Kinematic consistency relations of large-scale structures

A spectrum of oscillations covering a wide range of wave numbers is specified for a homogeneous fluid in a finite volume. Considering the range dominated by gravity and low wave number acoustic modes, a correspondence is established between the latter and a certain field associated with the former. It is shown that these two forms of oscillations are governed by the Helmholtz equation, with gravity modes as the driving source. This equation is solved by Green's function methods and a point source solution is derived from which the eigensolutions can be constructed. Finally, these solutions are subjected to integral transformation which allows the amplitude spectrum of the acoustic modes to be determined. The result appears to suggest that the amplitude is inversely proportional to the associated wave number. In addition, it is deduced that resonant coupling of energy between the two systems takes place when the exciting and excited wave numbers are nearly equal.

We perform a series of high-resolution N-body simulations of cosmological structure formation starting from Gaussian and non-Gaussian initial conditions. We adopt the best-fitting cosmological parameters of WMAP (3rd- and 5th-year) and we consider non-Gaussianity of the local type parameterised by 8 different values of the non-linearity parameter F_NL. Building upon previous work based on the Gaussian case, we show that, expressed in terms of suitable variables, the mass function of friends-of-friends haloes is approximately universal (i.e. independent of redshift, cosmology, and matter transfer function) to good precision (nearly 10 per cent) also in non-Gaussian scenarios. We provide fitting formulae for the high-mass end (M>10^13 M_sol/h) of the universal mass function in terms of F_NL, and we also present a non-universal fit in terms of both F_NL and z to be used for applications requiring higher accuracy. In the Gaussian case, we extend our fit to a wider range of halo masses (M>2.4 x 10^10 M_sol/h) and we also provide a consistent fit of the linear halo bias. We show that, for realistic values of F_NL, the matter power-spectrum in non-Gaussian cosmologies departs from the Gaussian one by up to 2 per cent on the scales where the baryonic- oscillation features are imprinted on the 2-point statistics. We confirm the strong k-dependence of the halo bias on large scales (k<0.05 h Mpc^-1) which was already detected in previous studies. However, we find that commonly used parameterisations based on the peak-background split do not provide an accurate description of our simulations which present extra dependencies on the wavenumber, the non-linearity parameter and, possibly, the clustering strength. We provide an accurate fit of the simulation data that can be used as a benchmark for future determinations of F_NL with galaxy surveys.

The properties of gravitational-wave (GW) propagation are modified in alternative theories of gravity and are crucial observables to test gravity at cosmological distance. The propagation speed has already been measured from GW170817 so precisely and pinned down to the speed of light, while other properties of GW propagation have not constrained tightly yet. In this paper, we investigate the measurement precisions of the amplitude damping rate (equivalently, the time variation of the gravitational coupling for GWs) and graviton mass in the generalized framework of GW propagation with the future detectors such as Voyager, Cosmic Explorer, and Einstein Telescope. As a result, we show that the future GW observation can reach 1% error for the amplitude damping. We also study the time variation of the gravitational couplings in Horndeski theory by performing Monte Carlo-based numerical simulations. From the simulation results, we find that the current accelerating Universe prefers the models with less damping of GWs and that the equivalence principle can be tested at the level of 1% by the future GW observation.

Modified Gravity (MG) scenarios have been advocated to account for the dark energy phenomenon in the universe. These models predict departures from General Relativity on large cosmic scales that can be tested through a variety of probes such as observations of galaxy clusters among others. Here, we investigate the imprint of MG models on the internal mass distribution of cluster-like halos as probed by the dark matter halo sparsity. To this purpose we perform a comparative analysis of the properties of the halo sparsity using N-body simulation halo catalogs of a standard flat $\Lambda$CDM model and MG scenarios from the DUSTGRAIN-pathfinder simulation suite. We find that the onset of the screening mechanism leaves a distinct signature in the redshift evolution of the ensemble average halos sparsity. Measurements of the sparsity of galaxy clusters from currently available mass estimates are unable to test MG models due to the large uncertainties on the cluster masses. We show that this should be possible in the future provided large cluster samples with cluster masses determined to better than $30\%$ accuracy level.

