Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation

Abstract

We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane is non-relativistic and we show that it tends to violate the null energy condition and to render cosmological fluctuations ghosts. There nonetheless exists an interesting parameter space in which a stable phase of quasi-exponential expansion can be achieved while the induced gravity leaves non trivial imprints. We derive the exact second-order action governing the dynamics of linear perturbations and we show that it can be simply understood through a bimetric perspective. In the relativistic regime, we also calculate the dominant contribution to the primordial bispectrum and demonstrate that large non-Gaussianities of orthogonal shape can be generated, for the first time in a concrete model. More generally, we find that the sign and the shape of the bispectrum offer powerful diagnostics of the precise strength of the induced gravity.

Figures (9)

• Figure 1: Different shape $S_X\left(1,\frac{k_2}{k_1},\frac{k_3}{k_1}\right)$ as a function of $\left(\frac{k_2}{k_1},\frac{k_3}{k_1}\right)$. We set them to zero outside the region $1-k_2/k_1 \leq k_3/k_1 \leq k_2/k_1$ and normalize them to one for equilateral triangles $\frac{k_2}{k_1}=\frac{k_3}{k_1}$.
• Figure 2: $A_{\dot Q_{\sigma}^3}$ in Eq. (\ref{['Afirst']}) (dashed red) and $A_{\dot Q_{\sigma} (\partial Q_{\sigma})^2}$ in Eq. (\ref{['Asecond']}) (plain blue) as we vary $\alpha$ with $c_{{\cal D}}^2 \ll 1$.
• Figure 3: Correlation of the adiabatic shape $S^{(\sigma \sigma \sigma)}$ with the equilateral ansatz (top) and the orthogonal ansatz (bottom) as a function of $\alpha$ in the relativistic limit $c_{{\cal D}}^2 \ll 1$.
• Figure 4: Absolute value of the adiabatic shape $S^{(\sigma \sigma \sigma)}$ for $\alpha=0.097$ (left) and of the entropic shape $S^{(\sigma ss)}$ for $\alpha=0.080$. We use the same conventions as in Fig. \ref{['fig:subfigureExample']}.
• Figure 5: $f_{\rm NL} ^{eq \,(\sigma\sigma\sigma)}$ in Eq. (\ref{['fnl_equil_ad_prediction']}) as a function of $\alpha$ for $c_{{\cal D}}=0.1$ and $T_{\sigma s}^2=0$ (left). $f_{\rm NL} ^{eq \,(\sigma s s)}$ in Eq. (\ref{['fnl_equil_en_prediction']}) as a function of $\alpha$ for $c_{{\cal D}}=0.1$ and $T_{\sigma s}^2=1$ (right).