cosmological datasets. We compare the approaches implemented by two different patches of the cosmological solver : and __. In our analysis we uncover a deviation of the growth index from its expected ΛCDM value of 0.55 when utilizing the Planck dataset, both in the case and in the __ case, but in opposite directions. This deviation is accompanied by a change in the direction of correlations with derived cosmological parameters. However, the incorporation of cosmic microwave background lensing data helps reconcile γL with its Λ-cold dark matter value in both cases. Conversely, the alternative ground-based telescopes Atacama Cosmology Telescope and South Pole Telescope consistently yield growth index values in agreement with γL=0.55. We conclude that the presence of the Alens problem in the Planck dataset contributes to the observed deviations, underscoring the importance of additional datasets in resolving these discrepancies. Published by the American Physical Society 2024

Phenomenology of wavelike vector dark matter nonminimally coupled to gravity

We study three astrophysical/cosmological consequences of nonminimal couplings to gravity in wavelike vector dark matter. In the nonrelativistic limit, the nonminimal coupling with the lowest mass dimension leads to effective self-interactions that affect the mass-radius relation of vector solitons, growth of linear perturbations during structure formation, and the speed of gravitational waves (GWs). Based on the success of cold dark matter on large-scale perturbations and the current limits on GW speed, we constrain the dark matter mass and nonminimal coupling strength to be within the range |ξ 1|/m 2 ≪ 1050 eV-2 and -3 × 1046 eV-2 ≲ ξ 2/m 2 ≲ 8 × 1048 eV-2.

Perturbations in the interacting vacuum

In this study, we present the evolution of cosmological perturbations in a universe consisting of standard matter and interacting vacuum. We use the 1 + 3 covariant formalism in perturbation framework and consider two different models for the interacting vacuum; namely, a linear interacting model and interaction with creation pressure model. For both models, we derive the evolution equations governing the growth of linear perturbations for both radiation- and dust-dominated universe. We find numerical solutions in appropriate limits, namely long and short wavelengths. For both models, the perturbations grow with time (decay with redshift), showing that structure formation is possible in an accelerated cosmic background. The perturbation amplitudes — and their relative scalings with those of [Formula: see text]CDM — depend on the values of the interaction parameters considered, and in a way that can be used to constrain the models using existing and future large-scale structure data. In the vanishing limits of the coupling parameters of the interaction, we show that standard [Formula: see text]CDM cosmology, both background and perturbed, is recovered.

The lure of sirens: joint distance and velocity measurements with third-generation detectors

ABSTRACT The next generation of detectors will detect gravitational waves from binary neutron stars at cosmological distances, for which around a 1000 electromagnetic follow-ups may be observed per year. So far, most work devoted to the expected cosmological impact of these standard sirens employed them only as distance indicators. Only recently their use as tracers of clustering, similar to what already proposed for supernovae, has been studied. Focusing on the expected specifications of the Einstein Telescope (ET), we forecast here the performance on cosmological parameters of future standard sirens as both distance and density indicators, with emphasis on the linear perturbation growth index and on spatial curvature. We improve upon previous studies in a number of ways: a more detailed analysis of available telescope time, the inclusion of more cosmological and nuisance parameters, the Alcock–Paczynski correction, the use of sirens also as both velocity and density tracers, and a more accurate estimation of the distance posterior. We find that the analysis of the clustering of sirens improves the constraints on H0 by 30 per cent and on Ωk0 by over an order of magnitude, with respect to their use merely as distance indicators. With 5 yr of joint ET and Rubin Observatory follow-ups we could reach precision of 0.1 km s−1 Mpc−1 in H0 and 0.02 in Ωk0 using only data in the range 0 < z < 0.5. We also find that the use of sirens as tracers of density, and not only velocity, yields good improvements on the growth of structure constraints.

Effect of the Modified Gravity on the Large-scale Structure Formation

We investigate the formation of the large-scale structures in the present accelerated era in the f(R) gravity background. This is done by considering the linear growth of matter perturbations at low redshift z < 1. The effect of f(R) alters the behavior of the matter density perturbations from the matter-dominated universe to the late-time accelerated universe, which is encoded in the Newtonian gravitational constant as G → G eff. The modified gravitational constant (G eff) depends on the form of f(R). The late-time accelerated expansion affects the formation of large-scale structures by slowing down the growth of matter density. On the other hand, f(R) increases the growth rate of the matter density perturbations. We have found that the source term in the f(R) background, G effΩ m , overcomes the accelerated expansion and the effect of accelerated expansion suppresses the formation of the large-scale structures in the asymptotic future.

