Abstract
In this paper, conformal invariant gravitation, based on Weyl geometry, is considered. In addition to the gravitational and matter action integrals, the interaction between the Weyl vector (entered in Weyl geometry) and the vector, representing the world line of the independent observer, are introduced. It is shown that the very existence of such an interaction selects the exponentially growing scale factor solutions among the cosmological vacua.
Highlights
In the present paper, following Roger Penrose [1,2,3] and Gerard ‘t Hooft [4,5,6], it is suggested that the universe is conformal invariant
An attempt to introduce an outside observer in the least action integral, called "the supervisor’, is made’. Since such an observer is naturally described by some world line, the simplest geometry for the observer incorporation appeared to be Weyl geometry, which contains both the metric tensor and the vector field
The main feature of the presented approach is that the supervisor is not the dynamical variable and, is not subject to the variation
Summary
In the present paper, following Roger Penrose [1,2,3] and Gerard ‘t Hooft [4,5,6], it is suggested that the universe is conformal invariant. It is suggested that the conformal invariace is described by Weyl geometry. G. ’t Hooft [6] proposed that different observers may see different pictures, i.e., different geometries. This becomes possible only if the observer interacts somehow with the geometry. It is Weyl geometry that provides us with such a possibility. After the variation procedure, it is possible, in principle, to identify the observer with the matter flow
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