Cosmological perturbations on local systems

Abstract

We study the effect of cosmological expansion on orbits--galactic, planetary, or atomic--subject to an inverse-square force law. We obtain the laws of motion for gravitational or electrical interactions from general relativity--in particular, we find the gravitational field of a mass distribution in an expanding universe by applying perturbation theory to the Robertson-Walker metric. Cosmological expansion induces an ($\ddot{a}/a)\vec{r}$ force where $a(t)$ is the cosmological scale factor. In a locally Newtonian framework, we show that the $(\ddot{a}/a)\vec{r}$ term represents the effect of a continuous distribution of cosmological material in Hubble flow, and that the total force on an object, due to the cosmological material plus the matter perturbation, can be represented as the negative gradient of a gravitational potential whose source is the material actually present. We also consider the effect on local dynamics of the cosmological constant. We calculate the perihelion precession of elliptical orbits due to the cosmological constant induced force, and work out a generalized virial relation applicable to gravitationally bound clusters.

10 pages

References in corpus (11)

• A Universal Density Profile from Hierarchical Clustering
• The Structure of Cold Dark Matter Halos
• The Structure of Dark Matter Haloes in Hierarchical Clustering Models
• The structural and scaling properties of nearby galaxy clusters: I - The universal mass profile
• The influence of the cosmological expansion on local systems
• Standard Clocks, Orbital Precession and the Cosmological Constant
• XMM-Newton observations of three poor clusters: Similarity in dark matter and entropy profiles down to low mass
• Galaxy cluster mass profiles
• Can Solar System observations tell us something about the cosmological constant?
• Expansion-induced contribution to the precession of binary orbits
• Influence of the cosmological expansion on small systems

Cited by in corpus (28)

• Solar system constraints on f(T) gravity
• Cosmological expansion and local physics
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• Making sense of the bizarre behaviour of horizons in the McVittie spacetime
• On the anomalous secular increase of the eccentricity of the orbit of the Moon
• Tidal Dynamics in Cosmological Spacetimes
• Black Holes in the Universe: Generalized Lemaitre-Tolman-Bondi Solutions
• Quantum corrections to the gravitational potentials of a point source due to conformal fields in de Sitter
• Solar System motions and the cosmological constant: a new approach
• Gravitational waves in the presence of a cosmological constant
• Astronomical constraints on some long-range models of modified gravity
• Quasi-local masses and cosmological coupling of black holes and mimickers
• Cosmological Constant and Local Gravity
• Local cosmological effects of the order of H in the orbital motion of a binary system
• Perspectives on constraining a cosmological constant-type parameter with pulsar timing in the Galactic Center
• The lingering anomalous secular increase of the eccentricity of the orbit of the Moon: further attempts of explanation of cosmological origin
• Influence of cosmological expansion in local experiments
• Two-body orbit expansion due to time-dependent relative acceleration rate of the cosmological scale factor
• Four hints and test candidates of the local cosmic expansion
• The Pioneer Anomaly and a Rotating Gödel Universe
• Local measurement of Λ using pulsar timing arrays
• Turnaround physics beyond spherical symmetry
• The relativistic precession of the orbits
• Constraining an Expanding Locally Anisotropic metric from the Pioneer anomaly
• Pioneer 10 and 11 Spacecraft Anomalous Acceleration in the light of the Nonsymmetric Kaluza-Klein (Jordan-Thiry) Theory
• Orbital precession and other properties of two-body motion in the presence of dark energy
• Two body problem in presence of cosmological constant
• Are we close to put the anomalous perihelion precessions from Verlinde's emergent gravity to the test?