Cosmic Contraptions (a) The Friedmann equations describing our universe at large scales are 12(??(?)??)2−4???(?)3?2(?)=−??22ℓ2 and ???(?(?)?3(?))=−?(?)????3(?)...

Cosmic Contraptions

(a) The Friedmann equations describing our universe at large scales are 12(??(?)??)2−4???(?)3?2(?)=−??22ℓ2 and ???(?(?)?3(?))=−?(?)????3(?) for the scale factor ?(?). Explain the meaning of the quantities ?, ℓ, ?, and ? in these equations.

(b) Suppose that the scale factor ?(?)=?0?1/2. If ?=0, find the dependence of ? and ? on ?. What cosmic era does this correspond to?

(c) A theorist comes up with a theory of dark matter that indicates the equation of state of the dark matter is ?=79?. Find the time-dependence of ?(?) and ?(?), assuming ?=0. [2] (d) Which process dominates early times (small ?) -- the one in part (b) or the one in part (c)? Why?

Expert Solution

orchestra answered 2 years ago

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