Can the clustered dark matter and the smooth dark energy arise from the same scalar field?

Abstract

Cosmological observations suggest the existence of two different kinds of energy densities dominating at small ($ \lesssim 500$ Mpc) and large ($\gtrsim 1000 $ Mpc) scales. The dark matter component, which dominates at small scales, contributes $\Omega_m \approx 0.35$ and has an equation of state $p=0$ while the dark energy component, which dominates at large scales, contributes $\Omega_V \approx 0.65$ and has an equation of state $p\simeq -\rho$. It is usual to postulate wimps for the first component and some form of scalar field or cosmological constant for the second component. We explore the possibility of a scalar field with a Lagrangian $L =- V(\phi) \sqrt{1 - \del^i \phi \del_i \phi}$ acting as {\it both} clustered dark matter and smoother dark energy and having a scale dependent equation of state. This model predicts a relation between the ratio $ r = \rho_V/\rho_{\rm DM}$ of the energy densities of the two dark components and expansion rate $n$ of the universe (with $a(t) \propto t^n$) in the form $n = (2/3) (1+r) $. For $r \approx 2$, we get $n \approx 2$ which is consistent with observations.