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Intuition Behind Scale Invariance Power Spectrum

  1. May 22, 2015 #1
    In the book "Statistical physics for cosmic structures" at p. 171 a read a definition of scale invariance (leading to the so called scale invariant power spectrum) given as the requirement that ##\sigma^2_M(R=R_H(t)) = constant##, where ##R_H(t)## is the horizon, i.e. the maximal distance that light could have traveled in cosmological time ##t##.

    In other words, the normalised mass variance over a sphere of radius the horizon distance should be independent of time. So if we computed the mass variance at some time ##t_0## when the horizon was ##R_H(t_0)## this should be the same as if we computed it at any other ##t_1## when the horizon was ##R_H(t_1)## even though ##R_H(t_0)## might be much smaller than ##R_H(t_1)##.

    I am trying to get intuition for why one would believe such a requirement to be true. Does anyone have some enlightening explanations/insights?
     
  2. jcsd
  3. May 22, 2015 #2

    bapowell

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    Scale invariance is only true for de Sitter expansion in which [itex]\dot{\rho} = 0[/itex]. The background is steady state, so there are no time-dependent dynamics that would impart a scale dependence on the perturbations.
     
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