Constraints on the epoch of dark matter formation from Milky Way satellites

A small fraction of thermalized dark radiation that transitions into cold dark matter (CDM) between big bang nucleosynthesis and matter-radiation equality can account for the entire dark matter relic density. Because of its transition from dark radiation, "late-forming dark matter" (LFDM) suppresses the growth of linear matter perturbations and imprints the oscillatory signatures of dark radiation perturbations on small scales. The cutoff scale in the linear matter power spectrum is set by the redshift $z_T$ of the phase transition; tracers of small-scale structure can therefore be used to infer the LFDM formation epoch. Here, we use a forward model of the Milky Way (MW) satellite galaxy population to address the question: How late can dark matter form? For dark radiation with strong self-interactions, which arises in theories of neutrinolike LFDM, we report $z_{T}>5.5\times 10^6$ at $95\%$ confidence based on the abundance of known MW satellite galaxies. This limit rigorously accounts for observational incompleteness corrections, marginalizes over uncertainties in the connection between dwarf galaxies and dark matter halos, and improves upon galaxy clustering and Lyman-$\alpha$ forest constraints by nearly an order of magnitude. We show that this limit can also be interpreted as a lower bound on $z_T$ for LFDM that free-streams prior to its phase transition, although dedicated simulations will be needed to analyze this case in detail. Thus, dark matter created by a transition from dark radiation must form no later than one week after the big bang.

Control of instability by injection rate oscillations in a radial Hele-Shaw cell

Small spatial perturbations grow into fingers along the unstable interface of a fluid displacing a more viscous fluid in a porous medium or a Hele-Shaw cell. Mitigating this Saffman-Taylor instability increases the efficiency of fluid displacement applications (e.g., oil recovery), whereas amplifying these perturbations is desirable in, e.g., mixing applications. In this work, we investigate the Saffman-Taylor instability through analysis and experiments in which air injected with an oscillatory flow rate outwardly displaces silicone oil in a radial Hele-Shaw cell. A solution for linear instability growth that shows the competing effects of radial growth and surface tension, including wetting effects, is defined given an arbitrary reference condition. We use this solution to define a condition for stability relative to the constant flow rate case and make initial numerical predictions of instability growth by wave number for a variety of oscillations. These solutions are then modified by incorporating reference conditions from experimental data. The morphological evolution of the interface is tracked as the air bubble expands and displaces oil between the plates. Using the resulting images, we analyze and compare the linear growth of perturbations about the mean interfacial radius for constant injection rates with and without superimposed oscillations. Three distinct types of flow rate oscillations are found to modulate experimental linear growth over a constant phase-averaged rate of fluid displacement. In particular, instability growth at the interface is mildly mitigated by adding to the base flow rate provided by a peristaltic pump a second flow with low-frequency oscillations of small magnitude and, to a lesser extent, high-frequency oscillations of large amplitude. In both cases, the increased stability results from the selective suppression of the growth of large wave numbers in the linear regime. Contrarily, intermediate oscillations consistently destabilize the interface and significantly amplify the growth of the most unstable wave numbers of the constant flow rate case. Numerical predictions of low-frequency oscillations of opposite sign (initially decreasing) show promise of even greater mitigation of linear instability growth than that observed in this investigation. Looking forward, proper characterization of the unsteady, wetting, and nonlinear dynamics of instability growth will give further insight into the efficacy of oscillatory injection rates.

A Linear Inverse Model of Tropical and South Pacific Climate Variability: Optimal Structure and Stochastic Forcing

AbstractA stochastically forced linear inverse model (LIM) of the combined modes of variability from the tropical and South Pacific Oceans is used to investigate the linear growth of optimal initial perturbations and to identify the spatiotemporal features of the stochastic forcing associated with the atmospheric Pacific–South American patterns 1 and 2 (PSA1 and PSA2). Optimal initial perturbations are shown to project onto El Niño–Southern Oscillation (ENSO) and South Pacific decadal oscillation (SPDO), where the inclusion of subsurface South Pacific Ocean temperature variability significantly increases the multiyear linear predictability of the deterministic system. We show that the optimal extratropical sea surface temperature (SST) precursor is associated with the South Pacific meridional mode, which takes from 7 to 9 months to linearly evolve into the final ENSO and SPDO peaks in both the observations and as simulated in an atmosphere-forced ocean model. The optimal subsurface precursor resembles its peak phase, but with a weak amplitude, representing oceanic Rossby waves in the extratropical South Pacific. The stochastic forcing is estimated as the residual by removing the deterministic dynamics from the actual tendency under a centered difference approximation. The resulting stochastic forcing time series satisfies the Gaussian white noise assumption of the LIM. We show that the PSA-like variability is strongly associated with stochastic SST forcing in the tropical and South Pacific Oceans and contributes not only to excite the optimal initial perturbations associated with ENSO and the SPDO but in general to activate the entire stochastic SST forcing, especially in austral summer.

