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Title: The power of general relativity

Abstract

We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to R{sup 1+{delta}}. This scale-free extension reduces to general relativity when {delta}{yields}0. In order to constrain generalizations of general relativity of this power class, we analyze the behavior of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires {delta}>0 or {delta}<-1/4. The stable attractors of the evolution are found. By considering the synthesis of light elements (helium-4, deuterium and lithium-7) we obtain the bound -0.017<{delta}<0.0012. We evaluate the effect on the power spectrum of clustering via the shift in the epoch of matter-radiation equality. The horizon size at matter-radiation equality will be shifted by {approx}1% for a value of {delta}{approx}0.0005. We study the stable extensions of the Schwarzschild solution in these theories and calculate the timelike and null geodesics. No significant bounds arise from null geodesic effects but the perihelion precession observations lead to the strong bound {delta}=2.7{+-}4.5x10{sup -19} assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound 0{<=}{delta}<7.2x10{sup -19} on theories of this type.

Authors:
;  [1]
  1. DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
Publication Date:
OSTI Identifier:
20711523
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.103005; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ATTRACTORS; COSMOLOGY; DEUTERIUM; DIFFERENTIAL GEOMETRY; ENERGY SPECTRA; GENERAL RELATIVITY THEORY; GEODESICS; GRAVITATION; HELIUM 4; IDEAL FLOW; LAGRANGIAN FUNCTION; LITHIUM 7; NUCLEOSYNTHESIS; SCHWARZSCHILD METRIC; SPACE-TIME; UNIVERSE

Citation Formats

Clifton, Timothy, and Barrow, John D. The power of general relativity. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.103005.
Clifton, Timothy, & Barrow, John D. The power of general relativity. United States. doi:10.1103/PhysRevD.72.103005.
Clifton, Timothy, and Barrow, John D. Tue . "The power of general relativity". United States. doi:10.1103/PhysRevD.72.103005.
@article{osti_20711523,
title = {The power of general relativity},
author = {Clifton, Timothy and Barrow, John D.},
abstractNote = {We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to R{sup 1+{delta}}. This scale-free extension reduces to general relativity when {delta}{yields}0. In order to constrain generalizations of general relativity of this power class, we analyze the behavior of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires {delta}>0 or {delta}<-1/4. The stable attractors of the evolution are found. By considering the synthesis of light elements (helium-4, deuterium and lithium-7) we obtain the bound -0.017<{delta}<0.0012. We evaluate the effect on the power spectrum of clustering via the shift in the epoch of matter-radiation equality. The horizon size at matter-radiation equality will be shifted by {approx}1% for a value of {delta}{approx}0.0005. We study the stable extensions of the Schwarzschild solution in these theories and calculate the timelike and null geodesics. No significant bounds arise from null geodesic effects but the perihelion precession observations lead to the strong bound {delta}=2.7{+-}4.5x10{sup -19} assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound 0{<=}{delta}<7.2x10{sup -19} on theories of this type.},
doi = {10.1103/PhysRevD.72.103005},
journal = {Physical Review. D, Particles Fields},
number = 10,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • Recently one of us proposed a general theory of variable rest masses (VMT) compatible with post-Newtonian solar-system experiments for a wide range of its two parameters r and q, provided the asymptotic value of its fundamental field f is in a certain narrow range. Here we show that the stationary matter-free black-hole solutions of the VMT are identical to those of general relativity. In addition for r < 0 and q > 0 (part of the range mentioned), relativistic neutron-star models in the VMT are very similar to their general-relativistic counterparts. Thus experimental discrimination between the two theories in themore » strong-field limit seems unfeasible. We show that in all isotropic cosmological models of the VMT capable of describing the present epoch, the Newtonian gravitational constant G/sub N/ is positive throughout the cosmological expansion. There exist nonsingular VMT cosmological solutions; this is an advantage the VMT has over general relativity. For r < 0 and q > 0 all VMT cosmological models converge to their general-relativistic analogs at late times. As a consequence the asymptotic f attains just the required values to guarantee agreement of the VMT with post-Newtonian experiments. The VMT with r < 0 and q > 0 all VMT cosmological models converge to their general-relativistic analogs at late times. As a consequence the asymptotic f attains just the required values to guarantee agreement of the VMT with post-Newtonian experiments. The VMT with r < 0 and q > 0 predicts a positive Nordtvedt-effect coefficient. It also predicts that G/sub N/ is currently decreasing on a time scale which could be long compared to the Hubble time. Verification of these predictions would rule out general relativity; its most natural replacement would be the VMT with r < 0 and q > 0, and not a generic scalar-tensor theory. The success of general relativity in most respects could then be understood because the VMT with R < 0 and q > 0 mimics it.« less