Bounce and cyclic cosmology in weakly broken Galileon theories

We investigate the bounce and cyclicity realization in the framework of weakly broken Galileon theories. We study bouncing and cyclic solutions at the background level, reconstructing the potential and the Galileon functions that can give rise to a given scale factor and presenting analytical expressions for the bounce requirements. We proceed to a detailed investigation of the perturbations, which after crossing the bouncing point give rise to various observables, such as the scalar and tensor spectral indices and the tensor-to-scalar ratio. Although the scenario at hand shares the disadvantage of all bouncing models, namely that it provides a large tensor-to-scalar ratio, introducing an additional light scalar significantly reduces it through the kinetic amplification of the isocurvature fluctuations.

Figure 1

The reconstructed scalar potential $V(\varphi )$ that generates the bouncing scale factor (3.1), in the case where $G_2=G_4=X^2$, $G_3=X$, $G_5=0$. The bouncing parameters have been chosen as $a_b=0.2$, $B={10}^{-5}$, while ${\mathrm{\Lambda }}_2=0.9$, ${\mathrm{\Lambda }}_3=0.01$, in $M_{\mathrm{pl}}$ units.

Figure 2

The evolution of the scale factor $a(t)$ that is generated by the simple parabolic potential (3.11), in the case where $G_2=G_4=X^2$, $G_3=X$, $G_5=0$. The potential parameters have been chosen as $V_0=8.5$, ${\varphi }_0=7.0$, while ${\mathrm{\Lambda }}_2=0.9$, ${\mathrm{\Lambda }}_3=0.01$, in $M_{\mathrm{pl}}$ units.

Figure 3

The reconstructed Galileon function $G_3(X)$ that generates the bouncing scale factor (3.1), in the case where $V(\varphi )=0$, and with $G_2=G_4=X^2$, $G_5=0$. The bouncing parameters have been chosen as $a_b=0.2$, $B={10}^{-5}$, while ${\mathrm{\Lambda }}_2=0.9$, ${\mathrm{\Lambda }}_3=0.01$, in $M_{\mathrm{pl}}$ units.

Figure 4

The reconstructed scalar potential $V(\varphi )$ that generates the cyclic scale factor (3.39), in the case where $G_2=G_4=X^2$, $G_3=X$, $G_5=0$. The model parameters have been chosen as $a_c=0.01$, $A={10}^{-4}$, $w=15$, ${\rho }_{mb}=0.01$, while ${\mathrm{\Lambda }}_2=0.9$, ${\mathrm{\Lambda }}_3=0.01$, in $M_{\mathrm{pl}}$ units.

Figure 5

The evolution of the scale factor $a(t)$ that is generated by the simple oscillatory potential (3.40), in the case where $G_2=G_4=X^2$, $G_3=X$, $G_5=0$. The potential parameters have been chosen as $V_1=1$, $V_2=0.1$, and $w_V=3$, and the matter energy density at the bounce as ${\rho }_{mb}=0.01$, while ${\mathrm{\Lambda }}_2=0.9$, ${\mathrm{\Lambda }}_3=0.01$, in $M_{\mathrm{pl}}$ units.

Figure 6

The evolution of the sound speed square, for the bouncing solution of Sec. 3a1, i.e. for the bouncing scale factor (3.1), in the case where $G_2=G_4=X^2$, $G_3=X$, $G_5=0$, and with $a_b=0.2$, $B={10}^{-5}$, ${\mathrm{\Lambda }}_2=0.9$, ${\mathrm{\Lambda }}_3=0.01$, in $M_{\mathrm{pl}}$ units.