Island of Stability for Consistent Deformations of Einstein’s Gravity

We construct deformations of general relativity that are consistent and phenomenologically viable, since they respect, in particular, cosmological backgrounds. These deformations have unique symmetries in accordance with their Minkowski cousins (Fierz-Pauli theory for massive gravitons) and incorporate a background curvature induced self-stabilizing mechanism. Self-stabilization is essential in order to guarantee hyperbolic evolution in and unitarity of the covariantized theory, as well as the deformation’s uniqueness. We show that the deformation’s parameter space contains islands of absolute stability that are persistent through the entire cosmic evolution.

Figure 1

Parameter plot in the $\alpha \mathrm{\text{−}}\beta$ plane, for $m_0=0$. The green (top center) line corresponds to case (i), the yellow (top left) region to case (ii), the red (right) to case (iii), and the black (bottom) region to case (iv). (For $m_0=H_0$ the plot looks essentially the same.).

Figure 2

$\Phi (t)$ on a purely matter dominated background, $m_0=H_0$, and $\beta$, $\gamma =0$. The dashed blue curve corresponds to $\alpha =0$, while the solid red line corresponds to the absolutely stable situation with $\alpha =-1$.

Figure 3

The evolution of $h_{00}(k)$ at different times for $\mu =\sqrt{\Lambda /3}=1$ and $m=5$. The blue line (upper one) is at $t=0$, the red line (middle one) at $t=0.4$ and yellow line (lower one) at $t=1$.