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##.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Intuition Behind Scale Invariance Power Spectrum

**Physics Forums | Science Articles, Homework Help, Discussion**