The abnormally weighting energy hypothesis consists of assuming that the dark sector of cosmology violates the weak equivalence principle (WEP) on cosmological scales, which implies a violation of the strong equivalence principle for ordinary matter. In this paper, dark energy is shown to result from the violation of WEP by pressureless (dark) matter. This allows us to build a new cosmological framework in which general relativity is satisfied at low scales, as WEP violation depends on the ratio of the ordinary matter over dark matter densities, but at large scales, we obtain a general relativity-like theory with a different value of the gravitational coupling. This explanation is formulated in terms of a tensor-scalar theory of gravitation without WEP for which there exists a revisited convergence mechanism toward general relativity. The consequent dark energy mechanism build upon the anomalous gravity of dark matter (i) does not require any violation of the strong energy condition p<-{rho}c{sup 2}/3, (ii) offers a natural way out of the coincidence problem thanks to the nonminimal couplings to gravitation, (iii) accounts fairly for supernovae data from various simple couplings and with density parameters very close to the ones of the concordance model {lambda}CDM, and therefore suggests anmore » explanation to its remarkable adequacy. Finally, (iv) this mechanism ends up in the future with an Einstein-de Sitter expansion regime once the attractor is reached.« less

Numerical experiments of rotating stratified turbulence are conducted in order to investigate the mesoscale energy cascade process in the free atmosphere. We examine the downscale energy cascade process originated by energy injection at large scales. The energy spectrum created by this injection follows a power law, and its slope depends on planetary rotation rate and static stability. While the spectral slope tends to be steeper with increased static stability in cases without planetary rotation, it becomes insensitive to the planetary rotation rate and static stability and converges to the range from −1.9 to −2.1 in cases with an increased rotation rate. The roles of geostrophic and gravity modes in the cascade processes are discussed. It is shown that nonlinear interactions between geostrophic and gravity modes play a crucial role in the downscale energy cascades. In particular, the effect of the planetary rotation mainly influences the triad interaction composed of one geostrophic and two gravity modes in the energy cascade process. Energy flux to smaller scales is intensified by this type of triad interaction with increased planetary rotation rate.

Scalar-tensor theories of gravity provide a consistent framework to accommodate an ultralight quintessence scalar field. While the equivalence principle is respected by construction, deviations from general relativity and standard cosmology may show up at nucleosynthesis, cosmic microwave background, and solar system tests of gravity. After imposing all the bounds coming from these observations, we consider the expansion rate of the Universe at weakly interacting massive particle decoupling, showing that it can lead to an enhancement of the dark matter relic density up to few orders of magnitude with respect to the standard case. This effect can have an impact on supersymmetric candidates for dark matter.

Multibrane worlds and modification of gravity at large scales

The acceleration of the Universe can be explained either through dark energy or through the modification of gravity on large scales. In this paper we investigate modified gravity models and compare their observable predictions with dark energy models. Modifications of general relativity are expected to be scale independent on superhorizon scales and scale dependent on subhorizon scales. For scale-independent modifications, utilizing the conservation of the curvature scalar and a parametrized post-Newtonian formulation of cosmological perturbations, we derive results for large-scale structure growth, weak gravitational lensing, and cosmic microwave background anisotropy. For scale-dependent modifications, inspired by recent f(R) theories we introduce a parametrization for the gravitational coupling G and the post-Newtonian parameter {gamma}. These parametrizations provide a convenient formalism for testing general relativity. However, we find that if dark energy is generalized to include both entropy and shear stress perturbations, and the dynamics of dark energy is unknown a priori, then modified gravity cannot in general be distinguished from dark energy using cosmological linear perturbations.

