Numerical Bianchi type I solutions in semiclassical gravitation

It is believed that soon after the Planck era, spacetime should have a semiclassical nature. In this context we consider quantum fields propagating in a classical gravitational field and study the backreaction of these fields, using the expected value of the energy-momentum tensor as source of the gravitational field. According to this theory, the escape from general relativity theory is unavoidable. Two geometric counter-term are needed to regularize the divergences which come from the expected value. There is a parameter associated to each counter-term and in this work we found numerical solutions of this theory to particular initial conditions, for general Bianchi Type I spaces. We show that even though there are spurious solutions some of them can be considered physical. These physical solutions include de Sitter and Minkowski that are obtained asymptotically.

Figure 1

Using $\alpha =0.1$, $\beta =-0.1$, $\Lambda =0$.

Figure 2

Using $\alpha =1000$, $\beta =-1000$, $\Lambda =0$.

Figure 3

Using $\alpha =-0.1$, $\beta =0.1$, $\Lambda =0$.

Figure 4

Using $\alpha =0.1$, $\beta =0.1$, $\Lambda =0$.

Figure 5

Using $\alpha =0.1$, $\beta =0.1$, $\Lambda =0$.