Newtonian Perturbation Theory Research Articles

Analytical Gaussian process cosmography: unveiling insights into matter-energy density parameter at present

In this study, we introduce a novel analytical Gaussian Process (GP) cosmography methodology, leveraging the differentiable properties of GPs to derive key cosmological quantities analytically. Our approach combines cosmic chronometer (CC) Hubble parameter data with growth rate (f) observations to constrain the Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}$$\\end{document} parameter, offering insights into the underlying dynamics of the Universe. By formulating a consistency relation independent of specific cosmological models, we analyze under a flat FLRW metric and first-order Newtonian perturbation theory framework. Our analytical approach simplifies the process of Gaussian Process regression (GPR), providing a more efficient means of handling large datasets while offering deeper interpretability of results. We demonstrate the effectiveness of our methodology by deriving precise constraints on Ωm0h2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}h^2$$\\end{document}, revealing Ωm0h2=0.139±0.017\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _\ extrm{m0}h^2=0.139\\pm 0.017$$\\end{document}. Moreover, leveraging H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} observations, we further constrain Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}$$\\end{document}, uncovering an inverse correlation between mean H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} and Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}$$\\end{document}. Our investigation offers a proof of concept for analytical GP cosmography, highlighting the advantages of analytical methods in cosmological parameter estimation.

Nonlinear mode-tide coupling in coalescing binary neutron stars with relativistic corrections

We compute the internal modes of a nonspinning neutron star and its tidal metric perturbation in general relativity, and determine the effect of relativistic corrections to the modes on mode coupling. Claims have been made that a new hydrodynamic instability can occur in a neutron star in a binary neutron star system triggered by the nonlinear coupling of the companion's tidal field to pairs of p-modes and g-modes in it as the binary inspirals toward merger. This "PG" instability may be significant since it can influence the binary's inspiral phase by extracting orbital energy, thereby potentially causing large deviations in their gravitational waveforms from those predicted by theoretical models that do not account for it. This can result in incorrect parameter estimation, at best, or mergers going undetected, at worst, owing to the use of deficient waveform models. On the other hand, better modeling of this instability and its effect on binary orbits can unravel a new phenomenon and shed light on stellar instabilities, via gravitational wave observations. So far, all mode-tide coupling instability studies have been formulated in Newtonian perturbation theory. Neutron stars are compact objects, so relativistic corrections might be important. We present and test a new code to calculate the relativistic eigenmodes of nonrotating relativistic stars. We use these relativistic tide and neutron star eigenmodes to compute the mode-tide coupling strength (MTCS) for a few selected equations of state. The MTCS thus calculated can be at most tens of percent different from its purely Newtonian value, but we confirm the dependencies on orbital separation and equation of state found by Newtonian calculations. For some equations of state, the MTCS is very sensitive to the neutron star crust region, demonstrating the importance of treating this region accurately.

Multi-scale perturbation theory II: Solutions and leading-order bispectrum in the ΛCDM universe

Two-parameter perturbation theory (2PPT) is a framework designed to include the relativistic gravitational effects of small-scale nonlinear structures on the large-scale properties of the Universe. In this paper we use the 2PPT framework to calculate and study the bispectrum of matter in a spatially-flat ΛCDM cosmology. This is achieved by deploying Newtonian perturbation theory to model the gravitational fields of quasi-nonlinear structures, and then subsequently using them as source terms for the large-scale cosmological perturbations. We find that our approach reproduces some of the expected relativistic effects from second-order cosmological perturbation theory, but not all. This work therefore provides a first step in deploying a formalism that can simultaneously model the weak gravitational fields of both linear and nonlinear structures in a realistic model of the Universe.

