Poincaré Coordinates for Study of Big Crunch

Abstract

A biggest challenge for today’s astrophysicist is to solve the mystery of primordial evolution of the universe. This is also known as belongs to Planck’s era. In this stage space-time singularity and inflationary phase all occur when universe was just of the size 10-5m. All this evolution occurs in a tiny fraction of a second. This description is made by joining the cosmological principle of isotropy and homogeneity, the Hubble law, and the Einstein’s field equations of General Relativity in the Big Bang Theory or Standard Cosmological Model (SCM). The SCM is failed to describe first moment in which universe emerges out in presence of singularity. Due to failure of above model quantum theory of gravitation is needed to understand the evolution of early universe. Quantum gravity (QG) is a field of theoretical physics that need to describe gravity by the principles of quantum mechanics, and where quantum effects cannot be ignored, such as in the vicinity of black holes or similar compact astrophysical objects where the effects of gravity are strong(such as neutron stars). Though the theory is able to unfold many mystery but the observational results to prove it are still not exist. The Quantum Cosmology provides some simulating models to understand the primordial evolution by adding some hypothesis. The SCM well explain the observational data with consistency but have some limitations. In present paper Anti de Sitter and Conformal Field Theory are combined together to study condensed matter made up of extra dimensional particles like Dilaton and Strings which are going to decide ultimate fate; the Big Crunch of our Universe. The AdS/CFT correspondence is used to understand the transition from expanding universe to non relativistic transformation to obtain Big Crunch.