Growth of linear perturbations in a universe with superfluid dark matter

The Lambda-Cold Dark Matter (ΛCDM) model agrees with most of the cosmological observations, but has some hindrances from observed data at smaller scales such as galaxies. Recently, Berezhiani and Khoury proposed a new theory involving interacting superfluid dark matter with three model parameters in [1], which explains galactic dynamics with great accuracy. In the present work, we study the cosmological behaviour of this model in the linear regime of cosmological perturbations. In particular, we compute both analytically and numerically the matter linear growth factor and obtain new bounds for the model parameters which are significantly stronger than previously found. These new constraints come from the fact that structures within the superfluid dark matter framework grow quicker than in ΛCDM, and quite rapidly when the DM-baryon interactions are strong.

Transient growth in turbulent particle-laden channel flow

Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this work. The problem is formulated in the framework of a Eulerian–Eulerian approach, employing two-way coupling between fine particles and fluid flow. The model is first validated in laminar cases, after which the transient growth of coherent perturbations in turbulent channel flow is investigated, where the mean particle concentration distribution is obtained by direct numerical simulation. It is shown that the optimal small-scale structures for particles are streamwise streaks just below the optimal streamwise velocity streaks, as was previously found in numerical simulations of particle-laden channel flow. This indicates that the optimal growth of perturbations is a dominant mechanism for the distribution of particles in the near-wall region. The current study also considers the transient growth of small- and large-scale perturbations at relatively high Reynolds numbers, which reveals that the optimal large-scale structures for particles are in the near-wall region while the optimal large-scale structures for fluid enter the outer region.

Unified superfluid dark sector

We present a novel theory of a unified dark sector, where late-time cosmic acceleration emerges from the dark matter superfluid framework. The system is described by a superfluid mixture consisting of two distinguishable states with a small energy gap, such as the ground state and an excited state of dark matter. Given their contact in the superfluid, interaction between those states can happen, converting one state into the other. This long range interaction within the superfluid couples the two superfluid phonon species through a cosine potential motivated by Josephson/Rabi interactions. As a consequence of this potential, a new dynamics of late-time accelerated expansion emerges in this system, without the need of dark energy, coming from a universe containing only this two-state DM superfluid. Because the superfluid species are non-relativistic, their sound speeds remain suitably small throughout the evolution. We calculate the expansion history and growth of linear perturbations, and compare the results to ΛCDM cosmology. For the fiducial parameters studied here, the predicted expansion and growth function are close to those of ΛCDM, but the difference in the predicted growth rate is significant at late times. The present theory nicely complements the recent proposal of dark matter superfluidity to explain the empirical success of MOdified Newtonian Dynamics (MOND) on galactic scales, thus offering a unified framework for dark matter, dark energy, and MOND phenomenology.

Transition in channel flow with streamwise magnetic field

Abstract Transition to turbulence in a magnetohydrodynamic channel flow is studied numerically under a uniform and constant streamwise magnetic field. The laminar–turbulence transition can be triggered with transient growth and subsequent breakdown of linear optimal perturbations in different forms: streamwise mode, a single oblique mode and a pair of symmetric oblique modes. The nonlinear evolution of optimal modes is analyzed via a series of direct numerical simulations at a single subcritical Reynolds number R e = 5000 and different Hartmann numbers H a ranged from 10 to 70. It is found that, the superposition of symmetric oblique modes can trigger the transition most efficiently even with a lower perturbation energy level. The streamwise mode is less efficient and transition can be observed only after adding three dimensional random noise at the moment of strongest energy amplification. The magnetic damping effect is significant at high Hartmann number and no transition is found under a sufficiently strong magnetic field with H a larger than approximately 70. This critical value can be predicted straightforwardly from the linear relationship of friction coefficient of channel flow and magnetic interaction parameter.

Dark energy with zero pressure: Accelerated expansion and large scale structure in action-dependent Lagrangian theories

We develop a cosmological model based on action-dependent Lagrangian theories. The main feature here is the nonconservation of the energy momentum tensor due to the nontrivial geometrical construction of the theory. We provide the basic set of equations necessary to study both the cosmological background expansion as well as the linear matter perturbation growth. We show that the simplest realization of the Universe as described by only one component is not viable as expected from the existing correspondence between this model and the case of viscous cosmological fluids. However, modeling the energy content of the Universe as composed by two pressureless fluids, i.e., one a typical cold dark matter fluid and the other a pressureless dark energy fluid which is responsible for driving the late-time acceleration expansion, is qualitatively compatible with observational data.

