Extended Born-Infeld dynamics and cosmology

We introduce an extension of the Born-Infeld action for a scalar field and show that it can act as unifying dark matter, providing an explanation for both structure formation and the accelerated expansion of the universe. We investigate the cosmological dynamics of this theory in a particular case, referred to as the “Milne-Born-Infeld” (MBI) Lagrangian. We show that this model, whose equation of state has effectively a single free parameter, is consistent with recent type Ia supernovae data, providing a fit as good as for the $\Lambda \mathrm{C}\mathrm{D}\mathrm{M}$ model with the same number of degrees of freedom. Furthermore, this parameter is tightly constrained by current data, making the model easily testable with other observables. Contrary to previous candidates for unifying dark matter, the sound velocity of the MBI model is vanishing both close to the dark-matter state as well as near the cosmological constant state. This could avoid the problems on the matter power spectrum that were present in previous adiabatic dark-matter/dark-energy unification models. We also present a short discussion on the causal propagation in nonlinear scalar field theories such as the one proposed here.

Figure 1

Equation of state of the MBI model. The dimensionless pressure $p/(A{\Sigma }^2)$ is plotted as a function of $\rho /(A{\Sigma }^2)$ starting from the fundamental state ${\rho }_{\mathrm{v}}=A{\Sigma }^2/2$. Also displayed is the vacuum eos (dashed curve).

Figure 2

The sound velocity squared as a function of the dimensionless density $\rho /(A{\Sigma }^2)$ in the MBI model.

Figure 3

The sound velocity $c_s^2$ as a function of the equation of state parameter $w$ for the MBI case and other quartessence models. (a) Results for the MBI model (thick line) and the generalized Chaplygin gas, with $\alpha =0.1$, 0.25, 0.5, and 0.75 (from bottom to top, short dashed curves), and $\alpha =1$ (equivalent to the Born-Infeld model, long dashed line). (b) Exponential quartessence with $\alpha =0.1$, 0.5, $1$, $2$, and $e$ (from bottom to top). (c) Logarithmic quartessence with $\alpha ={10}^{-3}$, ${10}^{-2}$, ${10}^{-1}$, and $e^{-1}$ (from bottom to top). (d) Results for the $n$th order Dirac-Born-Infeld theory with $n=2$, 5, 20, 100, and 500 (from top to bottom).

Figure 4

Vector field and trajectories of the MBI model in the $(\rho ,\theta )$ plane. The dashed curve is the trajectory for a flat universe. The dots correspond to the four stationary points $M$, $N$, $Q$, and $O$ discussed in the text.