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Additional info for Cosmological evolution in brane-worlds with large transverse dimensions: Inflation and dark matter

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Nevertheless, many useful cosmological matter sources do obey this relation with a constant value of w. 2. The Standard Model of Cosmology, the early Universe and inflation w = 0 corresponds to pressureless matter, or dust – any collection of massive non-relativistic particles would qualify. Similarly, w = 1/3 corresponds to a gas of radiation, whether it be actual photons or other highly relativistic species. A constant w leads to a great simplification in solving our equations. 77) 3(1+w) a(t) Note that the behaviors of dust (w = 0) and radiation (w = 1/3) are consistent with what we would have obtained by more heuristic reasoning.

Let us begin by discussing the conditions under which a particle species will be in equilibrium with the surrounding thermal plasma. A given species remains in thermal equilibrium as long as its interaction rate is larger than the expansion rate of the universe. Roughly speaking, equilibrium requires it to be possible for the products of a given reaction to have the opportunity to recombine in the reverse reaction and if the expansion of the universe is rapid enough this won’t happen. A particle species for which the interaction rates have fallen below the expansion rate of the universe is said to have frozen out or decoupled.

Here x denotes a point in spacetime, φ(x) is the complex scalar, ψ the fermion, and F is an auxiliary field. As in this expression, we shall generally use the same symbol to represent a superfield and its scalar component. 35) δF = − 2i∂µ ψσ ζ 21 Preliminaries ¯ Here and in the following, for any generic two-component Weyl spinor λ, λ indicates the complex conjugate of λ. For a gauge theory one has to introduce vector superfields and the physical content is most transparent in the WessZumino gauge.

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