Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

94 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
obeys the following “dynamic” equation
together with its constraint
Its solutions determine the way these models expand via the scale factor
function which, from Eq.(11), is given by
Eq.(12) whose integral is
together with Eq.(13) turn out the following solutions. For k= 0,
with
while and remain undetermined. Therefore, for the FRW flat
space three different cosmic solutions exist, distinguished by the sign of
the discriminant which depends the coupling parameter
and through on the equation of state. For the discriminants
the scalar field has two branches: one with an
increasing function of time, and the other with a decreasing function
of time [7].
For spaces one obtains a similar solution: