The Raychaudhuri equation in homogeneous cosmologies

Understand

In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation.

• In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes.
• The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity.
• However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter.