Showing papers on "Gravitational field published in 2012"

The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)

Abstract: [1] EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed by a least squares combination of the ITG-GRACE03S gravitational model and its associated error covariance matrix, with the gravitational information obtained from a global set of area-mean free-air gravity anomalies defined on a 5 arc-minute equiangular grid This grid was formed by merging terrestrial, altimetry-derived, and airborne gravity data Over areas where only lower resolution gravity data were available, their spectral content was supplemented with gravitational information implied by the topography EGM2008 is complete to degree and order 2159, and contains additional coefficients up to degree 2190 and order 2159 Over areas covered with high quality gravity data, the discrepancies between EGM2008 geoid undulations and independent GPS/Leveling values are on the order of ±5 to ±10 cm EGM2008 vertical deflections over USA and Australia are within ±11 to ±13 arc-seconds of independent astrogeodetic values These results indicate that EGM2008 performs comparably with contemporary detailed regional geoid models EGM2008 performs equally well with other GRACE-based gravitational models in orbit computations Over EGM96, EGM2008 represents improvement by a factor of six in resolution, and by factors of three to six in accuracy, depending on gravitational quantity and geographic area EGM2008 represents a milestone and a new paradigm in global gravity field modeling, by demonstrating for the first time ever, that given accurate and detailed gravimetric data, asingle global model may satisfy the requirements of a very wide range of applications

The Theory of Fields

Abstract: Fields play a fundamental role in the modern formulation of fundamental interactions. We introduce the basic equation of motion for fields, and discuss their most important solutions: The wave solution is relevant both for electromagnetic radiation and for the description of a beam of particles within the framework of quantum field theory. The Coulomb solution describes fields around point-like bodies. The existence of a wave solution for the gravitational field leads to the prediction of the existence of gravitational waves. These are being searched for in experiments being carried out today; the design of these experiments is sketched.

Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies

Abstract: The availability of high-resolution global digital elevation data sets has raised a growing interest in the feasibility of obtaining their spherical harmonic representation at matching resolution, and from there in the modelling of induced gravity perturbations. We have therefore estimated spherical Bouguer and Airy isostatic anomalies whose spherical harmonic models are derived from the Earth’s topography harmonic expansion. These spherical anomalies differ from the classical planar ones and may be used in the context of new applications. We succeeded in meeting a number of challenges to build spherical harmonic models with no theoretical limitation on the resolution. A specific algorithm was developed to enable the computation of associated Legendre functions to any degree and order. It was successfully tested up to degree 32,400. All analyses and syntheses were performed, in 64 bits arithmetic and with semi-empirical control of the significant terms to prevent from calculus underflows and overflows, according to IEEE limitations, also in preserving the speed of a specific regular grid processing scheme. Finally, the continuation from the reference ellipsoid’s surface to the Earth’s surface was performed by high-order Taylor expansion with all grids of required partial derivatives being computed in parallel. The main application was the production of a 1′ × 1′ equiangular global Bouguer anomaly grid which was computed by spherical harmonic analysis of the Earth’s topography–bathymetry ETOPO1 data set up to degree and order 10,800, taking into account the precise boundaries and densities of major lakes and inner seas, with their own altitude, polar caps with bedrock information, and land areas below sea level. The harmonic coefficients for each entity were derived by analyzing the corresponding ETOPO1 part, and free surface data when required, at one arc minute resolution. The following approximations were made: the land, ocean and ice cap gravity spherical harmonic coefficients were computed up to the third degree of the altitude, and the harmonics of the other, smaller parts up to the second degree. Their sum constitutes what we call ETOPG1, the Earth’s TOPography derived Gravity model at 1′ resolution (half-wavelength). The EGM2008 gravity field model and ETOPG1 were then used to rigorously compute 1′ × 1′ point values of surface gravity anomalies and disturbances, respectively, worldwide, at the real Earth’s surface, i.e. at the lower limit of the atmosphere. The disturbance grid is the most interesting product of this study and can be used in various contexts. The surface gravity anomaly grid is an accurate product associated with EGM2008 and ETOPO1, but its gravity information contents are those of EGM2008. Our method was validated by comparison with a direct numerical integration approach applied to a test area in Morocco–South of Spain (Kuhn, private communication 2011) and the agreement was satisfactory. Finally isostatic corrections according to the Airy model, but in spherical geometry, with harmonic coefficients derived from the sets of the ETOPO1 different parts, were computed with a uniform depth of compensation of 30 km. The new world Bouguer and isostatic gravity maps and grids here produced will be made available through the Commission for the Geological Map of the World. Since gravity values are those of the EGM2008 model, geophysical interpretation from these products should not be done for spatial scales below 5 arc minutes (half-wavelength).

Solar system constraints on f(T) gravity

Abstract: We use recent observations of Solar system orbital motions in order to constrain f(T) gravity. In particular, imposing a quadratic f(T) correction to the linear-in-T form, which is a good approximation for every realistic case, we extract the spherical solutions of the theory. Using these spherical solutions to describe the Sun's gravitational field, we use recently determined supplementary advances of planetary perihelia, to infer upper bounds on the allowed f(T) corrections. We find that the maximal allowed divergence of the gravitational potential in f(T) gravity from that in the teleparallel equivalent of General Relativity is of the order of 6.2 × 10−10, in the applicability region of our analysis. This is much smaller than the corresponding (significantly small too) divergence that is predicted from cosmological observations, as expected. Such a tiny allowed divergence from the linear form should be taken into account in f(T) model building.

Making the Case for Conformal Gravity

Abstract: We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a PT symmetric rather than a Hermitian theory. We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no independent quantization of its own, with it being quantized solely by virtue of its being coupled to a quantized matter source. Moreover, because it is this very coupling that fixes the strength of the gravitational field commutators, the gravity sector zero-point energy density and pressure fluctuations are then able to identically cancel the zero-point fluctuations associated with the matter sector. In addition, we show that when the conformal symmetry is spontaneously broken, the zero-point structure automatically readjusts so as to identically cancel the cosmological constant term that dynamical mass generation induces. We show that the macroscopic classical theory that results from the quantum conformal theory incorporates global physics effects that provide for a detailed accounting of a comprehensive set of 138 galactic rotation curves with no adjustable parameters other than the galactic mass to light ratios, and with the need for no dark matter whatsoever. With these global effects eliminating the need for dark matter, we see that invoking dark matter in galaxies could potentially be nothing more than an attempt to describe global physics effects in purely local galactic terms. Finally, we review some recent work by ’t Hooft in which a connection between conformal gravity and Einstein gravity has been found.

Flat-space chiral gravity.

Abstract: We provide the first evidence for a holographic correspondence between a gravitational theory in flat space and a specific unitary field theory in one dimension lower. The gravitational theory is a flat-space limit of topologically massive gravity in three dimensions at a Chern-Simons level of k=1. The field theory is a chiral two-dimensional conformal field theory with a central charge of c=24.

Gravitational Anomalies and Thermal Hall effect in Topological Insulators

Abstract: It has been suggested that after being gapped by a small symmetry-breaking field, the Majorana quasiparticles localized on the surface of a class DIII topological insulator will exhibit a thermal Hall effect that arises from a gravitational Chern-Simons term. We critically examine this idea, and argue that the thermogravitational Hall effect is more complicated than its familiar analog. A conventional Hall current is generated by a uniform electric field, but computing the flux from the gravitational Chern-Simons functional shows that gravitational field gradients---i.e., tidal forces---are needed to induce an energy-momentum flow. We relate the resulting surface energy-momentum flux to a domain-wall gravitational anomaly via the Callan-Harvey inflow mechanism. We stress that the gauge invariance of the combined bulk-plus-boundary theory ensures that the current in the domain wall always experiences a ``covariant'' rather than ``consistent'' anomaly. We use this observation to confirm that the tidally induced energy-momentum current exactly accounts for the covariant gravitational anomaly in $(1+1)$-dimensional domain-wall fermions. The same anomaly arises whether we write the Chern-Simons functional in terms of the Christoffel symbol or in terms of the spin connection.

