Geodesic
Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 162-176 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $p=\omega\rho$, where $p$ is the pressure and $\rho$ is the energy density. We study the dynamics of the model for all values of the parameter $\omega$ and also for all values of the conformal anomaly coefficients $\alpha$ and $\beta$. We show that singularities can be avoided only in the case where $\alpha>0$ and $\beta<0$. To obtain an expanding Friedmann universe at late times with $\omega>-1$ (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 $\omega<-1$ (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 $\alpha$ and $\beta$ to obtain a behavior without future singularities: only a one-parameter 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.
Keywords: cosmological singularity avoidance, semiclassical approximation, conformal anomaly. 
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     title = {Can quantum effects due to a~massless conformally coupled field avoid gravitational singularities?},
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J. Haro. Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 162-176. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a14/

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