Application of the 3-space approach to the Bianchi II cosmological model

Abstract

Einstein used 4-dimensional space time geometry to explain gravity. However, in 1962, Baierlein, Sharp and Wheeler proposed a Jacobi type timeless Lagrangian based on the 3-dimensional geometry of space to reproduce the same physics. In 2002, Barbour $et$. $al$. further extended this idea and they call it 3-space approach. Here we use Bianchi II cosmological model to demonstrate the 3-space idea. Indeed, we find that this theory is more fundamental and the manipulation is more practical. We recover the known and find a new solutions.