# I Scale invariance in the power spectrum

1. Sep 19, 2016

### windy miller

I understand the inflation predicts a nearly scale invariant power spectrum but some have claimed this was predicted before inflation (by Harrison and Zeldovitch?)
My understanding is that perfectly scale invariance would predict ns=1 but inflation predicts ns =.96. So did the prior prediction ( if this claim is true) predict ns=1 or ns=.96 ?

2. Sep 19, 2016

### Chalnoth

Inflation doesn't predict a specific value of the scalar spectral index ($n_s$). Instead, there are a wide variety of models of inflation and they can all have rather different values for $n_s$. Inflation predicts a spectral index different from one (usually less) because inflation has to come to an end. The different inflation models end in slightly different ways, leading to different predictions.

From what I recall, the Harrison-Zeldovitch spectrum, which simply assumes scale invariance, wasn't ever a proper physical model of the universe. It more or less just assumes that there are these perturbations, and that they are scale invariant, but doesn't actually have a workable model that would cause that.

So when we got to the point of measuring this spectrum in the early 2000's with the launch of WMAP, the prevailing view was that the most likely result would have been a spectral index somewhat different from one, with $n_s = 1$ considered to be a null hypothesis.

3. Sep 19, 2016

### windy miller

Thanks you for thats its very interesting. Would I be correct to assume then the Harrison Zeldovich spectrum would have assume to be exactly one if they were just assuming scale invariance without a model to produce it?

4. Sep 20, 2016

### bapowell

Yes. The HZ spectrum has n=1.