Primordial matter density contrast and the size of the very early universe in the Quantum Big Bang theory of the cosmological constant

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Ram, Budh
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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.
Comment: 7 pages, no figs. v2: 8 pages, title changed, abstract and text enlarged. Refs added
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General Relativity and Quantum Cosmology, Astrophysics, Quantum Physics
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