Anisotropic $2$-form dark energy

Abstract

We study the dynamics of dark energy in the presence of a 2-form field coupled to a canonical scalar field $\phi$. We consider the coupling proportional to $e^{-\mu \phi/M_{\rm pl}} H_{\alpha \beta \gamma}H^{\alpha \beta \gamma}$ and the scalar potential $V(\phi) \propto e^{-\lambda \phi/M_{\rm pl}}$, where $H_{\alpha \beta \gamma}$ is the 2-form field strength, $\mu, \lambda$ are constants, and $M_{\rm pl}$ is the reduced Planck mass. We show the existence of an anisotropic matter-dominated scaling solution followed by a stable accelerated fixed point with a non-vanishing shear. Even if $\lambda \geq {\cal O}(1)$, it is possible to realize the dark energy equation of state $w_{\rm DE}$ close to $-1$ at low redshifts for $\mu \gg \lambda$. The existence of anisotropic hair and the oscillating behavior of $w_{\rm DE}$ are key features for distinguishing our scenario from other dark energy models like quintessence.