The Schr\"odinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields

Abstract: In this paper we show that the Schr\"odinger-Newton equation for spherically symmetric gravitational fields can be derived in a WKB-like expansion in 1/c from the Einstein-Klein-Gordon and Einstein-Dirac system.

The Schrödinger-Newton equation as a non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields

Abstract: In this paper, we show that the Schrodinger–Newton equation for spherically symmetric gravitational fields can be derived in a WKB-like expansion in 1/c from the Einstein–Klein–Gordon and Einstein–Dirac systems.

Gravitational collapse in f(R) theories

Abstract: We study the gravitational collapse in modified gravitational theories. In particular, we analyze a general f(R) model with uniformly collapsing cloud of self-gravitating dust particles. This analysis shares analogies with the formation of large-scale structures in the early Universe and with the formation of stars in a molecular cloud experiencing gravitational collapse. In the same way, this investigation can be used as a first approximation to the modification that stellar objects can suffer in these modified theories of gravity. We study concrete examples, and find that the analysis of gravitational collapse is an important tool to constrain models that present late-time cosmological acceleration.

Effective action approach to cosmological perturbations in dark energy and modified gravity

Abstract: In light of upcoming observations modelling perturbations in dark energy and modified gravity models has become an important topic of research. We develop an effective action to construct the components of the perturbed dark energy momentum tensor which appears in the perturbed generalized gravitational field equations, ?G?? = 8?G?T??+?U?? for linearized perturbations. Our method does not require knowledge of the Lagrangian density of the dark sector to be provided, only its field content. The method is based on the fact that it is only necessary to specify the perturbed Lagrangian to quadratic order and couples this with the assumption of global statistical isotropy of spatial sections to show that the model can be specified completely in terms of a finite number of background dependent functions. We present our formalism in a coordinate independent fashion and provide explicit formulae for the perturbed conservation equation and the components of ?U?? for two explicit generic examples: (i) the dark sector does not contain extra fields, = (g??) and (ii) the dark sector contains a scalar field and its first derivative = (g??,,??). We discuss how the formalism can be applied to modified gravity models containing derivatives of the metric, curvature tensors, higher derivatives of the scalar fields and vector fields.

Subtraction of Newtonian noise using optimized sensor arrays

Abstract: Fluctuations in the local Newtonian gravitational field present a limit to high precision measurements, including searches for gravitational waves using laser interferometers. In this work, we present a model of this perturbing gravitational field and evaluate schemes to mitigate the effect by estimating and subtracting it from the interferometer data stream. Information about the Newtonian noise is obtained from simulated seismic data. The method is tested on causal as well as acausal implementations of noise subtraction. In both cases it is demonstrated that broadband mitigation factors close to 10 can be achieved removing Newtonian noise as a dominant noise contribution. The resulting improvement in the detector sensitivity will substantially enhance the detection rate of gravitational radiation from cosmological sources.

