FLRW cosmology in Weyl-Integrable Space-Time

Abstract

We investigate the Weyl space-time extension of general relativity (GR) for studying the FLRW cosmology through focusing and defocusing of the geodesic congruences. We have derived the equations of evolution for expansion, shear and rotation in the Weyl space-time. In particular we consider the Starobinsky modification, $f(R)=R+\beta R^2-2\Lambda$, of gravity in the Einstein-Palatini formalism, which turns out to reduce to the Weyl integrable space-time (WIST) with the Weyl vector being a gradient. The modified Raychaudhuri equation takes the form of the Hill-type equation which is then analysed for studying formation of the caustics. In this model, it is possible to have a Big Bang singularity free cyclic Universe but unfortunately the periodicity turns out to be extremely short.

8 pages, 2 figures, version published in JCAP

References in corpus (9)

• The Raychaudhuri equations: a brief review
• TASI Lectures on Inflation
• Kinematics of geodesic flows in stringy black hole backgrounds
• Kinematics of deformable media
• Geodesic congruences in warped spacetimes
• Formation of caustics in Dirac-Born-Infeld type scalar field systems
• Weyl Geometry as Characterization of Space-Time
• Weyl Geometries and Timelike Geodesics
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Cited by in corpus (6)

• General Relativity and Weyl Geometry
• From Brans-Dicke gravity to a geometrical scalar-tensor theory
• Analytic Solution of the Starobinsky Model for Inflation
• Space-time singularities in Weyl manifolds
• On the embedding of Weyl manifolds
• Painlevé analysis for the cosmological field equations in Weyl Integrable Spacetime