Bouncing cosmologies in Palatini $f(R)$ gravity

We consider the early time cosmology of $f(R)$ theories in Palatini formalism and study the conditions that guarantee the existence of homogeneous and isotropic models that avoid the big bang singularity. We show that for such models the big bang singularity can be replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for pressureless dust. We give a characterization of such models and discuss their dynamics in the region near the bounce. We also find that power-law Lagrangians with a finite number of terms may lead to nonsingular universes, which contrasts with the infinite-series Palatini $f(R)$ Lagrangian that one needs to fully capture the effective dynamics of loop quantum cosmology. We argue that these models could also avoid the formation of singularities during stellar gravitational collapse.

Figure 1

Comparison of the ansatz $f_R$ given in (14) (solid line) with the numerical curve obtained in 6 (dashed line). The plot represents $df/dR$ versus $|R|$.

Figure 2

Bouncing cosmologies with $K=0$ compared with the GR solution (red lines). The continuous black curve represents the case $w=0$, corresponding to $f(R)=R-R^2/|R_P|$. The dashed line represents the case $w=1$ of the theory $f(R)=R+R^2/|R_P|$. The initial density is the same for the four curves.

Figure 3

Cyclic cosmologies with $K>0$. The continuous black curve represents the case $w=0$, corresponding to $f(R)=R-R^2/|R_P|$. The dashed line represents the case $w=1$ of the theory $f(R)=R+R^2/|R_P|$. The initial density is the same as in Fig. 2.

Figure 4

Evolution of $f_R$ for $K=0$ (dashed line), $K>0$ (dotted line), and $K<0$ (solid line). The initial density is the same as in Fig. 2.