The Scale-Invariant Vacuum (SIV) Theory: A Possible Origin of Dark Matter and Dark Energy

Abstract

The Scale Invariant Vacuum (SIV) theory rests on the basic hypothesis that the macroscopic empty space is scale invariant. This hypothesis is applied in the context of the Integrable Weyl Geometry, where it leads to considerable simplifications in the scale covariant cosmological equations. After an initial explosion and a phase of braking, the cosmological models show a continuous acceleration of the expansion. Several observational tests of the SIV cosmology are performed: on the relation between H 0 and the age of the Universe, on the m − z diagram for SNIa data and its extension to z = 7 with quasars and GRBs, and on the H ( z ) vs. z relation. All comparisons show a very good agreement between SIV predictions and observations. Predictions for the future observations of the redshift drifts are also given. In the weak field approximation, the equation of motion contains, in addition to the classical Newtonian term, an acceleration term (usually very small) depending on the velocity. The two-body problem is studied, showing a slow expansion of the classical conics. The new equation has been applied to clusters of galaxies, to rotating galaxies (some proximities with Modifies Newtonian Dynamics, MOND, are noticed), to the velocity dispersion vs. the age of the stars in the Milky Way, and to the growth of the density fluctuations in the Universe. We point out the similarity of the mechanical effects of the SIV hypothesis in cosmology and in the Newtonian approximation. In both cases, it results in an additional acceleration in the direction of motions. In cosmology, these effects are currently interpreted in terms of the dark energy hypothesis, while in the Newtonian approximation they are accounted for in terms of the dark matter (DM) hypothesis. These hypotheses appear no longer necessary in the SIV context.

On the relation of the lunar recession and the length-of-the-day

“…In the framework of scale invariant models, a general scale invariant field equation has been obtained (Canuto et al 1977) in the line of developments made by Dirac (1973). The scale invariant vacuum (SIV) theory rests on the specific hypothesis that the macroscopic empty space is invariant to a scale transformation ds = λ(t) ds, a property present in Maxwell's equation of electrodynamics, as well as in General Relativity in absence of a cosmological constant, see review by Maeder and Gueorguiev (2020b). Cosmological equations have been obtained leading to accelerated Universe models (Maeder 2017).…”

Guessing the Riddle of a Black Hole

“…The analysis of the general properties of 240 different galaxies [34,35] shows that the difference between the observed centripetal acceleration and the Newtonian one decreases with increasing acceleration; see Figure 4. The straight 1:1 line shows where the observed and Newtonian accelerations coincide.…”

“…The connection (35) separates a regular solution to Equations ( 21)-( 24), continuous at the interface x = x g between the regions of different signatures of the metric tensor:…”

“…The analysis of general properties of 240 di¤erent galaxies [32], [33] shows that the di¤erence between the observed centripetal acceleration and the Newtonian one decreases with increasing acceleration, see [34,35]. Logarithmic scales along both axes.…”

“…Figure 4. The observed acceleration (vertical axis) as a function of the expected one from the distribution of baryons (horizontal axis) for 240 galaxies[34,35]. Logarithmic scales along both axes.…”