Cosmology in a Scalar Ether Theory of Gravitation
| Scientific Paper | |
|---|---|
| Title | Cosmology in a Scalar Ether Theory of Gravitation |
| Read in full | Link to paper |
| Author(s) | Mayeul Arminjon |
| Keywords | gravitation, ether, relativity, cosmic acceleration, infinite dilution, cyclic universe |
| Published | 2000 |
| No. of pages | 15 |
Read the full paper here
Abstract
Some motivation for an ether theory of gravitation is presented. The equations of one such theory, based on just one scalar field, are given. It is a preferred-frame theory with a flat background metric and a curved physical metric. Motion is governed by an extension of the special-relativistic form of Newton’s second law. The current status of the observational test is favourable. In particular, the new theory reduces to Newton’s when it has to, and it does explain the effects of gravitation on light rays. In the most general form of the metric, cosmic space expansion occurs with a cosmological time-dilation. Expansion is necessarily accelerated, according to that theory. An analytical cosmological solution is got for a general form of the matter tensor. Two kinds of scenarios are possible: either expansion from an infinite density at past infinity, or contraction-expansion cycles beginning and ending with infinite dilution, and with a bounce at a finite maximum density. In the most likely scenario, there is an infinite number of non-identical such cycles. The time scale for the current cycle is very large.
Overview
Mayeul Arminjon, of the Laboratoire "Sols, Solides, Structures" at the Institut de Mécanique de Grenoble, presents here the cosmological consequences of a gravitation theory he had been developing through the 1990s: a scalar, preferred-frame theory in which gravity is not spacetime curvature imposed by field equations of the Einstein type, but a pressure effect in an ether. The paper is in two halves. The first summarises the theory's motivation and equations and reviews how it fares against the standard tests of a gravitation theory. The second applies it to a homogeneous universe and derives the cosmological scenarios it permits.
The departure from the mainstream account is structural rather than cosmetic. General relativity is rejected as the framework, not merely amended. Arminjon's argument for doing so is that quantum theory, descending from Hamiltonian mechanics, needs a preferred time coordinate, whereas general relativity forbids any preferred foliation; that the Casimir effect shows the vacuum to have physical properties, again pointing toward an ether; and that the Einstein equations do not by themselves fix a metric on a given manifold, so that practical calculations quietly add four gauge equations whose interpretive status he regards as unsettled. He also notes the failure of identified baryonic candidates to supply galactic dark matter as a hint that the gravitation theory itself may be wrong at large scales.
The theory
Ether pressure as the gravitational field
Gravitation is carried by a single scalar field pe, the macroscopic "ether pressure", with an associated ether density ρe related by pe = c2ρe. The gravity acceleration is g = −grad pe / ρe, so that pressure and density decrease toward an attracting body: gravitation is read heuristically as Archimedes' thrust in the ether. The field equation couples the Laplacian of pe to its second derivative with respect to a local time and to the mass-energy density σ, so it is a genuinely hyperbolic wave-type equation rather than a Poisson equation.
Two metrics coexist. A flat Euclidean background metric g0 lives on the space manifold; the physical metric g differs from it by a contraction of rods in the direction of g, in the ratio β ≡ ρe(t,x)/ρe∞(t), where the superscripted infinity denotes the value far from matter. Since β ≤ 1 this is a contraction analogous to length contraction, and clock rates are dilated in the inverse ratio, so that a local time tx runs slow relative to an absolute time t with dtx/dt = β. Motion is governed not by a geodesic postulate but by an extension of Newton's second law, which for dust yields Tμν;ν = bμ with a specified non-zero right-hand side, reducing to the general-relativistic conservation law when the field is static.
The standard tests
A post-Newtonian expansion in the small parameter ε2 ≈ Umax/c2 reproduces Newtonian gravity at zeroth order, with solar-system deviations of order 10−6, as in general relativity. Gravitational redshift follows because γ00 = 1 − 2U/c2 + O(ε4) also holds here and non-gravitational physics is written in the physical metric. Light deflection and Shapiro delay follow from Schwarzschild motion, which the theory also predicts. Mercury's perihelion is the open case: preferred-frame effects enter the motion of massive test particles already at first post-Newtonian order, and Arminjon argues that one cannot pronounce on the residual advance until the entire celestial-mechanical fit is redone within the new theory, with the solar system's velocity V through the ether as an output. For binary pulsars he reports a formula closely analogous to the quadrupole formula, giving an energy loss with no monopole or dipole terms.