Multi-scale perturbation theory. Part I. Methodology and leading-order bispectrum corrections in the matter-dominated era

Two-parameter perturbation theory is a scheme tailor-made to consistently include nonlinear density contrasts on small scales (<100 Mpc), whilst retaining a traditional approach to cosmological perturbations in the long-wavelength universe. In this paper we study the solutions that arise from this theory in a spatially-flat dust-filled cosmology, and what these imply for the bispectrum of matter. This is achieved by using Newtonian perturbation theory to model the gravitational fields of nonlinear structures in the quasi-linear regime, and then using the resulting solutions as source terms for the cosmological equations. We find that our approach results in the leading-order part of the cosmological gravitational potentials being identical to those that result from standard cosmological perturbation theory at second-order, while the dark matter bispectrum itself yields some differences on Hubble scales. This demonstrates that our approach is sufficient to capture most leading-order relativistic effects, but within a framework that is far easier to generalize. We expect this latter property to be particularly useful for calculating leading-order relativistic corrections to the matter power spectrum, as well as for deriving predictions for relativistic effects in alternative theories of gravity.

Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

Cosmological non-linear density and velocity power spectra including non-linear vector and tensor modes

We present the leading order non-linear density and velocity power spectra in the complete form; previous studies have omitted the vector- and tensor-type perturbations simultaneously excited by the scalar-type perturbation in nonlinear order. These additional contributions are comparable to the scalar-type purely relativistic perturbations, and thus negligible in the current paradigm of concordance cosmology: i.e., concerning density and velocity perturbations of the pressureless matter in perturbation regime well inside of matter-dominated epoch, we show that pure Einstein's gravity contributions appearing from the third order are entirely negligible (five orders of magnitude smaller than the Newtonian contributions) in all scales. We thus prove that Newtonian perturbation theory is quite reliable in calculating the amplitude of matter fluctuations even in the precision era of cosmology. Therefore, besides the ones imprinted as the initial condition generated in the earlier phase, the other relativistic effect relevant for interpreting observational data must be the projection effect that occurs when mapping galaxies on to the observed coordinate.

Linear Newtonian perturbation theory from the Schrödinger-Poisson equations

We obtain solutions to the coupled Schr\odinger-Poisson equations. The solutions describe the evolution of cold dark matter density perturbations in an otherwise homogeneous expanding Friedmann universe. We discuss the relationships between descriptions of cold dark matter in terms of a pressureless fluid, in terms of a wave function, of a classical scalar field, and a quantum scalar field. We identify the regimes where the various descriptions coincide and where they differ.

Frame dragging and Eulerian frames in general relativity

The physical interpretation of cold dark matter perturbations is clarified by associating Bertschinger's Poisson gauge with a Eulerian/observer's frame of reference. We obtain such an association by using a Lagrangian approach to relativistic cosmological structure formation. Explicitly, we begin with the second-order solution of the Einstein equations in a synchronous/comoving coordinate system---which defines the Lagrangian frame, and transform it to a Poissonian coordinate system. The generating vector of this coordinate/gauge transformation is found to be the relativistic displacement field. The metric perturbations in the Poissonian coordinate system contain known results from standard/Eulerian Newtonian perturbation theory, but contain also purely relativistic corrections. On sub-horizon scales these relativistic corrections are dominated by the Newtonian bulk part. These corrections however set up non-linear constraints for the density and for the velocity which become important on scales close to the horizon. Furthermore, we report the occurence of a transverse component in the displacement field, and find that it induces a non-linear frame dragging as seen in the observer's frame, which is sub-dominant at late-times and sub-horizon scales. Finally, we find two other gauges which can be associated with a Eulerian frame. We argue that the Poisson gauge is to be preferred because it comes with the simplest physical interpretation.

Time evolution of rapidly rotating stratified neutron stars

We study the time evolution of non-axisymmetric oscillations of rapidly rotating neutron stars. The rotation is assumed uniform and the stellar models have composition gradients that generate gravity restored oscillation modes. We work in linear Newtonian perturbation theory and in Cowling approximation, i.e. we neglect the gravitational potential perturbations. We study for the first time the behaviour of the inertia-gravity modes in fast spinning stars, and carry out a detailed comparison of non-stratified and stratified models. In particular, we show that each g-mode becomes rotation-dominated, i.e. approaches a particular inertial mode, as the rotation rate of the star is increased.