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14. Experimental tests of gravitational theory 1

14. EXPERIMENTAL TESTS OF

GRAVITATIONAL THEORY

Revised October 2001 by T. Damour (IHES, Bures-sur-Yvette,France).

Einsteins General Relativity, the current standard theory of gravitation, describesgravity as a universal deformation of the Minkowski metric:

g(x) = + h(x

) , where = diag(1, +1, +1, +1) . (14.1)Alternatively, it can be defined as the unique, consistent, local theory of a massless

spin-2 field h, whose source must then be the total, conserved energy-momentumtensor [1]. General Relativity is classically defined by two postulates. One postulatestates that the Lagrangian density describing the propagation and self-interaction of thegravitational field is

LEin[g] =

c4

16GN

ggR(g) , (14.2)

R(g) = + , (14.3)

= 12

g(g+ g g) , (14.4)where GN is Newtons constant, g= det(g), and g is the matrix inverse ofg. Asecond postulate states that g couples universally, and minimally, to all the fields ofthe Standard Model by replacing everywhere the Minkowski metric . Schematically(suppressing matrix indices and labels for the various gauge fields and fermions and forthe Higgs doublet),

LSM[, A, H , g] =

14

gggFaF

a

g D 1

2

ggDHDHg V(H)

g H , (14.5)

where + = 2g, and where the covariant derivative D contains, besides theusual gauge field terms, a (spin dependent) gravitational contribution (x) [2]. From thetotal actionStot[g, , A, H] =c1

d4x(LEin+LSM) follow Einsteins field equations,

R 12

Rg= 8GN

c4 T . (14.6)

Here R= gR, T =ggT, and T = (2/g)LSM/g is the (symmetric)

energy-momentum tensor of the Standard Model matter. The theory is invariantunder arbitrary coordinate transformations: x =f(x). To solve the field equationsEq. (14.6) one needs to fix this coordinate gauge freedom. E.g. the harmonic gauge(which is the analogue of the Lorentz gauge, A = 0, in electromagnetism) correspondsto imposing the condition (

gg) = 0.

CITATION: D.E. Groom et al., European Physical Journal C15, 1 (2000)

available on the PDG WWW pages (URL: http://pdg.lbl.gov/) November 19, 2001 09:52

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2 14. Experimental tests of gravitational theory

In this Review, we only consider the classical limit of gravitation (i.e. classicalmatter and classical gravity). Considering quantum matter in a classical gravitationalbackground already poses interesting challenges, notably the possibility that the zero-pointfluctuations of the matter fields generate a nonvanishing vacuum energy density vac,corresponding to a term g vacin LSM[3]. This is equivalent to adding a cosmologicalconstant term + g on the left-hand side of Einsteins equations Eq. (14.6), with

= 8GNvac/c4

. Recent cosmological observations (see the followingReviews) suggesta positive value of corresponding to vac (2.3 103eV)4. Such a small value hasa negligible effect on the tests discussed below. Quantizing the gravitational field itselfposes a very difficult challenge because of the perturbative non-renormalizability ofEinsteins Lagrangian. Superstring theory offers a promising avenue toward solving thischallenge.

14.1. Experimental tests of the couplingbetween matter and gravity

The universality of the coupling between g and the Standard Model matterpostulated in Eq. (14.5) (Equivalence Principle) has many observable consequences.First, it predicts that the outcome of a local non-gravitational experiment, referred tolocal standards, does not depend on where, when, and in which locally inertial frame,the experiment is performed. This means, for instance, that local experiments shouldneither feel the cosmological evolution of the universe (constancy of the constants), norexhibit preferred directions in spacetime (isotropy of space, local Lorentz invariance).These predictions are consistent with many experiments and observations. The best limiton a possible time variation of the basic coupling constants concerns the fine-structureconstant em and has been obtained by analyzing a natural fission reactor phenomenonwhich took place at Oklo, Gabon, two billion years ago [4]

6.7 1017yr1