Cosmology
Because rod contraction responds to spatial heterogeneity of ρe, Arminjon argues that temporal heterogeneity must also act, isotropically, giving a scale factor R(t) multiplying the metric. Conservation of ether then requires R3ρe∞ = constant, so expansion is not optional but forced by the theory. He postulates a cosmological time dilation dtx/dt = β/Rn with n a free real exponent, and the homogeneous case yields a flat Robertson-Walker line element in cosmic time τ. With β = 1 everywhere there is no gravitational attraction at all in a homogeneous universe.
The field equation becomes ρ̈e + 4πGσρe = 0, and rearrangement gives a deceleration parameter q ≤ −4: expansion is necessarily accelerated, and the greater the matter density the stronger the acceleration — the opposite of the general-relativistic result. Two families of solutions follow. For n > 9/2 with integration constant A ≥ 0, density grows without bound into the infinite past, giving arbitrarily high early density with no big bang singularity; Arminjon regards this branch as unphysical because infinite dilution arrives at a finite cosmic time but an infinite absolute time. Otherwise one gets symmetric contraction-expansion cycles, each beginning and ending in infinite dilution with a non-singular bounce at finite maximum density; for n < 3 there is an infinite sequence of non-identical cycles, which he takes as the most likely case. If the cosmic microwave background is to be explained by a past high-density stage, the resulting "age of the Universe" since maximum density is of order 1019 years; even a modest εmax/ε0 ≈ 100, the minimum needed to read z ≈ 4 redshifts as cosmological, gives hundreds of billions of years.
Assessment
The distinctive achievement here is that acceleration is not fitted but forced. The paper was written just after the 1998–1999 supernova results, and a theory that had been developed for quite other reasons turns out to make q ≤ −4 unavoidable, with no cosmological constant and no dark-energy component inserted by hand. That is a real prediction rather than an accommodation, and it is the strongest thing the paper has. The framework is also honest in a way that alternative-gravity papers often are not: Arminjon states plainly that Mercury's perihelion is unresolved, explains precisely why (the zeroth-order parameters of celestial mechanics are themselves fitted outputs, so they are theory-dependent), and identifies the fit's output V as a number that could destroy the theory. Deriving the Robertson-Walker form from ether conservation rather than assuming it is elegant, and the bounce replaces both the initial singularity and the point-singularity endpoint of collapse.
The difficulties are equally clear. The cosmological time dilation of equation (4.4) is postulated, not derived, and it carries a free real exponent n; the qualitative outcome — single cycle, infinite cycles, or unbounded past density — depends entirely on n and on an integration constant A that the theory does not fix. Arminjon himself notes that the case n = 0 is ruled out by z ≈ 4 redshifts and that with time dilation the ratio εmax/ε0 "is not constrained by the cosmological model". A prediction of acceleration whose magnitude and history are not pinned down is weaker than it first appears, and no numerical comparison with the supernova magnitude-redshift data is attempted. The strong result q ≤ −4 is itself a hazard rather than a triumph: the measured value is near −0.5, so the theory as stated appears to overshoot the observed acceleration by an order of magnitude, and the paper does not confront this.
The deeper conflict is with the microwave background. Arminjon's preferred cyclic branch needs only a density ratio of order 102, whereas the standard account of the CMB and of light-element abundances requires roughly 109; his response is to lean on the quasi-steady-state alternative of Hoyle, Burbidge and Narlikar, in which matter is created in bursts within very massive objects, and to note that his theory independently predicts collapse-then-explosion and matter production in exploding fluid balls. But the load-bearing observational fact is not merely that a background exists: it is the near-perfect blackbody spectrum measured by COBE FIRAS to a few parts in 105, which thermalised starlight reprocessed by dust must reproduce, and the acoustic peak structure of the anisotropies. Neither is addressed. Similarly, the deuterium and helium-4 abundances are mentioned only in passing as something the standard scenario explains. Finally, an age of 1019 years, offered as an advantage because galaxies need not form "in a hurry", sits badly against stellar-evolution ages of globular clusters near 1.3×1010 years and against the observed evolution of galaxy populations with redshift, both of which suggest a universe whose contents are far younger than its cycle.
Within its own terms the derivation is careful and the mathematics is not in dispute; the analytical solution in inverse form is a genuine result. The theory's fate rests on two numbers not settled in this paper: the ether velocity V extracted from a full celestial-mechanical fit, and whether an accelerating solution can be tuned to match the supernova data without abandoning the q ≤ −4 bound that is the theory's main selling point.