Sourcing Dark Matter and Dark Energy from $\alpha$-attractors

Recently, Kallosh and Linde have drawn attention to a new family of superconformal inflationary potentials, subsequently called $\alpha$-attractors. The $\alpha$-attractor family can interpolate between a large class of inflationary models. It also has an important theoretical underpinning within the framework of supergravity. We demonstrate that the $\alpha$-attractors have an even wider appeal since they may describe dark matter and perhaps even dark energy. The dark matter associated with the $\alpha$-attractors, which we call $\alpha$-dark matter ($\alpha$DM), shares many of the attractive features of fuzzy dark matter, with $V(\varphi) = \frac{1}{2}m^2\varphi^2$, while having none of its drawbacks. Like fuzzy dark matter, $\alpha$DM can have a large Jeans length which could resolve the cusp-core and substructure problems faced by standard cold dark matter. $\alpha$DM also has an appealing tracker property which enables it to converge to the late-time dark matter asymptote, $\langle w\rangle \simeq 0$, from a wide range of initial conditions. It thus avoids the enormous fine-tuning problems faced by the $m^2\varphi^2$ potential in describing dark matter.