Simulation study of a follow-on gravity mission to GRACE

Abstract: The gravity recovery and climate experiment (GRACE) has been providing monthly estimates of the Earth's time-variable gravity field since its launch in March 2002. The GRACE gravity estimates are used to study temporal mass variations on global and regional scales, which are largely caused by a redistribution of water mass in the Earth system. The accuracy of the GRACE gravity fields are primarily limited by the satellite-to-satellite range-rate measurement noise, accelerometer errors, attitude errors, orbit errors, and temporal aliasing caused by unmodeled high-frequency variations in the gravity signal. Recent work by Ball Aerospace and Technologies Corp., Boulder, CO has resulted in the successful development of an interferometric laser ranging system to specifically address the limitations of the K-band microwave ranging system that provides the satellite-to-satellite measurements for the GRACE mission. Full numerical simulations are performed for several possible configurations of a GRACE Follow-On (GFO) mission to determine if a future satellite gravity recovery mission equipped with a laser ranging system will provide better estimates of time-variable gravity, thus benefiting many areas of Earth systems research. The laser ranging system improves the range-rate measurement precision to approximately 0.6 nm/s as compared to approx. 0.2 micro-seconds for the GRACE K-band microwave ranging instrument. Four different mission scenarios are simulated to investigate the effect of the better instrument at two different altitudes. The first pair of simulated missions is flown at GRACE altitude (approx. 480 km) assuming on-board accelerometers with the same noise characteristics as those currently used for GRACE. The second pair of missions is flown at an altitude of approx. 250 km which requires a drag-free system to prevent satellite re-entry. In addition to allowing a lower satellite altitude, the drag-free system also reduces the errors associated with the accelerometer. All simulated mission scenarios assume a two satellite co-orbiting pair similar to GRACE in a near-polar, near-circular orbit. A method for local time variable gravity recovery through mass concentration blocks (mascons) is used to form simulated gravity estimates for Greenland and the Amazon region for three GFO configurations and GRACE. Simulation results show that the increased precision of the laser does not improve gravity estimation when flown with on-board accelerometers at the same altitude and spacecraft separation as GRACE, even when time-varying background models are not included. This study also shows that only modest improvement is realized for the best-case scenario (laser, low-altitude, drag-free) as compared to GRACE due to temporal aliasing errors. These errors are caused by high-frequency variations in the hydrology signal and imperfections in the atmospheric, oceanographic, and tidal models which are used to remove unwanted signal. This work concludes that applying the updated technologies alone will not immediately advance the accuracy of the gravity estimates. If the scientific objectives of a GFO mission require more accurate gravity estimates, then future work should focus on improvements in the geophysical models, and ways in which the mission design or data processing could reduce the effects of temporal aliasing.

Characterizing Vainshtein solutions in massive gravity

Abstract: We study static, spherically symmetric solutions in a recently proposed ghost-free model of nonlinear massive gravity We focus on a branch of solutions where the helicity-0 mode can be strongly coupled within certain radial regions, giving rise to the Vainshtein effect We truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all nonlinearities of the helicity-0 mode We determine analytically the number and properties of local solutions that exist asymptotically on large scales, and of local (inner) solutions that exist on small scales We find two kinds of asymptotic solutions, one of which is asymptotically flat, while the other one is not, and also two types of inner solutions, one of which displays the Vainshtein mechanism, while the other exhibits a self-shielding behavior of the gravitational field We analyze in detail in which cases the solutions match in an intermediate region The asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while the nonasymptotically flat solutions can connect with both kinds of inner solutions We show furthermore that there are some regions in the parameter space where global solutions do not exist, and characterize precisely in which regions of the phase space the Vainshtein mechanism takes place

Deformed Heisenberg algebra with minimal length and the equivalence principle

Abstract: Studies in string theory and quantum gravity lead to the generalized uncertainty principle (GUP) and suggest the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra. The first look on the classical motion of bodies in a space with corresponding deformed Poisson brackets in a uniform gravitational field can give an impression that bodies of different mass fall in different ways and, thus, the equivalence principle is violated. Analyzing the kinetic energy of a composite body, we find that the motion of its center of mass in the deformed space depends on some effective parameter of deformation. It gives a possibility to recover the equivalence principle in the space with deformed Poisson brackets and, thus, GUP is reconciled with the equivalence principle. We also show that the independence of kinetic energy on composition leads to the recovering of the equivalence principle in the space with deformed Poisson brackets.

Gravitational waves from quasicircular black-hole binaries in dynamical Chern-Simons gravity.

