Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?
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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 = 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.
CitationHaro, J. Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?. "Theoretical and mathematical physics", Abril 2012, vol. 171, núm. 1, p. 563-574.