The recent and unexpected measurement of the accelerating expansion of the universe has provided new
motivation for exploring the nature of spacetime. Models that predict modification of gravity at large
distances, such as brane-world models, have recently become of interest [18]. These theories exhibit a strong
coupling phenomenon that makes the gravitational force source-dependent. These theories become testable
at shorter distances, where the coupling sets in for lighter sources [19]. The Earth-Moon system provides a
testbed for investigating the nature of spacetime at solar-system scales. For example, GR predicts that a
gyroscope moving through curved spacetime will precess with respect to a rest frame. This is referred to as
geodetic or de Sitter precession. The Earth-Moon system behaves as a gyroscope with a predicted
geodetic precession of 19.2 msec/year. This is observed using LLR by measuring the lunar perigee
precession [8]. The current limit on the deviation of the geodetic procession from the GR prediction is:
[79
]. This measurement can also be used to set a limit on a possible
cosmological constant:
[61], which has implications for our understanding of dark
energy.
It is also useful to look at violations of GR in the context of metric theories of gravity. Parameterized
Post-Newtonian (PPN) formalism provides a convenient way to describe a class of deviations from GR [50].
The most often considered PPN parameters are
and
:
indicates how much space curvature is
produced per unit mass, while
indicates how nonlinear gravity is (self-interaction).
and
are
identically one in GR. Also of interest are the preferred-frame parameters
and
, which are
identically zero in GR [73, 57].
Limits on can be set from geodetic precession measurements [50], but the best limits presently come
from measurements of the gravitational time delay of light, i.e., the Shapiro effect [62]. Doppler
measurements to the Cassini spacecraft set the current limit on
:
[9].
The Equivalence Principle parameter depends on the PPN parameters
and
:
A nonzero preferred frame would show up as an oscillation of the lunar range at the sum and the
difference of the anomalistic frequency and the annual period [16, 37]. Recent analysis of LLR data sets the
current limit on the PPN parameter [38
]. LLR has also been used to set a
limit on
[38
]. However, the close solar spin axis alignment with the
total solar system angular momentum produces a much tighter constraint on
of order
[51].
Lunar laser ranging also places limits on the gravitomagnetic interaction, the same physical interaction that leads to the Lense–Thirring and Schiff precession phenomena as tested by precession of the Laser Geodynamics Satellites (LAGEOS) orbital plane and by the precession of a gyroscope in Gravity Probe B respectively [41]. In the case of the lunar orbit, rotation is not involved, but rather translation of the Earth and Moon point-masses in the solar system barycenter frame that produce 6 meter amplitude range signatures at both the synodic frequency and twice the synodic frequency. The amplitudes of these signatures are frame-dependent, reflecting the deep connection gravitomagnetism has with the covariant property of relativistic dynamics. Soffel et al. showed the need for the gravitomagnetic term in the LLR equations of motion at the level of 0.15%, whether confined to a PPN context or allowed to vary independently [67]. If another experiment claimed a gravitomagnetic, or “frame-dragging” departure from GR at even the 1% level, LLR data would stand in conflict [39].
http://www.livingreviews.org/lrr-2010-7 |
Living Rev. Relativity 13, (2010), 7
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