Primordial matter density contrast and the size of the very early   universe in the Quantum Big Bang theory of the cosmological constant
  We calculate the amount of primordial matter density contrast and the size of the very early universe in the recent Quantum Big Bang theory [arXiv:0705.4549 [gr-qc](2007)] of the cosmological constant. We obtain $(\delta\rho/\rho)_M = 1.75 \times 10^{-5}$, {\it without} the introduction of an adjustable free parameter. Harrison-Zel'dovich $k$-dependence with $A = 64/9\pi^2 = 0.72$ and $n = 1$ in $|\delta_k|^2 = Ak^n$ arises inherently. The size of the universe with which it enters the classical Friedmann-Robertson-Walker (FRW) phase comes out to be 0.2 cm. We conclude that the hypothesis of classical inflation at an early stage of cosmic evolution is {\bf not} needed. 
Budh Ram