2007/09/30 by Martín Reiris, Martin Reiris
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc
paper · pdf · doi:10.1088/0264-9381/25/8/085001
published as Class.Quant.Grav.25:085001,2008 · Revised version. 32 pages, 1 figure
openalex publication_date 2008/03/26 · arxiv created 2008/06/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We introduce the notion of general Friedman–Lemaître (compact) cosmologies and the notion of averaged evolution by means of an averaging map. We then analyze the Friedman–Lemaître equations and the role of gravitational energy on the universe evolution. We distinguish two asymptotic behaviors: radiative and mass gap. We discuss the averaging problem in cosmology for them through precise definitions. We then describe in quantitative detail the radiative case, stressing on precise estimations on the evolution of the gravitational energy and its effect in the universe's deceleration. Also in the radiative case, we present a smoothing property which tells that the long-time H 3 × H 2 stability of the flat Friedman–Lemaître (FL) models implies H i +1 × H i stability independently of how big the initial state was in H i +1 × H i , i.e. there is long-time smoothing of the spacetimeThe word smoothing here is referring to the decay toward zero of the spacetime Bel–Robinson curvatures (and therefore of the derivatives), and not to a gain in Sobolev regularity as in usual PDE terminology.. Finally we discuss the existence of initial 'big-bang' states of large gravitational energy, showing that there is no mathematical restriction to assume it to be low at the beginning of time.