  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.
