By far the most important aspect of inflation is that it provides a
possible explanation for the origin of cosmic structures. The mechanism
is fundamentally quantum mechanical; although inflation is doing its
best to make the Universe homogeneous, it cannot defeat the uncertainty
principle which ensures that
residual inhomogeneities are left over.
^{(2)}
These are stretched to astrophysical scales by the inflationary
expansion. Further,
because these are determined by fundamental physics, their magnitude can be
predicted independently of the initial state of the Universe before
inflation.
However, the magnitude does depend on the model of inflation; different
potentials predict different cosmic structures.

One way to think of this is that the field experiences a quantum
"jitter" as it rolls down the potential. The observed temperature
fluctuations in the cosmic microwave background are one part in
10^{5}, which ultimately means that the
quantum effects should be suppressed compared to the classical evolution
by this amount.

Inflation models generically predict two independent types of perturbation:

**Density perturbations**_{H}^{2}(*k*):- These are caused by perturbations in the scalar field driving inflation, and the corresponding perturbations in the space-time metric.
**Gravitational waves***A*_{T}^{2}(*k*):- These are caused by perturbations in the space-time metric alone.

They are sometimes known as scalar and tensor perturbations respectively, because of the way they transform. Density perturbations are responsible for structure formation, but gravitational waves can also affect the microwave background.

We do not expect to be able to predict the precise locations of cosmic
structures from first principles (any more than one can predict the precise
position of a quantum mechanical particle in a box). Rather, we need to
focus on
statistical measures of clustering. Simple models of inflation predict
that the
amplitudes of waves of a given wavenumber *k* obey gaussian
statistics, with the
amplitude of each wave chosen independently and randomly from a
gaussian. What
it does predict is how the width of the gaussian, known as its
amplitude, varies with scale; this is known as the ** power spectrum**.

With current observations it is a good approximation to take the power spectra as being power laws with scale, so

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In principle this gives four parameters - two amplitudes and two spectral
indices - but in practice the spectral index of the gravitational waves is
unlikely to be measured with useful accuracy, which is rather
disappointing as the simplest inflation models predict a so-called
consistency relation relating
*n*_{T} to the amplitudes of the two spectra, which would
be a distinctive
test of inflation. The assumption of power-laws for the spectra requires
assessment both in extreme areas of parameter space and whenever
observations significantly improve.

^{2} For a detailed account of the
inflationary model of the origin of structure, see Ref.
[4].
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