Lp. Chimento, SELF-CONSISTENT SOLUTIONS OF THE SEMICLASSICAL EINSTEIN EQUATIONS WITH COSMOLOGICAL CONSTANT, General relativity and gravitation, 25(10), 1993, pp. 979-989
The general solution to the semiclassical backreaction equation is fou
nd for conformally invariant free quantum fields in spatially flat hom
ogeneous and isotropic spacetime with cosmological constant and with n
o classical source when the ratio of the renormalisation parameters be
ta/alpha = 9/4. It contains a two-parameter family of bouncing solutio
ns that avoid the singularity. There are several one-parameter familie
s which do not have particle horizons. The stability of these solution
s is investigated and it is found that they are stable when alpha and
lambda have different signs. However, when both parameters have the sa
me sign the set of stable solutions is restricted by the condition 0 <
lambda < 1/9. ln both cases these solutions have a final de Sitter st
age.