  We investigate the quantum to classical transition of small inhomogeneous
fluctuations in the early Universe using the decoherence functional of
Gell-Mann and Hartle. We study two types of coarse graining; one due to coarse
graining the value of the scalar field and the other due to summing over an
environment. We compare the results with a previous study using an environment
and the off-diagonal rule proposed by Zurek. We show that the two methods give
different results.
