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Volume 4 PROGRESS IN PHYSICS A Note on the Quantization Mechanism within the Cold Big Bang Cosmology A Note on the Quantization Mechanism within the Cold Big Bang Cosmology

Armando Assis, Armando Assis

2011
unpublished

In my paper [3] , I obtain a Cold Big Bang Cosmology, fitting the cosmological data, with an absolute zero primordial temperature, a natural cutoff for the cosmological data to a vanishingly small entropy at a singular microstate of a comoving domain of the cosmological fluid. This solution resides on a negative pressure solution from the general relativity field equation and on a postulate regarding a Heisenberg indeterminacy mechanism related to the energy fluctuation obtained from the
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... n of the field equations under the Robertson-Walker comoving elementar line element context in virtue of the adoption of the Cosmological Principle. In this paper, we see the, positive, differential energy fluctuation, purely obtained from the general relativity cosmological solution in [3] , leads to the quantum mechanical argument of the postulate in [3] , provided this energy fluctuation is quantized, strongly supporting the postulate in [3] . I discuss the postulate in [3] , showing the result for the energy fluctuation follows from a discreteness hypothesis. To the Heisenberg Indeterminacy Relation Recalling the eqn. (53) in [3], purely derived from the general relativity field equations under the cosmological context: the δE ρ , given by the eqn. (1), seems to be exclusively valid when δṘ is infinitesimal, since this expression is a first order expansion term, where we do tacitly suppose the vanishing of high order terms. But its form will remain valid in a case of finite variation, as derived is this paper, under the same conditions presented in [3] . The eqn. (1), in terms of indeterminacy, says: • There is an indeterminacy δE ρ , at a given t, hence at a given R(t) andṘ(t), related to a small inteterminacy δṘ(t). A given spherical shell within a t-sliced hypersurface of simultaneity must enclose the following indeterminacy, if the least possible infinitesimal continuous variation given by the field equations in [3], eqn.(1) here, presents discreteness, viz., if the δE ρ cannot be an infinitesimal in its entire meaning, albeit mantaining its very small value, as a vanishingly small quantity, but reaching a minimum, reaching a discrete quantum of energy fluctuation, The eqn. (2) is obtained from eqn. (1) by the summation over the simultaneous fluctuations within the spherical shell (since the quantum minimal energy is a spatially localized object, and the t-sliced spherical shell, a R(t)-spherical subset of simultaneous cosmological points pertaining to a t-sliced hypersurface of simultaneity, is full of cosmological substratum), where k denotes a partition, k fundamental fluctuating pieces of the simultaneous spacelike spherical shell within a t-sliced hypersurface. This sum gives the entire fluctuation within the shell. Since these pieces are within a hypersurface of simulteneity, they have got the same cosmological instant t. Hence, they have the same R(t) and the sameṘ(t) (points within the t-sliced spherical shell cannot have different R(t), since R(t) is a one-to-one function R(t) : t → R(t), and does not depend on spacelike variables; the t-sliced spherical shell is a set of instantaneous points pertaining to a t-sliced hypersurface of simultaneity such that these points are spatially distributed over an t-instantaneous volume enclosed by a tinstantaneous spherical surface with radius R(t)), the reason why the summation index l does not take into account the common factor at the right-hand side of the eqn. (2). From eqn. (57) in [3], we rewrite the eqn. (2) : Now, we reach the total instantaneous fluctuations within the spherical shell at the cosmological instant t, a sum of spacelike localized instantaneous fundamental fluctuations within the spherical shell, giving the total instantaneous fuctuation within this shell. Being the instantaneous spherical shell full of cosmological fluid at t, at each fundamental position within the spherical shell we have got a fundamental energy fluctuation with its intrinsical and fundamental quantum R 0 = 2Gh/c 3 of indeterminacy [3], an inherent spherically symmetric indeterminacy at each position within the t-sliced spacelike shell.

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