On Quantum Spacetime and the horizon problem

Details On Quantum Spacetime and the horizon problem On Quantum Spacetime and the horizon problem

2012-01-12

arxiv.org/abs/1201.2519v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages. v2: explanations added in sec. 3.2, references updated

Scientific paper

In the special case of a spherically symmetric solution of Einstein equations coupled to a scalar massless field, we examine the consequences on the exact solution imposed by a semiclassical treatment of gravitational interaction when the scalar field is quantized. In agreement with the work of Doplicher, Fredenhagen and Roberts (DFR), imposing the principle of gravitational stability against localization of events, we find that the region where an event is localized, or where initial conditions can be assigned, has a minimal extension, of the order of the Planck length. This conclusion, though limited to the case of spherical symmetry, is more general than that of DFR since it does not require the use of the notion of energy through the Heisenberg Principle, nor of any approximation as the linearized Einstein equations. Using this result in a cosmological setting, taking as a source for the semiclassical equations the energy momentum tensor as calculated on the basic model of quantum Minkowski space in a KMS state describing the Cosmic Microwave Background, we find a scenario, similar to a power law inflation, where the horizon problem does not arise. This indication goes in the same direction as those drawn at a heuristic level from a full use of the principle of gravitational stability against localization of events.

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