**7.2. The inflationary energy scale**

The most solid observational result is the interpretation of the cosmic
microwave anisotropies seen by COBE as giving the amplitude of the
initial power spectrum. COBE is a particularly powerful probe because
its large beam size makes it sensitive only to scales much larger than
the horizon size when the microwave background formed. The perturbations
are therefore seen in their primordial form, and depend only
on the initial perturbations and not all the other
parameters. ^{(9)}

The COBE normalization requires the perturbation at the present Hubble
scale,
_{H}
_{H}(*k* =
*a*_{0}*H*_{0}), to be
given by [25]

Since

then unless proves to be tiny (say much less than a hundredth) this will give

at the time when observable scales crossed outside the horizon, pretty much the scale that particle physicists associate with Grand Unified Theories.

^{9} There is a residual dependence on
_{0} and
which determine the relation
between the metric perturbations
and the matter perturbations, and also the evolution of perturbations,
but that is easily dealt with. I will assume critical density for
simplicity.
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