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Gravitation
About: Gravitation is a research topic. Over the lifetime, 29306 publications have been published within this topic receiving 821510 citations.
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TL;DR: In this article, the authors derived the covariant nonlinear dynamical equations for the gravitational and matter fields on the brane, and then linearized to find the perturbation equations on the Brane.
Abstract: In Randall-Sundrum-type brane-world cosmologies, the dynamical equations on the three-brane differ from the general relativity equations by terms that carry the effects of embedding and of the free gravitational field in the five-dimensional bulk. Instead of starting from an ansatz for the metric, we derive the covariant nonlinear dynamical equations for the gravitational and matter fields on the brane, and then linearize to find the perturbation equations on the brane. The local energy-momentum corrections are significant only at very high energies. The imprint on the brane of the nonlocal gravitational field in the bulk is more subtle, and we provide a careful decomposition of this effect into nonlocal energy density, flux and anisotropic stress. The nonlocal energy density determines the tidal acceleration in the off-brane direction, and can oppose singularity formation via the generalized Raychaudhuri equation. Unlike the nonlocal energy density and flux, the nonlocal anisotropic stress is not determined by an evolution equation on the brane, reflecting the fact that brane observers cannot in general make predictions from initial data. In particular, isotropy of the cosmic microwave background may no longer guarantee a Friedmann geometry. Adiabatic density perturbations are coupled to perturbations in the nonlocal bulk field, and in general the system is not closed on the brane. But on super- Hubble scales, density perturbations satisfy a decoupled third-order equation, and can be evaluated by brane observers. Tensor perturbations on the brane are suppressed by local bulk effects during inflation, while nonlocal effects can serve as a source or a sink. Vorticity on the brane decays as in general relativity, but nonlocal bulk effects can source the gravito-magnetic field, so that vector perturbations can be generated in the absence of vorticity.
373 citations
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TL;DR: In this paper, the Lagrangian Lagrangians were derived using a Palatini variation in which the connection and metric are varied independently, leading to equations whose solutions approach a de Sitter universe at late times.
Abstract: Corrections to Einstein's equations that become important at small curvatures are considered. The field equations are derived using a Palatini variation in which the connection and metric are varied independently. In contrast with the Einstein-Hilbert variation, which yields fourth order equations, the Palatini approach produces second order equations in the metric. The Lagrangian $L(R)=R\ensuremath{-}{\ensuremath{\alpha}}^{2}/R$ is examined and it is shown that it leads to equations whose solutions approach a de Sitter universe at late times. Thus, the inclusion of $1/R$ curvature terms in the gravitational action offers an alternative explanation for the cosmological acceleration.
372 citations
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TL;DR: In this paper, the authors measured the statistics of galaxy peculiar velocities using redshift-space distortions, fσ8mass provides a good test of dark energy models, even without the knowledge of bias or σ8mass required to extract f from this measurement (here f is the logarithmic derivative of the linear growth rate, and σ 8mass is the root-mean-square mass fluctuation in spheres with radius 8h−1Mpc).
Abstract: Measuring the statistics of galaxy peculiar velocities using redshift-space distortions is an excellent way of probing the history of structure formation Because galaxies are expected to act as test particles within the flow of matter, this method avoids uncertainties due to an unknown galaxy density bias We show that the parameter combination measured by redshift-space distortions, fσ8mass provides a good test of dark energy models, even without the knowledge of bias or σ8mass required to extract f from this measurement (here f is the logarithmic derivative of the linear growth rate, and σ8mass is the root-mean-square mass fluctuation in spheres with radius 8h−1Mpc) We argue that redshift-space distortion measurements will help to determine the physics behind the cosmic acceleration, testing whether it is related to dark energy or modified gravity, and will provide an opportunity to test possible dark energy clumping or coupling between dark energy and dark matter If we can measure galaxy bias in addition, simultaneous measurement of both the overdensity and velocity fields can be used to test the validity of equivalence principle, through the continuity equation
372 citations
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TL;DR: In this article, a parametrized post-Einsteinian framework is proposed to interpolate between templates constructed in general relativity and well-motivated alternative theories of gravity, and also include extrapolations that follow sound theoretical principles such as consistency with conservation laws and symmetries.
Abstract: We consider the concept of fundamental bias in gravitational wave astrophysics as the assumption that general relativity is the correct theory of gravity during the entire wave-generation and propagation regime. Such an assumption is valid in the weak field, as verified by precision experiments and observations, but it need not hold in the dynamical strong-field regime where tests are lacking. Fundamental bias can cause systematic errors in the detection and parameter estimation of signals, which can lead to a mischaracterization of the Universe through incorrect inferences about source event rates and populations. We propose a remedy through the introduction of the parametrized post-Einsteinian framework, which consists of the enhancement of waveform templates via the inclusion of post-Einsteinian parameters. These parameters would ostensibly be designed to interpolate between templates constructed in general relativity and well-motivated alternative theories of gravity, and also include extrapolations that follow sound theoretical principles, such as consistency with conservation laws and symmetries. As an example, we construct parametrized post-Einsteinian templates for the binary coalescence of equal-mass, nonspinning compact objects in a quasicircular inspiral. The parametrized post-Einsteinian framework should allow matched filtered data to select a specific set of post-Einsteinian parameters without a priori assuming the validity of the former, thus either verifying general relativity or pointing to possible dynamical strong-field deviations.
370 citations
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TL;DR: In this article, the authors evaluate the consistency of the LIGO-Virgo data with predictions from the theory and find no evidence for new physics beyond general relativity, for black hole mimickers, or for any unaccounted systematics.
Abstract: Gravitational waves enable tests of general relativity in the highly dynamical and strong-field regime. Using events detected by LIGO-Virgo up to 1 October 2019, we evaluate the consistency of the data with predictions from the theory. We first establish that residuals from the best-fit waveform are consistent with detector noise, and that the low- and high-frequency parts of the signals are in agreement. We then consider parametrized modifications to the waveform by varying post-Newtonian and phenomenological coefficients, improving past constraints by factors of ∼2; we also find consistency with Kerr black holes when we specifically target signatures of the spin-induced quadrupole moment. Looking for gravitational-wave dispersion, we tighten constraints on Lorentz-violating coefficients by a factor of ∼2.6 and bound the mass of the graviton to mg≤1.76×10-23 eV/c2 with 90% credibility. We also analyze the properties of the merger remnants by measuring ringdown frequencies and damping times, constraining fractional deviations away from the Kerr frequency to δf^220=0.03-0.35+0.38 for the fundamental quadrupolar mode, and δf^221=0.04-0.32+0.27 for the first overtone; additionally, we find no evidence for postmerger echoes. Finally, we determine that our data are consistent with tensorial polarizations through a template-independent method. When possible, we assess the validity of general relativity based on collections of events analyzed jointly. We find no evidence for new physics beyond general relativity, for black hole mimickers, or for any unaccounted systematics.
368 citations