Modified gravity (MOG) is a covariant, relativistic, alternative gravitational theory whose field equations are derived from an action that supplements the spacetime metric tensor with vector and scalar fields. Both gravitational (spin 2) and electromagnetic waves travel on null geodesics of the theory's one metric. MOG satisfies the weak equivalence principle and is consistent with observations of the neutron star merger and gamma ray burster event GW170817/GRB170817A.

Direct numerical simulations at 2563 resolution have been carried out to study the response of isotropic turbulence to the concurrent effects of solid-body rotation and stochastic, isotropic forcing at the large scales. Because spectral transfer to the smaller scales is weakened by rotation, energy input from forcing gradually builds up at the large scales, causing the overall kinetic energy to increase. At intermediate wave numbers the energy spectrum undergoes a transition from a limited k−5/3 inertial range to k−2 scaling recently predicted in the literature. Although the Reynolds stress tensor remains approximately isotropic and three-component, evidence for anisotropy and quasi-two-dimensionality in length scales and spectra in different velocity components and directions is strong. The small scales are found to deviate from local isotropy, primarily as a result of anisotropic transfer from the large scales. To understand the spectral dynamics of this flow, we study the detailed behavior of nonlinear triadic interactions in wave number space. Spectral transfer in the velocity component parallel to the axis of rotation is qualitatively similar to that in nonrotating turbulence; however, the perpendicular component is characterized by a much weakened energy cascade at high wave numbers and a local reverse transfer at the largest scales. The broader implications of this work are briefly addressed.

We expand our analysis of Newtonian Fractional-Dimension Gravity (NFDG), an extension of the classical laws of Newtonian gravity to lower dimensional spaces, including those with fractional (i.e., non-integer) dimension. We apply our model to four rotationally supported galaxies (NGC 5033, NGC 6674, NGC 5055, NGC 1090), in addition to other three galaxies (NGC 7814, NGC 6503, NGC 3741) which were analyzed in previous studies. NFDG is able to fit the rotation curves of all these galaxies without any dark matter component. We also investigate the possible violation of the strong equivalence principle, in relation to the External Field Effect (EFE), i.e., the dependence of the internal motion of a self-gravitating system under freefall on an external gravitational field. This effect is not present in Newtonian or Einstein gravity, but is predicted by some alternative theories of gravity. On the contrary, we show that NFDG does not imply the EFE, at least for values of the fractional dimension in the range $1 \leq D \leq 3$. Using improved NFDG numerical computations, we analyze the rotation curves of the aforementioned galaxies and obtain perfect fits to the experimental data, by using a fractional-dimension function $D\left (R\right )$ which characterizes each individual galaxy. In the galactic sample studied here with NFDG methods, we do not detect any significant differences between galaxies that are supposed to show/not show the EFE according to other alternative theories. A larger sample of galaxies will be needed to fully determine the absence of any external field effect in NFDG.

Lunar laser ranging (LLR) is used to conduct high-precision measurements of ranges betweenan observatory on Earth and a laser retro-reflector on the lunar surface. Over the years, LLR hasbenefited from a number of improvements both in observing technology and data modeling, which ledto the current accuracy of post-fit residuals of ∼ 2 cm. Today LLR is a primary technique to studythe dynamics of the Earth-Moon system and is especially important for gravitational physics, geodesyand studies of the lunar interior. When the gravitational physics is concerned, LLR is used to performhigh-accuracy tests of the equivalence principle, to search for a time-variation in the gravitationalconstant, and to test predictions of various alternative theories of gravity. The gravitational physicsparameters cause both secular and periodic effects on the lunar orbit that are detectable with thepresent day LLR; in addition, the accuracy of their determination benefits from the 35 years of theLLR data span. On the geodesy front, LLR contributes to the determination of Earth orientationparameters, such as nutation, precession (including relativistic precession), polar motion, and UT1,i.e. especially to the long-term variation of these effects. LLR contributes to the realization of boththe terrestrial and selenocentric reference frames. The realization of a dynamically defined inertialreference frame, in contrast to the kinematically realized frame of VLBI, offers new possibilities formutual cross-checking and confirmation. Finally, LLR also investigates the processes related to theMoon’s interior dynamics. Here, we review the LLR technique focusing on its impact on relativityand give an outlook to further applications, e.g. in geodesy. We present results of our dedicatedstudies to investigate the sensitivity of LLR data with respect to the relativistic quantities; we alsopresent the computed corresponding spectra indicating the typical periods related to the relativisticeffects. We discuss the current observational situation and the level of LLR modeling implementedto date. We emphasis the need for the modeling improvement for the near future LLR opportunities.We also address improvements needed to fully utilize the scientific potential of LLR.Keywords. Lunar Laser Ranging, Relativity, Earth-Moon dynamics

