Resolution of curvature singularities in higher derivative gravity

We consider possible resolutions of singularities in a contracting anisotropic universe for a class of higher derivative gravity theories. We give evidence that for our models the big crunch singularity may be replaced by a nearly flat Minkowski-like phase before the Universe reenters an anisotropic expansion in a time-symmetric manner.

Figure 1

Qualitative behavior of a possible solution bouncing through Minkowski spacetime. $\varphi (t)$ diverges symmetrically around $t=0$ while $F(t)$ diverges symmetrically. $H(t)$ is smooth at $t=0$.

Figure 2

Two numerical solutions [solid and dashed lines; $H=F$ (thick, negative axis), $\varphi$ (thin, positive axis)] starting with isotropic initial conditions.

Figure 3

Two numerical solutions [solid and dashed lines; $H$, $F$ (thick), and $H-F$ (thin) where the latter is rescaled with a factor of 10] starting with initial conditions slightly perturbed from isotropy.

Figure 4

Sketch of the proposed matching of the numerical solution on the left and the possible approximate continuation on the right. There is no overlap between the respective regions of validity of the two approximations.