An Ether Theory of Gravity: the Exponential Metric, Gravitational Waves, Galaxies, Galaxy Clusters and the Expansion of the Universe

We present an ether theory of gravity. Space is filled with an incompressible medium that flows into bodies as they condense it into matter. A body accelerates as g = k0 ve, where ve is the local inflow velocity, and its energy in this medium gives the factor γ and the exponential metric ds 2 = −e−2φc 2dt 2 + e2φ (dR 2 + R 2dΩ2), as read by clocks and rulers that interact with the ether. Light is a shear wave of the same medium, with a Lagrangian that gives its equation; in the potential of a sink the equation gives the refractive index of the exponential metric, the bending of light, the change of frequency and an exact exchange of energy and momentum with a moving mirror. The theory does not take the form of general relativity (GR), but agrees with GR at first order. It reproduces the gravitational shift of clocks, muon lifetimes, Ives–Stilwell and Michelson–Morley results, the perihelion advance of Mercury (42.98″ per century, β = γPPN = 1), and the first-order deflection and delay of light. Its gravitational waves obey the linear tensor equation of GR, with the coupling fixed to 0.2% by the orbital decay of PSR B1913+16; at second post-Newtonian order and in the ringdown it differs from GR, but present data cannot decide. When the ether flow is confined to a layer instead of a sphere, the same equation gives the rotation curves of 129 galaxies without dark matter, with a median error of 9% per galaxy (102 galaxies with at least eight points), comparable to RAR and MOND, and the mass inside R500 of 21 galaxy clusters to 0.09 dex with one constant. That cluster model fails in radius in the X-COP clusters. A thickness with the two factors used for the galaxies, but with an exponent of opposite sign, gives 0.11 dex on 24 cluster points, against 0.13 dex for MOND and 0.08 dex for ΛCDM, the order of the models differing between the cluster samples; this form was chosen after the data were seen. For the expansion of the universe, the energy output per comoving volume follows (1+z)², but the chosen expansion rate does not reproduce 1580 supernovae (χ² 3143 against 1387 for ΛCDM). These results use fitted constants. We state the open points and the observations that would decide.