The clustering of galaxies in ongoing and upcoming galaxy surveys contains a wealth of cosmological information, but extracting this information is a nontrivial task since galaxies and their host haloes are stochastic tracers of the nonlinear matter density field. This stochasticity is usually modeled as the Poisson shot noise, which is constant as a function of wave number with amplitude given by $1/\overline{n}$, where $\overline{n}$ is the number density of galaxies. Here we use dark matter haloes in $N$-body simulations to show evidence for deviations from this simple behavior and develop models that explain the behavior of the stochasticity on large scales. First, haloes are extended, nonoverlapping objects, i.e., their correlation function needs to go to $\ensuremath{-}1$ on small scales. This leads to a negative correction to the stochasticity relative to the Poisson value at low wave number $k$, decreasing to zero for wave numbers large compared to the inverse exclusion scale. Second, haloes show a nonlinear enhancement of clustering outside the exclusion scale, leading to a positive stochasticity correction. Both of these effects go to zero for high $k$, making the stochasticity scale dependent even for $k&lt;0.1h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. We show that the corrections in the low-$k$ regime are the same in Eulerian and Lagrangian space, but that the transition scale is pushed to smaller scales for haloes observed at present time (Eulerian space), relative to the initial conditions (Lagrangian space). These corrections vary with halo mass, and we present approximate scalings with halo mass and redshift. We also discuss simple applications of these effects to galaxy samples with nonvanishing satellite fraction, where the stochasticity can again deviate strongly from the fiducial Poisson expectation. Overall, these effects affect the clustering of galaxies at a level of a few percent even on very large scales and need to be modeled properly if we want to extract high precision cosmological information from the upcoming galaxy redshift surveys.

This study revisits the problem of advective transfer and spectra of a diffusive scalar field in large-scale incompressible flows in the presence of a (large-scale) source. By "large scale" it is meant that the spectral support of the flows is confined to the wave-number region k<kd , where kd is relatively small compared with the diffusion wave number kkappa. Such flows mediate couplings between neighboring wave numbers within kd of each other only. It is found that the spectral rate of transport (flux) of scalar variance across a high wave number k>kd is bounded from above by UkdkTheta(k,t) , where U denotes the maximum fluid velocity and Theta(k,t) is the spectrum of the scalar variance, defined as its average over the shell (k-kd,k+kd) . For a given flux, say vartheta>0 , across k>kd , this bound requires Theta(k,t)> or =(varthetaUkd)k(-1) . This is consistent with recent numerical studies and with Batchelor's theory that predicts a k(-1) spectrum (with a slightly different proportionality constant) for the viscous-convective range, which could be identified with (kd,kkappa) . Thus, Batchelor's formula for the variance spectrum is recovered by the present method in the form of a critical lower bound. The present result applies to a broad range of large-scale advection problems in space dimensions > or =2 , including some filter models of turbulence, for which the turbulent velocity field is advected by a smoothed version of itself. For this case, Theta(k,t) and vartheta are the kinetic energy spectrum and flux, respectively.