Using quantum corrections from massless fields conformally coupled to gravity, we study the possibility of
avoiding singularities that appear in the flat Friedmann–Robertson–Walker model. We assume that the
universe contains a barotropic perfect fluid with the state equation p = ωρ, where p is the pressure and
ρ is the energy density. We study the dynamics of the model for all values of the parameter ω and also
for all values of the conformal anomaly coefficients α and β. We show that singularities can be avoided
only in the case where α > 0 and β < 0. To obtain an expanding Friedmann universe at late times
with ω > −1 (only a one-parameter family of solutions, but no a general solution, has this behavior at
late times), the initial conditions of the nonsingular solutions at early times must be chosen very exactly.
These nonsingular solutions consist of a general solution (a two-parameter family) exiting the contracting
de Sitter phase and a one-parameter family exiting the contracting Friedmann phase. On the other hand,
for ω < −1 (a phantom field), the problem of avoiding singularities is more involved because if we consider
an expanding Friedmann phase at early times, then in addition to fine-tuning the initial conditions, we
must also fine-tune the parameters α and β to obtain a behavior without future singularities: only a oneparameter
family of solutions follows a contracting Friedmann phase at late times, and only a particular
solution behaves like a contracting de Sitter universe. The other solutions have future singularities.
two-point function, adiabatic regularization, de Sitter phase
We calculate a renormalized two-point function using the adiabatic regularization method. We study the
conformally and minimally coupled cases for massless and massive scalar fields in full detail. We reproduce
previous results in a rigorous mathematical form and clarify some empirical approximations and bounds.
We consider some applications to inflationary models.