The Local Effects of Cosmological Variations in Physical 'Constants' and Scalar Fields I. Spherically Symmetric Spacetimes

Abstract

We apply the method of matched asymptotic expansions to analyse whether cosmological variations in physical `constants' and scalar fields are detectable, locally, on the surface of local gravitationally bound systems such as planets and stars, or inside virialised systems like galaxies and clusters. We assume spherical symmetry and derive a sufficient condition for the local time variation of the scalar fields that drive varying constants to track the cosmological one. We calculate a number of specific examples in detail by matching the Schwarzschild spacetime to spherically symmetric inhomogeneous Tolman-Bondi metrics in an intermediate region by rigorously construction matched asymptotic expansions on cosmological and local astronomical scales which overlap in an intermediate domain. We conclude that, independent of the details of the scalar-field theory describing the varying `constant', the condition for cosmological variations to be measured locally is almost always satisfied in physically realistic situations. The proof of this statement provides a rigorous justification for using terrestrial experiments and solar system observations to constrain or detect any cosmological time variations in the traditional `constants' of Nature.

30 pages, 3 figures; corrected typos

References in corpus (1)

• The Local Effects of Cosmological Variations in Physical 'Constants' and Scalar Fields II. Quasi-Spherical Spacetimes

Cited by in corpus (29)

• Modified Gravity and Cosmology
• Evading Equivalence Principle Violations, Cosmological and other Experimental Constraints in Scalar Field Theories with a Strong Coupling to Matter
• Environmental Dependence of Masses and Coupling Constants
• Cosmological expansion and local physics
• Accelerated expansion from structure formation
• Does the mass of a black hole decrease due to the accretion of phantom energy
• Detecting Chameleons: The Astronomical Polarization Produced by Chameleon-like Scalar Fields
• The Effect of a Chameleon Scalar Field on the Cosmic Microwave Background
• Making sense of the bizarre behaviour of horizons in the McVittie spacetime
• A Generalized Theory of Varying Alpha
• General Dynamics of Varying-Alpha Universes
• On the Magnitude of Dark Energy Voids and Overdensities
• Black Holes in the Universe: Generalized Lemaitre-Tolman-Bondi Solutions
• Varying-Alpha Cosmologies with Potentials
• Local Experiments See Cosmologically Varying Constants
• Varying Alpha: New Constraints from Seasonal Variations
• Composition-dependent long range forces from varying m_p/m_e
• Shortcomings of Shapiro delay-based tests of the equivalence principle on cosmological scales
• The Local Effects of Cosmological Variations in Physical 'Constants' and Scalar Fields II. Quasi-Spherical Spacetimes
• On the cosmological evolution of alpha and mu and the dynamics of dark energy
• Varying alpha from N-body Simulations
• Local cosmological effects of the order of H in the orbital motion of a binary system
• Bouncing Anisotropic Universes with Varying Constants
• Varying-Alpha and K-Essence
• Impact of the matter density uncertainty on the dark energy reconstruction
• Observable Effects of Scalar Fields and Varying Constants
• Assessing the viability of successful reconstruction of the dynamics of dark energy using varying fundamental couplings
• Impact of inhomogeneities on slowly rolling Quintessence: implications for the local variations of the fine-structure constant
• Cosmological Consequences of Topological Defects: Dark Energy and Varying Fundamental Constants