Abstract
When initial radius Rinitial 0 if Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of Rinitial 0 are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto, and show that there are consequences due to initial entanged Sentropy=0.3rH2/a2 for a time dependent horizon radius rH in cosmology, with for flat space conditions rH= for conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time in line with ~H2/G H≈a-1. The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the length gets, Sentropy if it is entanglement entropy, will not go to zero. The requirement is that the smallest length of time, t, re scaled does not go to zero. Even if the length goes to zero. This preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial 0.
Highlights
Note a change in entropy formula given by Lee [3] about the inter relationship between energy, entropy and temperature as given by m c2 E TUS a 2π c kB (1)Lee’s formula is crucial for what we will bring up in the latter part of this document
We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto, and show that there are consequences due to initial entanged Sentropy 0.3rH2 a2 for a time dependent horizon radius rH in cosmology, with for flat space conditions rH for conformal time
In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time in line with ~ H 2 G
Summary
Note a change in entropy formula given by Lee [3] about the inter relationship between energy, entropy and temperature as given by m c2 E TUS a 2π c kB (1)Lee’s formula is crucial for what we will bring up in the latter part of this document. This preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial 0 .
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