  Dilaton coupled electromagnetic field is essential element of low-energy
string effective action or it may be considered as result of spherical
compactification of Maxwell theory in higher dimensions. The large $N$ and
large curvature effective action for $N$ dilaton coupled vectors is calculated.
Adding such quantum correction to classical dilaton gravity action we show that
effective dilaton-Maxwell gravity under consideration may generate
Schwarzschild-de Sitter black holes (SdS BHs) with constant dilaton as
solutions of the theory. That suggests a mechanism (alternative to BHs
production) for quantum generation of SdS BHs in early universe (actually, for
quantum creation of inflationary Universe) due to back-reaction of dilaton
coupled matter. The possibility of proliferation of anti-de Sitter space is
briefly discussed.