Abstract: Dynamical Chern-Simons gravity cannot be strongly constrained with current experiments because it reduces to general relativity in the weak-field limit. This theory, however, introduces modifications in the nonlinear, dynamical regime, and thus it could be greatly constrained with gravitational waves from the late inspiral of black-hole binaries. We complete the first self-consistent calculation of such gravitational waves in this theory. For favorable spin orientations, advanced ground-based detectors may improve existing solar system constraints by 6 orders of magnitude.

Second-order gravitational self-force

Abstract: The second-order gravitational self-force on a small body is an important problem for gravitational-wave astronomy of extreme mass-ratio inspirals. We give a first-principles derivation of a prescription for computing the first and second perturbed metric and motion of a small body moving through a vacuum background spacetime. The procedure involves solving for a ``regular field'' with a specified (sufficiently smooth) ``effective source'', and may be applied in any gauge that produces a sufficiently smooth regular field.

Spatial and Spectral Analysis of Refined Gravity Data for Modelling the Crust–Mantle Interface and Mantle-Lithosphere Structure

Abstract: We analyse spatial and spectral characteristics of various refined gravity data used for modelling and gravimetric interpretation of the crust–mantle interface and the mantle-lithosphere structure. Depending on the purpose of the study, refined gravity data have either a strong or weak correlation with the Moho depths (Moho geometry). The compilation of the refined gravity data is purely based on available information on the crustal density structure obtained from seismic surveys without adopting any isostatic hypothesis. We demonstrate that the crust-stripped relative-to-mantle gravity data have a weak correlation with the CRUST2.0 Moho depths of about 0.02. Since gravitational signals due to the crustal density structure and the Moho geometry are subtracted from gravity field, these refined gravity data comprise mainly the information on the mantle lithosphere and sub-lithospheric mantle. On the other hand, the consolidated crust-stripped gravity data, obtained from the gravity field after applying the crust density contrast stripping corrections, comprise mainly the gravitational signal of the Moho geometry, although they also contain the gravitational signal due to anomalous mass density structures within the mantle. In the absence of global models of the mantle structure, the best possible option of computing refined gravity data, suitable for the recovery/refinement of the Moho interface, is to subtract the complete crust-corrected gravity data from the consolidated crust-stripped gravity data. These refined gravity data, that is, the homogenous crust gravity data, have a strong absolute correlation of about 0.99 with the CRUST2.0 Moho depths due to removing a gravitational signal of inhomogeneous density structures within the crust and mantle. Results of the spectral signal decomposition and the subsequent correlation analysis reveal that the correlation of the homogenous crust gravity data with the Moho depths is larger than 0.9 over the investigated harmonic spectrum up to harmonic degree 90. The crust-stripped relative-to-mantle gravity data correlate substantially with the Moho depths above harmonic degree 50 where the correlation exceeds 0.5.

Emergent perspective of gravity and dark energy

Abstract: There is sufficient amount of internal evidence in the nature of gravitational theories to indicate that gravity is an emergent phenomenon like, e.g, elasticity. Such an emergent nature is most apparent in the structure of gravitational dynamics. It is, however, possible to go beyond the field equations and study the space itself as emergent in a well-defined manner in (and possibly only in) the context of cosmology. In the first part of this review, I describe various pieces of evidence which show that gravitational field equations are emergent. In the second part, I describe a novel way of studying cosmology in which I interpret the expansion of the universe as equivalent to the emergence of space itself. In such an approach, the dynamics evolves towards a state of holographic equipartition, characterized by an equality in the number of bulk and surface degrees of freedom in a region bounded by the Hubble radius. This principle correctly reproduces the standard evolution of a Friedmann universe. Further, (a) it demands the existence of an early inflationary phase as well as late time acceleration for its successful implementation and (b) allows us to link the value of late time cosmological constant to the e-folding factor during inflation.

Proposal for an observational test of the Vainshtein mechanism.

