Phase Transitions in the Early Universe

Details Phase Transitions in the Early Universe Phase Transitions in the Early Universe

2011-10-07

arxiv.org/abs/1110.1448v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

1 figure. arXiv admin note: substantial text overlap with arXiv:0705.4149

Scientific paper

It is believed that the temperature of the early Universe was once $300\, GeV$ at $10^{-11} sec$, or once $150\, MeV$ at $3.3 \times 10^{-5} sec$, and in fact even the hotter the earlier, e.g. $30\, TeV$ at $10^{-15} sec$. In this note, we are troubled by two basic questions: At very early times such as $10^{-15} sec$, we worry about the matter densities much too higher such that the space-time and the matter may join to assume the meaning. As for the cosmological QCD phase and others, the matter density sounds to be quite normal but we learned from the (quantum) statistical mechanics that some phase transitions are first=order and so the latent heat (energy) in the case should play an important role. At the times much earlier such as $10^{-15} sec$ or earlier, the standard theory gives the matter density so dense that the typical size of a hadron has to accommodate so many particles (by orders of magnitude more). At $10^{-15}\,sec$, we have $T=32 TeV$, $\rho_m= 3.2 \times 10^{18}gm/cm^3$ and $\rho_\gamma=6.4\times 10^{30}gm/cm^3$. (For comparison, the solar Schwarzschild density is $1.843\times 10^{16} gm/cm^3$ with $R_s=2.953\, km$ and the nuclear matter density is $2.0 \times 10^{14}gm/cm^3$.) Thus, we suggest that we might reach the so-called "super-quantum" regime, in which the non-commutativity among the coordinates dictates. The suggestion of Snyder in 1947, though for different reasons, offers a nice formulation of the problem. For the question about the importance of the latent heat (energy), we re-iterate the treatment of cosmological QCD phase transition and pinpoint where the latent heat eventually goes.

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