The question of the existence of Einstein metrics on homogeneous spaces
is a fundamental
one.  There are few existence theorems for Einstein metrics on
solvmanifolds.
We get theorems on the existence of Einstein solvmanifolds by showing
the existence
of Ricci soliton metrics on homogeneous nilmanifolds and using a theorem
of Jorge
Lauret.

Ricci soliton metrics may be considered the privileged metrics in the
category of nilmanifolds, as nonabelian homogeneous nilmanifolds do
not admit Einstein metrics.  A Ricci soliton metric on a homogeneous
nilmanifold
is one whose Ricci operator is in the same cohomology class as the
identity map in Lie algebra cohomology.  Jorge Lauret, in a variational
approach to Einstein metrics on homogeneous spaces, has shown that
a homogeneous nilmanifold has a Ricci soliton metric if and only if it
has a solvable extension by
an abelian group which is Einstein.  We show general methods of
constructing
large infinite classes of  Ricci soliton homogeneous nilmanifolds.
By Lauret's results, these give large infinite classes of Einstein
solvmanifolds.