Cosmological dynamics and double screening of DBI-Galileon gravity

We investigate cosmological dynamics and screening mechanism of the Dirac–Born–Infeld (DBI) Galileon model. The model has been divided into two regimes, one has positive signs in front of scalar field kinetic terms so-called the DBI Galileon, another one has negative signs and it is dubbed as the DBIonic Galileon. We find de Sitter solution and evolution of the Universe starting from radiation dominated era to late-time accelerated expansion in the DBI Galileon model without the presence of potential term. In one of the attractors, the ghost and Laplacian instabilities vanishes for the whole evolution. We find mixing of screening mechanisms between the Vainshtein mechanism and the DBIonic screening mechanism in the DBIonic Galileon model, in which a scale changing between these two mechanisms depends on a mass of a source.

Figure 1

The fixed point with $g\ne 0$ where thick lines represent in the range $g_{\mathrm{cr}}(\sim 1.788)\le g<3$ and dashed lines represent in the range $0<g<g_{\mathrm{cr}}$. The fixed point (b) is represented as a blue dotted-dashed line, where $x_3=0$.

Figure 2

The density parameters, ${\mathrm{\Omega }}_m$ (green line) and ${\mathrm{\Omega }}_{\varphi }$ (red line), and the equation of state of the scalar field (blue line) of the fixed point with $g\ne 0$. The thick lines represent values in the range $g_{\mathrm{cr}}(\sim 1.788)\le g<3$, while $0<g<g_{\mathrm{cr}}$ is represented as dashed lines.

Figure 3

Eigenvalues of the fixed point with $g\ne 0$ in the range $g_{\mathrm{cr}}(\sim 1.788)\le g<3$.

Figure 4

Trajectories of solutions of the autonomous equations (3.13)–(3.15) where we set initial conditions as $x_2=2$, and allow $x_1$ and $x_3$ to be arbitrary.

Figure 5

2D trajectories of solutions of two autonomous equations (3.13) and (3.14) where we assume $x_3=0$. We set initial conditions as $x_2=2$, and let $x_1$ to be arbitrary. The blue region is a forbidden region since it yields ${\mathrm{\Omega }}_{\varphi }>1$, and the black-thick line is ${\mathrm{\Omega }}_{\varphi }=1$.

Figure 6

Evolution of the density parameters and the equation of state parameters of the fixed point (a) (top) where initial conditions are $x_3=0.999$, $x_2=6.8\times {10}^{10}$, and $x_1=-0.01$ at $z=3.27\times {10}^6$. For the fixed point (b) (bottom) we choose initial conditions as $x_3=0.999$, $x_2=6.8\times {10}^{10}$, and $x_1=+0.01$ at $z=3.27\times {10}^6$.

Figure 7

Evolution of the sound speed square of the DBI Galileon model where initial conditions are the same as in the Fig. 6.

Figure 8

Evolution of the $Q_s$ parameter of the fixed point (a) (top) and the fixed point (b) (bottom). The initial conditions are the same as given in the Fig. 6.

Figure 9

A profile of the DBIonic Galileon scalar field where we set $\lambda =\mathrm{\Lambda }=\tilde{A}=1$. The limit $\lambda {\varphi }^{\prime 2}\ll 1$ satisfies at large distances.

Figure 10

The screening behavior of the DBIonic Galileon where we set $\lambda =\mathrm{\Lambda }=\tilde{A}=1$. The $F_{\text{unscreened}}\equiv 2g^2{F}_N$, and $F_N$ is the Newtonian force outside a point mass ($F_N=-M/8\pi M_{\mathrm{PL}}^2{r}^2$).