Abstract: Modified gravity theories capable of genuine self-acceleration typically invoke a Galileon scalar which mediates a long-range force but is screened by the Vainshtein mechanism on small scales. In such theories, nonrelativistic stars carry the full scalar charge (proportional to their mass), while black holes carry none. Thus, for a galaxy free falling in some external gravitational field, its central massive black hole is expected to lag behind the stars. To look for this effect, and to distinguish it from other astrophysical effects, one can correlate the gravitational pull from the surrounding structure with the offset between the stellar center and the black hole. The expected offset depends on the central density of the galaxy and ranges up to $\ensuremath{\sim}0.1\text{ }\text{ }\mathrm{kpc}$ for small galaxies. The observed offset in M87 cannot be explained by this effect unless the scalar force is significantly stronger than gravity. We also discuss the systematic offset of compact objects from the galactic plane as another possible signature.

Weyl-Cartan-Weitzenb\"{o}ck gravity as a generalization of teleparallel gravity

Abstract: We consider a gravitational model in a Weyl-Cartan space-time, in which the Weitzenbock condition of the vanishing of the sum of the curvature and torsion scalar is also imposed. Moreover, a kinetic term for the torsion is also included in the gravitational action. The field equations of the model are obtained from a Hilbert-Einstein type variational principle, and they lead to a complete description of the gravitational field in terms of two fields, the Weyl vector and the torsion, respectively, defined in a curved background. The cosmological applications of the model are investigated for a particular choice of the free parameters in which the torsion vector is proportional to the Weyl vector. Depending on the numerical values of the parameters of the cosmological model, a large variety of dynamic evolutions can be obtained, ranging from inflationary/accelerated expansions to non-inflationary behaviors. In particular we show that a de Sitter type late time evolution can be naturally obtained from the field equations of the model. Therefore the present model leads to the possibility of a purely geometrical description of the dark energy, in which the late time acceleration of the Universe is determined by the intrinsic geometry of the space-time.

GOCE satellite derived gravity and gravity gradient corrected for topographic effect in the South Central Andes region

Abstract: SUMMARY Global gravity field models, derived from satellite measurements integrated with terrestrial observations, provide a model of the Earth's gravity field with high spatial resolution and accuracy. The Earth Gravity Model EGM08, a spherical harmonic expansion of the geopotential up to degree and order 2159, has been used to calculate two functionals of the geopotential: the gravity anomaly and the vertical gravity gradient applied to the South Central Andes area. The satellite-only field of the highest resolution has been developed with the observations of satellite GOCE, up to degree and order 250. The topographic effect, a fundamental quantity for the downward continuation and validation of satellite gravity gradiometry data, was calculated from a digital elevation model which was converted into a set of tesseroids. This data is used to calculate the anomalous potential and vertical gravity gradient. In the Southern Central Andes region the geological structures are very complex, but not well resolved. The processing and interpreting of the gravity anomaly and vertical gradients allow the comparison with geological maps and known tectonic structures. Using this as a basis, a few features can be clearly depicted as the contact between Pacific oceanic crust and the Andean fold and thrust belt, the seamount chains over the Oceanic Nazca Plate, and the Famatinian and Pampean Ranges. Moreover the contact between the Rio de la Plata craton and the Pampia Terrain is of great interest, since it represents a boundary that has not been clearly defined until now. Another great lineament, the Valle Fertil-Desaguadero mega-lineament, an expression of the contact between Cuyania and Pampia terranes, can also be clearly depicted. The authors attempt to demonstrate that the new gravity fields can be used for identifying geological features, and therefore serve as useful innovative tools in geophysical exploration.

