Breaking the scale invariance of the primordial power spectrum in Hořava-Lifshitz cosmology

We study the spectral tilt of primordial perturbations in Hořava-Lifshitz cosmology. The uniform approximation, which is a generalization of the familiar Wentzel-Kramers-Brillouin method, is employed to compute the spectral index both numerically and analytically in a closed form. We clarify how the spectral index depends on the inflation model and parameters in the modified dispersion relation.

Figure 1

Growing mode solution to Eq. (1), obtained by employing the uniform approximation, is compared to the exact result. The parameters are given by $\mu =2$, $n=3$, $H_{*}=1$, and $k^3/M^2={10}^{-2}$. The horizon-crossing time is $\overline{\eta }=-4.14$.

Figure 2

(a) Contours of $n_{\mathrm{ini}}$ on the $1/n$ and $\kappa$ plane. The parameters are ${\alpha }_1=0$ and ${\alpha }_2=1$. The level of the contour is shown in the panel. (b) Same as (a), but with ${\alpha }_1=2$ and ${\alpha }_2=1$. (c) Same as (a), but with ${\alpha }_1=-2$ and ${\alpha }_2=1$.