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 $\varphi$. We consider the coupling proportional to $e^{-\mu \varphi /M_{\mathrm{pl}}}{H}_{\alpha \beta \gamma }{H}^{\alpha \beta \gamma }$ and the scalar potential $V(\varphi )\propto e^{-\lambda \varphi /M_{\mathrm{pl}}}$, where $H_{\alpha \beta \gamma }$ is the 2-form field strength, $\mu ,\lambda$ are constants, and $M_{\mathrm{pl}}$ 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 $\lambda \ge \mathcal{O}(1)$, it is possible to realize the dark energy equation of state $w_{\mathrm{DE}}$ close to $-1$ at low redshifts for $\mu \gg \lambda$. The existence of anisotropic hair and the oscillating behavior of $w_{\mathrm{DE}}$ are key features for distinguishing our scenario from other dark energy models like quintessence.

11 pages, 5 figures