36 research outputs found
Dark matter vs. modifications of the gravitational inverse-square law. Results from planetary motion in the solar system
Dark matter or modifications of the Newtonian inverse-square law in the
solar-system are studied with accurate planetary astrometric data. From
extra-perihelion precession and possible changes in the third Kepler's law, we
get an upper limit on the local dark matter density, rho_{DM} < 3*10^{-16}
kg/m^3 at the 2-sigma confidence level. Variations in the 1/r^2 behavior are
considered in the form of either a possible Yukawa-like interaction or a
modification of gravity of MOND type. Up to scales of 10^{11} m,
scale-dependent deviations in the gravitational acceleration are really small.
We examined the MOND interpolating function mu in the regime of strong gravity.
Gradually varying mu suggested by fits of rotation curves are excluded, whereas
the standard form mu(x)= x/(1+x^2)^{1/2} is still compatible with data. In
combination with constraints from galactic rotation curves and theoretical
considerations on the external field effect, the absence of any significant
deviation from inverse square attraction in the solar system makes the range of
acceptable interpolating functions significantly narrow. Future radio ranging
observations of outer planets with an accuracy of few tenths of a meter could
either give positive evidence of dark matter or disprove modifications of
gravity.Comment: 7 pages, 4 figures, accepted for publication in MNRA
Imprints of deviations from the gravitational inverse-square law on the power spectrum of mass fluctuations
Deviations from the gravitational inverse-square law would imprint
scale-dependent features on the power spectrum of mass density fluctuations. We
model such deviations as a Yukawa-like contribution to the gravitational
potential and discuss the growth function in a mixed dark matter model with
adiabatic initial conditions. Evolution of perturbations is considered in
general non-flat cosmological models with a cosmological constant, and an
analytical approximation for the growth function is provided. The coupling
between baryons and cold dark matter across recombination is negligibly
affected by modified gravity physics if the proper cutoff length of the
long-range Yukawa-like force is > 10 h^{-1} Mpc. Enhancement of gravity affects
the subsequent evolution, boosting large-scale power in a way that resembles
the effect of a lower matter density. This phenomenon is almost perfectly
degenerate in power-spectrum shape with the effect of a background of massive
neutrinos. Back-reaction on density growth from a modified cosmic expansion
rate should however also affect the normalization of the power spectrum, with a
shape distortion similar to the case of a non-modified background.Comment: 8 pages, 7 figures; submitted to MNRA
The basis of nonlocal curvature invariants in quantum gravity theory
A complete basis of nonlocal invariants in quantum gravity theory is built to
third order in spacetime curvature and matter-field strengths. The nonlocal
identities are obtained which reduce this basis for manifolds with
dimensionality . The present results are used in heat-kernel theory,
theory of gauge fields and serve as a basis for the model-independent approach
to quantum gravity and, in particular, for the study of nonlocal vacuum effects
in the gravitational collapse problem.Comment: 28 pages, REVTeX, Alberta Thy 14-9
Asymptotic behaviours of the heat kernel in covariant perturbation theory
The trace of the heat kernel is expanded in a basis of nonlocal curvature
invariants of th order. The coefficients of this expansion (the nonlocal
form factors) are calculated to third order in the curvature inclusive. The
early-time and late-time asymptotic behaviours of the trace of the heat kernel
are presented with this accuracy. The late-time behaviour gives the criterion
of analyticity of the effective action in quantum field theory. The latter
point is exemplified by deriving the effective action in two dimensions.Comment: 22 pages, REVTeX, Alberta Thy 45-9
An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges
The spacetime of the metric-affine gauge theory of gravity (MAG) encompasses
{\it nonmetricity} and {\it torsion} as post-Riemannian structures. The sources
of MAG are the conserved currents of energy-momentum and dilation, shear and
spin. We present an exact static spherically symmetric vacuum solution of the
theory describing the exterior of a lump of matter carrying mass and dilation,
shear and spin charges.Comment: 13 pages, RevTe
Partial summation of the nonlocal expansion for the gravitational effective action in 4 dimensions
The vacuum action for the gravitational field admits a known expansion in
powers of the Ricci tensor with nonlocal operator coefficients (form factors).
We show that going over to a different basis of curvature invariants makes
possible a partial summation of this expansion. Only the form factors of the
Weyl-tensor invariants need be calculated. The full action is then uniquely
recovered to all orders from the knowledge of the trace anomaly. We present an
explicit expression for the partially summed action, and point out
simplifications resulting in the vertex functions. An application to the effect
of the vacuum gravitational waves is discussed.Comment: 12 pages, LaTe
Some Spinor-Curvature Identities
We describe a class of spinor-curvature identities which exist for Riemannian
or Riemann-Cartan geometries. Each identity relates an expression quadratic in
the covariant derivative of a spinor field with an expression linear in the
curvature plus an exact differential. Certain special cases in 3 and 4
dimensions which have been or could be used in applications to General
Relativity are noted.Comment: 5 pages Plain TeX, NCU-GR-93-SSC
Modified Newton's gravity in Finsler Space as a possible alternative to dark matter hypothesis
A modified Newton's gravity is obtained as the weak field approximation of
the Einstein's equation in Finsler space. It is found that a specified Finsler
structure makes the modified Newton's gravity equivalent to the modified
Newtonian dynamics (MOND). In the framework of Finsler geometry, the flat
rotation curves of spiral galaxies can be deduced naturally without invoking
dark matter.Comment: some changes have been added, to be published in Phy. Lett.