Global Crust-Mantle Density Contrast Estimated from EGM2008, DTM2008, CRUST2.0, and ICE-5G

Abstract: We compute globally the consolidated crust-stripped gravity disturbances/anomalies. These refined gravity field quantities are obtained from the EGM2008 gravity data after applying the topographic and crust density contrasts stripping corrections computed using the global topography/bathymetry model DTM2006.0, the global continental ice-thickness data ICE-5G, and the global crustal model CRUST2.0. All crust components density contrasts are defined relative to the reference crustal density of 2,670 kg/m3. We demonstrate that the consolidated crust-stripped gravity data have the strongest correlation with the crustal thickness. Therefore, they are the most suitable gravity data type for the recovery of the Moho density interface by means of the gravimetric modelling or inversion. The consolidated crust-stripped gravity data and the CRUST2.0 crust-thickness data are used to estimate the global average value of the crust-mantle density contrast. This is done by minimising the correlation between these refined gravity and crust-thickness data by adding the crust-mantle density contrast to the original reference crustal density of 2,670 kg/m3. The estimated values of 485 kg/m3 (for the refined gravity disturbances) and 481 kg/m3 (for the refined gravity anomalies) very closely agree with the value of the crust-mantle density contrast of 480 kg/m3, which is adopted in the definition of the Preliminary Reference Earth Model (PREM). This agreement is more likely due to the fact that our results of the gravimetric forward modelling are significantly constrained by the CRUST2.0 model density structure and crust-thickness data derived purely based on methods of seismic refraction.

Topographic/isostatic evaluation of new-generation GOCE gravity field models

Abstract: [1] We use gravity implied by the Earth's rock-equivalent topography (RET) and modeled isostatic compensation masses to evaluate the new global gravity field models (GGMs) from European Space Agency (ESA)'s Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite gravimetry mission. The topography is now reasonably well-known over most of the Earth's landmasses, and also where conventional GGM evaluation is prohibitive due to the lack (or unavailability) of ground-truth gravity data. We construct a spherical harmonic representation of Earth's RET to derive band-limited topography-implied gravity, and test the somewhat simplistic Airy/Heiskanen and Pratt/Hayford hypotheses of isostatic compensation, but which did not improve the agreement between gravity from the uncompensated RET and GOCE. The third-generation GOCE GGMs (based on 12 months of space gravimetry) resolve the Earth's gravity field effectively up to spherical harmonic degree ∼200–220 (∼90–100 km resolution). Such scales could not be resolved from satellites before GOCE. From the three different GOCE processing philosophies currently in use by ESA, the time-wise and direct approaches exhibit the highest sensitivity to short-scale gravity recovery, being better than the space-wise approach. Our topography-implied gravity comparisons bring evidence of improvements from GOCE to gravity field knowledge over the Himalayas, Africa, the Andes, Papua New Guinea and Antarctic regions. In attenuated form, GOCE captures topography-implied gravity signals up to degree ∼250 (∼80 km resolution), suggesting that other signals (originating, e.g., from the crust-mantle boundary and buried loads) are captured as well, which might now improve our knowledge on the Earth's lithosphere structure at previously unresolved spatial scales.

Large-Scale Structure with Gravitational Waves I: Galaxy Clustering

Abstract: Observed angular positions and redshifts of large-scale structure tracers such as galaxies are affected by gravitational waves through volume distortion and magnification effects. Thus, a gravitational wave background can in principle be probed through clustering statistics of large-scale structures. We calculate the observed angular clustering of galaxies in the presence of a gravitational wave background at linear order including all relativistic effects. For a scale-invariant spectrum of gravitational waves, the effects are most significant at the smallest multipoles (2≤l≤5), but typically suppressed by six or more orders of magnitude with respect to scalar contributions for currently allowed amplitudes of the inflationary gravitational wave background. We also discuss the most relevant second-order terms, corresponding to the distortion of tracer correlation functions by gravitational waves. These provide a natural application of the approach recently developed in Schmidt and Jeong {arXiv:1204.3625 [Phys. Rev. D (to be published)]}.

