Focusing of geodesic congruences in an accelerated expanding Universe

Journal Article · Sat Dec 01 04:00:00 EST 2012 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2012/12/020· OSTI ID:22279575

Albareti, F. D.; Cembranos, J. A.R. ^[1]; Cruz-Dombriz, A. de la, ^[2]

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1. Departamento de Física Teórica I, Universidad Complutense de Madrid, Ciudad Universitaria, E-28040 Madrid (Spain)
2. Astrophysics, Cosmology and Gravity Centre (ACGC), University of Cape Town, 7701 Rondebosch, Cape Town (South Africa)

We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from space-time geometry which is usually interpreted as the manifestation of the attractive character of gravity is restored in an accelerated expanding Robertson-Walker space-time at high speeds.

• OSTI ID: 22279575
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 12 Vol. 2012; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
COSMOLOGY
EVOLUTION
EXPANSION
FIELD EQUATIONS
GEODESICS
GEOMETRY
GRAVITATION
INFLATIONARY UNIVERSE
INFLATONS
METRICS
SPACE-TIME
UNIVERSE
VELOCITY