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

TL;DR

This paper investigates whether a single scalar field with a specific Lagrangian can account for both dark matter and dark energy, predicting a scale-dependent equation of state and a relation between their energy densities and universe expansion.

Contribution

It proposes a unified scalar field model for dark matter and dark energy with a scale-dependent equation of state, linking their energy ratio to the universe's expansion rate.

Findings

The model predicts a relation n = (2/3)(1 + r) between energy density ratio and expansion rate.

For r ≈ 2, the model yields n ≈ 2, aligning with observational data.

The scalar field Lagrangian allows for both clustered dark matter and smooth dark energy within a single framework.

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.