FLRW cosmology in Weyl-Integrable Space-Time
  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.
