From Osher Doctorow
An alternative to feedback is the Chaplygin Dark Energy-Matter
Unification Model, which has an outstanding presentation by M. C.
Bento, O. Bertolami, and A. A. Sen, of Instituto Superior Tecnico
Departamento de Fisica Portugal (the second author is also at U. de
Lisboa Portugal), "Generalized Chaplygin gas model: dark energy - dark
matter unification and CMBR constraints," gr-qc/0305086 v1 22 may 2003
(they also have a Dec. 3 2005 successor paper in astro-ph).
Believe it or not, the evolution of the energy density according to
this model is:
1) rho_ch = [A + B/a^(3(1+alpha))]^(1/(1+alpha))
where alpha, which I also write as a* in (3) below, is usually in (0,
1], a is the scale factor of the Universe, B is an integration
constant, and alpha generalizes from a "soft" matter equation of state:
2) p = alpha rho (alpha not 1)
They point out that, "remarkably," (p. 3), the model interpolates
between a dust-dominated Universe and a De Sitter Universe with an
intermediate phase described by a maixture of vacuum energy density and
(2). They describe it more fundamentally in terms of a complex scalar
field with action a generalized Born-Infeld action:
3) L_GBI = -A^s[1 - (g^uv theta_,u theta_, v)^w]^z, s = 1/(1+a*), w =
(1+a*)/(2a*), z = a*/(1+a*)
Equations (1) and (3) are in the spirit of my variable phase-related
exponent Knowledge Equation from recent threads, so even if the
feedback models turn out to be wrong, the Knowledge Equation seems to
be on good footing in both models.
Readers can work out relationships of (1) and (3) to the Knowledge
Equation as homework.
Osher Doctorow
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