Thermal instability in a time-dependent base state due to sudden heating

When a large body of fluid is heated from below at a horizontal surface, the heat diffuses into the fluid, giving rise to a gravitationally unstable layer adjacent to the boundary. A consideration of the instantaneous Rayleigh number using the thickness of this buoyant layer as a length scale would lead one to expect that the heated fluid is initially stable, and only becomes unstable after a finite time. This transition would also apply to other situations, such as heating a large body of fluid from the side, where a buoyant upward flow develops near the boundary. In such cases, when the evolving thermal boundary layer first becomes unstable, the time scale for the growth of the instabilities may be comparable to the time scale of the evolution of the background temperature profile, and so analytical approximations such as the quasi-static approximation, where the time evolution of the background state is ignored, are not strictly appropriate. We develop a numerical scheme where we find the optimal growth of linear perturbations to the background flow over a given time interval. Part of this problem is to determine an appropriate measure of the amplitude to the disturbances, as inappropriate choices can lead to apparent growth of disturbances over finite time intervals even when the fluid is stable. By considering the Rayleigh–Bénard problem, we show that these problems can be avoided by choosing a measure of the amplitude that uses both the velocity and temperature perturbations, and which minimizes the maximum growth. We apply our analysis to the problems of heating a semi-infinite body of fluid from horizontal and vertical boundaries. We will show that for heating from a vertical boundary there are large- and small-Prandtl-number modes. For some Prandtl numbers, both modes may play a role in the growth of instabilities. In some cases there is transition during the evolution of the most unstable instabilities in fluids such as water, where initially the instabilities are large-Prandtl-number modes and then morph into small-Prandtl-number modes part of the way through their evolution.

Transition induced by linear and nonlinear perturbation growth in flow past a compressor blade

Flow past a NACA 65 blade at chord-based Reynolds number 138 500 is studied using stability analysis, generalized (spatially weighted) transient growth analysis and direct numerical simulations (DNS). The mechanisms of transition on various sections of the blade observed in previous work by Zaki et al. (J. Fluid Mech., vol. 665, 2010, pp. 57–98) are examined, with a focus on the pressure side around the leading edge. In this region, the linearly most energetic perturbation has spanwise wavenumber $40\unicode[STIX]{x03C0}$ (five boundary-layer thicknesses) and is tilted against the mean shear to take advantage of the Orr mechanism. In a DNS, the nonlinear development of this optimal perturbation induces $\unicode[STIX]{x1D6EC}$ structures, which are further stretched to hairpin vortices before breaking down to turbulence. At higher spanwise wavenumber, e.g. $120\unicode[STIX]{x03C0}$, a free-stream optimal perturbation is obtained upstream of the leading edge, in the form of streamwise vortices. During its nonlinear evolution, this optimal perturbation tilts the mean shear and generates spanwise periodic high- and low-speed streaks. Then through a nonlinear lift-up mechanism, the low-speed streaks are lifted above the high-speed ones. This layout of streaks generates a mean shear with two inflectional points and activates secondary instabilities, namely inner and outer instabilities previously reported in the literature.

Inhomogeneous cosmology with numerical relativity

We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in 10^6 in evolving a flat, dust Friedmann-Lemaitre-Roberston-Walker (FLRW) spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in 10^3 between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble flow over a factor of ~350 change in scale factor (redshift). We simulate the growth of linear perturbations into the non-linear regime, where effects such as gravitational slip and tensor perturbations appear. We therefore show that numerical relativity is a viable tool for investigating nonlinear effects in cosmology.

Constraining the halo mass function with observations

The abundances of dark matter halos in the universe are described by the halo mass function (HMF). It enters most cosmological analyses and parametrizes how the linear growth of primordial perturbations is connected to these abundances. Interestingly, this connection can be made approximately cosmology independent. This made it possible to map in detail its near-universal behavior through large-scale simulations. However, such simulations may suffer from systematic effects, especially if baryonic physics is included. In this paper we ask how well observations can constrain directly the HMF. The observables we consider are galaxy cluster number counts, galaxy cluster power spectrum and lensing of type Ia supernovae. Our results show that DES is capable of putting the first meaningful constraints on the HMF, while both Euclid and J-PAS can give stronger constraints, comparable to the ones from state-of-the-art simulations. We also find that an independent measurement of cluster masses is even more important for measuring the HMF than for constraining the cosmological parameters, and can vastly improve the determination of the halo mass function. Measuring the HMF could thus be used to cross-check simulations and their implementation of baryon physics. It could even, if deviations cannot be accounted for, hint at new physics.

Mechanical picture of the linear transient growth of vortical perturbations in incompressible smooth shear flows

A clever isomorphism to particles reflected on surfaces of maxima of the pressure leads to an interesting physical interpretation of the transient dynamics of perturbations in constant shear flows both in 2D and 3D configurations. Moreover this allows to reconstruct the linearized Euler equations.