**6.2. A worked example**

The easiest way to see what is going on is to work through a specific
example, the
*m*^{2}^{2} /
2 potential which we already saw in
Section 5.5. We'll see that we don't even
have to solve the
evolution equations to get our predictions.

- Inflation ends when
= 1, so
_{end}*m*_{Pl}/ (4). - We're interested in 60
*e*-foldings before this, which from Eq. (52) gives_{60}3*m*_{Pl}. - Substitute this in:
- Reproducing the COBE result requires
[25]
_{H}2×10^{-5}(provided*A*_{G}<<_{H}), so we need*m*10^{-6}*m*_{Pl}.

Because the required value of *m* is so small, that means it is easy to
get sufficient inflation to solve the cosmological problems, without
violating the classicality condition
*V* < *m*_{Pl}^{4}. That implies only that
<
*m*_{Pl}^{2} /
*m*
10^{6}*m*_{Pl}, and as
*N*_{tot}
2^{2} /
*m*_{Pl}^{2}, we can get up to about
10^{13} *e*-foldings in
principle. This compares extremely favourably with the 70 or so actually
required.