Eddington-Born-Infeld action for dark matter and dark energy

We argue that Einstein gravity coupled to a Born-Infeld theory provides an attractive candidate to represent dark matter and dark energy. For cosmological models, the Born-Infeld field has an equation of state which interpolates between matter, $p=0$ (small times), and a cosmological constant $p=-\rho$ (large times). On galactic scales, the Born-Infeld theory predicts asymptotically flat rotation curves.

Figure 1

$\alpha =0.99$, $Y_1=10.59$.

Figure 2

Evolution of the equation of state.

Figure 3

Two branches.

Figure 4

Rotation curves for $k_0=50$, 15, 5, 1.5.

Figure 5

Rotation curves for $k_0=1.5$, 1.03, 1.003, 1.0005.

Figure 6

$w_0(\mathrm{kpc})$ as a function of $k_0$.