Dark Energy and Extending the Geodesic Equations of Motion: Its Construction and Experimental Constraints

Abstract

With the discovery of Dark Energy, ${\Lambda }_{DE}$, there is now a universal length scale, ${\ell }_{DE}=c/({\Lambda }_{DE}G{)}^{1/2}$, associated with the universe that allows for an extension of the geodesic equations of motion. In this paper, we will study a specific class of such extensions, and show that contrary to expectations, they are not automatically ruled out by either theoretical considerations or experimental constraints. In particular, we show that while these extensions affect the motion of massive particles, the motion of massless particles are not changed; such phenomena as gravitational lensing remain unchanged. We also show that these extensions do not violate the equivalence principal, and that because ${\ell }_{DE}=14010_{820}^{800}$ Mpc, a specific choice of this extension can be made so that effects of this extension are not be measurable either from terrestrial experiments, or through observations of the motion of solar system bodies. A lower bound for the only parameter used in this extension is set.

19 pages. This is the published version of the first half of arXiv:0711.3124v2 with corrections included

References in corpus (26)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Quintessence, Cosmic Coincidence, and the Cosmological Constant
• The Cosmological Constant
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
• Chameleon Cosmology
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Tests of the Gravitational Inverse-Square Law
• 1/R gravity and Scalar-Tensor Gravity
• Study of the anomalous acceleration of Pioneer 10 and 11
• Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration
• Sub-millimeter tests of the gravitational inverse-square law: A search for "large" extra dimensions
• Detecting Dark Energy in Orbit -- the Cosmological Chameleon
• Sub-millimeter Tests of the Gravitational Inverse-square Law
• Modified gravity with $\ln R$ terms and cosmic acceleration
• Extended Gravity Theories and the Einstein-Hilbert Action
• Strongly Coupled Chameleon Fields: New Horizons in Scalar Field Theory
• f(R) actions, cosmic acceleration and local tests of gravity
• TASI Lectures on the Cosmological Constant
• Modified gravity, Dark Energy and MOND
• A Quantum Cosmology: No Dark Matter, Dark Energy nor Accelerating Universe

Cited by in corpus (3)

• An Empirical Explanation of the Anomalous Increases in the Astronomical Unit and the Lunar Eccentricity
• Dark Energy and Extending the Geodesic Equations of Motion: Connecting the Galactic and Cosmological Length Scales
• Dark Energy and Extending the Geodesic Equations of Motion: A Spectrum of Galactic Rotation Curves