Bounce in general relativity and higher-order derivative operators

Recent progress seems to suggest that one must modify general relativity (GR) to stably violate the null energy condition and avoid the cosmological singularity. However, with higher-order derivative operators of the scalar field (a subclass of the degenerate higher-order scalar-tensor theory), we show that at energies well below the Planck scale, fully stable nonsingular cosmologies can actually be implemented within GR.

Figure 1

${\dot{g}}_4$ is given by (23). We require ${\dot{g}}_4\sim H$ for simplicity. We have set $\mu =0.9$ and $M_P=10$ in the plot.

Figure 2

Coefficients $g_1$, $g_2$, and $g_3$ in $\tilde{P}(N,\eta )$ (20).

Figure 3

Throughout the whole evolution, $c_S^2>0$, while $c_S^2\to 1$ as $|\eta |\to \infty$.