Foundations for a Theory of Gravitation Theories

The Superspace of geometrodynamics

“…More precisely, the equivalence principle suggests to only take the metric as dynamical variable [76] representing the gravitational field (to which matter then couples universally), whereas diffeomorphism invariance, derivability from an invariant Lagrangian (alternatively: local energy-momentum conservation in the sense of covariant divergencelessness), dependence of the equations on the metric up to at most second derivatives, and, finally, four-dimensionality lead uniquely to the left-hand side of Einstein's equation, including a possibly non-vanishing cosmological constant [54]. Here we will review how this 'deduction' works in the Hamiltonian setting on phase space T * Riem(Σ), which goes back to [40,41,51,74].…”

Clocks in Space for Tests of Fundamental Physics

“…This principle implies that gravity can be identified to space-time geometry which is described mathematically by a symmetric order 2 tensor, the space-time metric . More precisely, the EEP implies that there exists only one space-time metric to which all matter minimally couples to (see Thorne et al, 1971). In practice, this means that the equations of motion for matter can be derived from the action of the Standard Model of particles in which the Minkowski metric is replaced by the space-time metric :…”

“…Several groups in the world have pursued effort to constrain such hypothetical linear drifts: at SYRTE, Observatoire de Paris (see Guéna et al, 2012), NIST (see Rosenband et al 2008), Berkeley (see Leefer et al, 2013), NPL (see Godun et al, 2014), PTB (see Huntemann et al, 2014), … The current constraints on the variation of the three constants (fine structure constant, ratio between the mass of the electron and the mass of the proton and ration between the mass of the light quarks and the QCD energy scale) are at the level of 10 -16 per year. More recently, searches for a harmonic temporal variation of the constants of Nature using atomic clocks have been performed in Berkeley (see Van Tilburg et al, 2015) and at SYRTE (see Hees et al, 2016a).…”

Slightly Bimetric Gravitation

“…Various equivalence principles are satisfied, or violated, as the case may be, for particular slightly bimetric theories, so different versions might provide tests of various equivalence principles. Theories in which matter is not universally coupled will tend to violate the weak equivalence principle [89]. Because some slightly bimetric theories grade continuously into general relativity, these versions ought to remain viable as long as general relativity's outstanding track record persists.…”

“…89,429), where M µρσν is a tensor density of weight 1 and b is a constant. This result follows from the converse of Poincaré's lemma in Minkowski spacetime.…”