Cosmological constraints on a classical limit of quantum gravity

We investigate the cosmology of a recently proposed deformation of Einstein gravity, emerging from quantum gravity heuristics. The theory is constructed to have de Sitter space as a vacuum solution, and thus to be relevant to the accelerating universe. However, this solution turns out to be unstable, and the true phase space of cosmological solutions is significantly more complex, displaying two late-time power-law attractors—one accelerating and the other dramatically decelerating. It is also shown that nonaccelerating cosmologies sit on a separatrix between the two basins of attraction of these attractors. Hence it is impossible to pass from a decelerating cosmology to an accelerating one, as required in standard cosmology for consistency with nucleosynthesis and structure formation and compatibility with the data inferred from supernovae Ia. We point out that alternative models of the early universe, such as the one investigated here might provide possible ways to circumvent these requirements.

Figure 1

Vacuum solutions for $\zeta =H_0=1$. The de Sitter vacuum sits on the $\dot{H}=0$ axis at this value (large dot). The two dashed curves mark the power-law attractors. The accelerator is the upper of the two curves and the decelerator is the lower one. The separatrix is indicated by the dotted line.

Figure 2

Solutions to Eq. (9), with ${\Omega }_m^{(0)}=0.28$, for a variety of different initial conditions. The thick solid line denotes initial conditions that are consistent with constraints on the evolution of the scale factor from observations of type Ia supernovae. These constraints exclude the other solutions at the $95\%$ confidence level.