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2013

Anisotropic power-law k-inflation

Ohashi, Junko, Soda, Jiro, Tsujikawa, Shinji

Understand

It is known that power-law k-inflation can be realized for the Lagrangian $P=Xg(Y)$, where $X=-(\partial \phi)^2/2$ is the kinetic energy of a scalar field $\phi$ and $g$ is an arbitrary function in terms of $Y=Xe^{\lambda \phi/M_{pl}}$ ($\lambda$ is a constant and $M_{pl}$ is the reduced Planck mass).

In the presence of a vector field coupled to the inflaton with an exponential coupling $f(\phi) \propto e^{\mu \phi/M_{pl}}$, we show that the models with the Lagrangian $P=Xg(Y)$ generally give rise to anisotropic inflationary solutions with $\Sigma/H=constant$, where $\Sigma$ is an anisotropic shear and $H$ is an isotropic expansion rate.
Provided these anisotropic solutions exist in the regime where the ratio $\Sigma/H$ is much smaller than 1, they are stable attractors irrespective of the forms of $g(Y)$.
We apply our results to concrete models of k-inflation such as the generalized dilatonic ghost condensate/the DBI model and we numerically show that the solutions with different initial conditions converge to the anisotropic power-law inflationary attractors.