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**Cosmic time variation of the gravtitational constant.**
*(English)*
Zbl 0966.83024

Summary: A pre-relativistic cosmological approach to electromagnetism and gravitation is explored that leads to a cosmic time variation of the fundamental constants. Space itself is supposed to have physical substance, which manifests itself by its permeability. The scale factors of the permeability tensor induce a time variation of the fundamental constants. Atomic radii, periods, and energy levels scale in cosmic time, which results in dispersionless redshifts without invoking a space expansion. Hubble constant and deceleration parameter are reviewed in this context. The time variation of the gravitational constant at the present epoch can be expressed in terms of these quantities. This provides a completely new way to restrain the deceleration parameter from laboratory bounds on the time variation of the gravitational constant. This variation also affects the redshift dependence of angular diameters and the surface brightness, and we study in some detail the redshift scaling of the linear sizes of radio sources. The effect of the varying constants on source counts is discussed, and an estimate on the curvature radius of the hyperbolic 3-space is inferred from the peak in the quasar distribution. The background radiation in this dispersionless, permeable space-time stays perfectly Planckian. Cosmic time is discussed in terms of atomic and gravitational clocks, as well as cosmological age dating, in particular how the age of the Universe relates to the age of the Galaxy in a permeable space-time.

### MSC:

83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |

83F05 | Relativistic cosmology |