Frequency Domain Analysis of Partial-Tensor Rotating Accelerometer Gravity Gradiometer

The output model of a rotating accelerometer gravity gradiometer (RAGG) established by the inertial dynamics method cannot reflect the change of signal frequency, and calibration sensitivity and self-gradient compensation effect for the RAGG is a very important stage in the development process that cannot be omitted. In this study, a model based on the outputs of accelerometers on the disc of RGAA is established to calculate the gravity gradient corresponding to the distance, through the study of the RAGG output influenced by a surrounding mass in the frequency domain. Taking particle, sphere, and cuboid as examples, the input-output models of gravity gradiometer are established based on the center gradient and four accelerometers, respectively. Simulation results show that, if the scale factors of the four accelerometers on the disk are the same, the output signal of the RAGG only contains (4k+2)ω (ω is the spin frequency of disc for RAGG) harmonic components, and its amplitude is related to the orientation of the surrounding mass. Based on the results of numerical simulation of the three models, if the surrounding mass is close to the RAGG, the input-output models of gravity gradiometer are more accurate based on the four accelerometers. Finally, some advantages and disadvantages of cuboid and sphere are compared and some suggestions related to calibration and self-gradient compensation are given.

Massive ghosts in higher-derivative models

This chapter describes the unsolved problem of the massive unphysical ghost and related instabilities in higher-derivative models of gravity. After explaining what ghosts and tachyons are, the chapter describes the situation with ghosts in polynomial models and non-local models. It is shown that the unitarity of the S-matrix cannot be regarded as the main criterion for consistency in gravitational models. The effective approach to the problem of ghosts is described from a general perspective. After that, the chapter presents a basic discussion of stable and unstable cosmological solutions in massive ghost theory, and their correspondence with the effective approach.

The induced gravity approach

This short chapter includes a general review and analysis of the induced gravity approach. Induced gravity is regarded as one way of resolving the contradiction between renormalizability and the presence of higher-derivative terms in quantum gravity. Following the classical works by Zeldovich and Sakharov, the chapter considers gravity induced from the cut-off and shows that the purely induced version does not provide a satisfactory output. After that, using the results of chapter 12, models of gravity induced from phase transitions in scalar field theory are discussed. The general result is that induced gravity does not resolve the fundamental problem of quantum gravity, owing to the presence of ghosts and their corresponding instabilities. In the last section of this chapter, the cosmological constant problem is discussed as another, equally fundamental problem, which remains unsolved to this day.

Schwarzschild-like solutions in Finsler–Randers gravity

In this work, we extend for the first time the spherically symmetric Schwarzschild and Schwarzschild–De Sitter solutions with a Finsler–Randers-type perturbation which is generated by a covector $$A_\gamma $$ A γ . This gives a locally anisotropic character to the metric and induces a deviation from the Riemannian models of gravity. A natural framework for this study is the Lorentz tangent bundle of a spacetime manifold. We apply the generalized field equations to the perturbed metric and derive the dynamics for the covector $$A_\gamma $$ A γ . Finally, we find the timelike, spacelike and null paths on the Schwarzschild–Randers spacetime, we solve the timelike ones numerically and we compare them with the classic geodesics of general relativity. The obtained solutions are new and they enrich the corresponding literature.

Analytical investigation of wave absorption by a rotating black hole analogue

Perturbations in a draining vortex can be described analytically in terms of confluent Heun functions. In the context of analogue models of gravity in ideal fluids, we investigate analytically the absorption length of waves in a draining bathtub, a rotating black hole analogue, using confluent Heun functions. We compare our analytical results with the corresponding numerical ones, obtaining excellent agreement.

Solar system tests of a new class of f(z) theory

Recently, a new kind of [Formula: see text] theory is proposed to provide a different perspective for the development of reliable alternative models of gravity in which the [Formula: see text] Lagrangian terms are reformulated as polynomial parametrizations [Formula: see text]. In the previous study, the parameters in the [Formula: see text] models have been constrained by using cosmological data. In this paper, these models will be tested by the observations in the solar system. After solving the Ricci scalar as a function of the redshift, one could obtain [Formula: see text] that could be used to calculate the standard Parametrized-Post-Newtonian (PPN) parameters. First, we fit the parametric models with the latest cosmological observational data. Then, the tests are performed by solar system observations. And last we combine the constraints of solar system and cosmology together and reconstruct the [Formula: see text] actions of the [Formula: see text] parametric models.

Measuring Gravity at Cosmological Scales

This review is a pedagogical introduction to models of gravity and how they are constrained through cosmological observations. We focus on the Horndeski scalar-tensor theory and on the quantities that can be measured with a minimum of assumptions. Alternatives or extensions of general relativity have been proposed ever since its early years. Because of the Lovelock theorem, modifying gravity in four dimensions typically means adding new degrees of freedom. The simplest way is to include a scalar field coupled to the curvature tensor terms. The most general way of doing so without incurring in the Ostrogradski instability is the Horndeski Lagrangian and its extensions. Testing gravity means therefore, in its simplest term, testing the Horndeski Lagrangian. Since local gravity experiments can always be evaded by assuming some screening mechanism or that baryons are decoupled, or even that the effects of modified gravity are visible only at early times, we need to test gravity with cosmological observations in the late universe (large-scale structure) and in the early universe (cosmic microwave background). In this work, we review the basic tools to test gravity at cosmological scales, focusing on model-independent measurements.

A HERO for General Relativity

HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios—a fast, 4-h orbit with high perigee height of 1047 km and a slow, 21-h path with a low perigee height of 642 km . HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment J 2 of the Earth which, among other things, affects the semimajor axis a via a secular trend of ≃4–12 cm yr − 1 , depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as 0 . 7 cm yr − 1 . Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations, not treated here. Moreover, the large eccentricity of the orbit would allow one to constrain several long-range modified models of gravity and accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the G J 2 / c 2 signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles J ℓ of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors σ J ℓ of a recent global Earth’s gravity field model are better than 1 % for all the post-Newtonian effects considered, with a peak of ≃ 10 − 7 for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable.

Recycling of depleted continental mantle by subduction and plumes at the Hikurangi Plateau large igneous province, southwestern Pacific Ocean

Seismic reflection and refraction data from Hikurangi Plateau (southwestern Pacific Ocean) require a crustal thickness of 10 ± 1 km, seismic velocity of 7.25 ± 0.35 km/s at the base of the crust, and mantle velocity of 8.30 ± 0.25 km/s just beneath the Moho. Published models of gravity data that assume normal crust and mantle density predict 5–10-km-thicker crust than we observe, suggesting that the mantle beneath Hikurangi Plateau has anomalously low density, which is inconsistent with previous suggestions of eclogite to explain observations of high seismic velocity. The combination of high seismic velocity and low density requires the mantle to be highly depleted and not serpentinized. We propose that Hikurangi Plateau formed by decompression melting of buoyant mantle that was removed from a craton root by subduction, held beneath 660 km by viscous coupling to slabs, and then rose as a plume from the lower mantle. Ancient Re-Os ages from mantle xenoliths in nearby South Island, New Zealand, support this hypothesis. Erosion of buoyant depleted mantle from craton roots by subduction and then recycling in plumes to make new lithosphere may be an important global geochemical process.