Spectral harmonic analysis and synthesis of Earth's crust gravity field

Abstract: We developed and applied a novel numerical scheme for a gravimetric forward modelling of the Earth’s crustal density structures based entirely on methods for a spherical analysis and synthesis of the gravitational field. This numerical scheme utilises expressions for the gravitational potentials and their radial derivatives generated by the homogeneous or laterally varying mass density layers with a variable height/depth and thickness given in terms of spherical harmonics. We used these expressions to compute globally the complete crust-corrected Earth’s gravity field and its contribution generated by the Earth’s crust. The gravimetric forward modelling of large known mass density structures within the Earth’s crust is realised by using global models of the Earth’s gravity field (EGM2008), topography/bathymetry (DTM2006.0), continental ice-thickness (ICE-5G), and crustal density structures (CRUST2.0). The crust-corrected gravity field is obtained after modelling and subtracting the gravitational contribution of the Earth’s crust from the EGM2008 gravity data. These refined gravity data mainly comprise information on the Moho interface and mantle lithosphere. Numerical results also reveal that the gravitational contribution of the Earth’s crust varies globally from 1,843 to 12,010 mGal. This gravitational signal is strongly correlated with the crustal thickness with its maxima in mountainous regions (Himalayas, Tibetan Plateau and Andes) with the presence of large isostatic compensation. The corresponding minima over the open oceans are due to the thin and heavier oceanic crust.

On the Rayleigh-Taylor instability for incompressible viscous magnetohydrodynamic equations

Abstract: We study the Rayleigh-Taylor problem for two incompressible, immiscible, viscous magnetohydrodynamic (MHD) flows, with zero resistivity, surface tension (or without surface tenstion) and special initial magnetic field, evolving with a free interface in the presence of a uniform gravitational field. First, we reformulate in Lagrangian coordinates MHD equations in a infinite slab as one for the Navier-Stokes equations with a force term induced by the fluid flow map. Then we analyze the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with an free interface separating the two fluids, and both fluids being in (unstable) equilibrium. By a general method of studying a family of modified variational problems, we construct smooth (when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces, thus leading to an global instability result for the linearized problem. Finally, using these pathological solutions, we demonstrate the global instability for the corresponding nonlinear problem in an appropriate sense. In addition, we compute that the so-called critical number indeed is equal $\sqrt{g[\varrho]/2}$.

Weyl-Cartan-Weitzenböck gravity as a generalization of teleparallel gravity

Abstract: We consider a gravitational model in a Weyl-Cartan space-time in which the Weitzenbock condition of the vanishing of the sum of the curvature and torsion scalar is imposed. In contrast to the standard teleparallel theories, our model is formulated in a four-dimensional curved spacetime. The properties of the gravitational field are then described by the torsion tensor and Weyl vector fields. A kinetic term for the torsion is also included in the gravitational action. The field equations of the model are obtained from a Hilbert-Einstein type variational principle, and they lead to a complete description of the gravitational field in terms of two fields, the Weyl vector and the torsion, respectively, defined in a curved background. The cosmological applications of the model are investigated for a particular choice of the free parameters in which the torsion vector is proportional to the Weyl vector. The Newtonian limit of the model is also considered, and it is shown that the Poisson equation can be recovered in the weak field approximation. Depending on the numerical values of the parameters of the cosmological model, a large variety of dynamic evolutions can be obtained, ranging from inflationary/accelerated expansions to non-inflationary behaviors. In particular we show that a de Sitter type late time evolution can be naturally obtained from the field equations of the model. Therefore the present model leads to the possibility of a purely geometrical description of the dark energy, in which the late time acceleration of the Universe is determined by the intrinsic geometry of the space-time.

High-precision maclaurin-based models of rotating liquid planets

Abstract: We present an efficient numerical self-consistent field method for calculating a gravitational model of a rotating liquid planet to spherical harmonic degree ~30 and a precision ~10–12 in the external gravity field. The method's accuracy is validated by comparing results, for Jupiter rotation parameters, with the exact Maclaurin constant-density solution. The method can be generalized to non-constant density.