Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?
J. Haro Department of Applied Mathematics~I,
Polytechnic University of Catalonia, Barcelona, Spain
Abstract:
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. Received: 02.02.2011
Revised: 12.04.2011
DOI:
10.4213/tmf6889
Fulltext:
PDF file (391 kB)