Towards anisotropy-free and nonsingular bounce cosmology with scale-invariant perturbations

We investigate nonsingular bounce realizations in the framework of ghost-free generalized Galileon cosmology, which furthermore can be free of the anisotropy problem. Considering an ekpyroticlike potential we can obtain a total equation of state larger than 1 in the contracting phase, which is necessary for the evolution to be stable against small anisotropic fluctuations. Since such a large equation of state forbids the Galileon field to generate the desired form of perturbations, we additionally introduce the curvaton field which can in general produce the observed nearly scale-invariant spectrum. In particular, we provide approximate analytical and exact semianalytical expressions under which the bouncing scenario is consistent with observations. Finally, the combined Galileon-curvaton system is free of the big rip after the bounce.

Figure 1

The evolution of the Galileon field $\varphi$ with respect to $t$. We choose the initial conditions to be ${\varphi }_i=-\sqrt{3}(\ln 20)/3$ and ${\dot{\varphi }}_i=\sqrt{3}/60$, and the parameters to be $c=2\sqrt{3}$, $g=1$, and $V_0=1/12$, respectively.

Figure 2

The evolution of the speed of the Galileon field $\dot{\varphi }$ with respect to $t$. We choose the initial conditions to be ${\varphi }_i=-\sqrt{3}(\ln 20)/3$ and ${\dot{\varphi }}_i=\sqrt{3}/60$, and the parameters to be $c=2\sqrt{3}$, $g=1$, and $V_0=1/12$, respectively.

Figure 3

The evolution of the Hubble parameter $H$ with respect to $t$. We choose the initial conditions to be ${\varphi }_i=-\sqrt{3}(\ln 20)/3$ and ${\dot{\varphi }}_i=\sqrt{3}/60$, and the parameters to be $c=2\sqrt{3}$, $g=1$, and $V_0=1/12$, respectively.

Figure 4

The evolution of the EOS $w$ with respect to $t$. We choose the initial conditions to be ${\varphi }_i=-\sqrt{3}(\ln 20)/3$ and ${\dot{\varphi }}_i=\sqrt{3}/60$, and the parameters to be $c=2\sqrt{3}$, $g=1$, and $V_0=1/12$, respectively.

Figure 5

The evolution of the total energy density $\rho$ of the Galileon field, with respect to $t$. We choose the initial conditions to be ${\varphi }_i=-\sqrt{3}(\ln 20)/3$ and ${\dot{\varphi }}_i=\sqrt{3}/60$, and the parameters to be $c=2\sqrt{3}$, $g=1$, and $V_0=1/12$, respectively.

Figure 6

The evolution of the squared speed of sound $c_s^2$ with respect to $t$. We choose the initial conditions to be ${\varphi }_i=-\sqrt{3}(\ln 20)/3$ and ${\dot{\varphi }}_i=\sqrt{3}/60$, and the parameters to be $c=2\sqrt{3}$, $g=1$, and $V_0=1/12$, respectively.

Figure 7

The evolution of the instability-related quantity $Q_{\mathcal{R}}$ with respect to $t$. We choose the initial conditions to be ${\varphi }_i=-\sqrt{3}(\ln 20)/3$ and ${\dot{\varphi }}_i=\sqrt{3}/60$, and the parameters to be $c=2\sqrt{3}$, $g=1$, and $V_0=1/12$, respectively.

Figure 8

The solution for the coupling function $\mathcal{F}(t)$ and the imposed Galileon field $\varphi (t)$, under the imposed bouncing Ansatz (69). We choose the parameters as $g=1$, $V_0=1/12$, $c=2\sqrt{3}$, $\omega =1$, ${\varphi }_I=0.1$, $t_I=-100$, and $t_{B\pm }=\pm 1$.

Figure 9

The reconstructed coupling function $\mathcal{F}(\varphi )$ under the imposed bouncing Ansatz (69), using Fig. 8. We choose the parameters as $g=1$, $V_0=1/12$, $c=2\sqrt{3}$, $\omega =1$, ${\varphi }_I=0.1$, $t_I=-100$, and $t_{B\pm }=\pm 1$.

Figure 10

The solution for the curvaton field $\sigma (t)$, under the imposed bouncing Ansatz (69). We choose the parameters as $g=1$, $V_0=1/12$, $c=2\sqrt{3}$, $\omega =1$, ${\varphi }_I=0.1$, $t_I=-100$, and $t_{B\pm }=\pm 1$.