Dark Energy versus Modified Gravity

TL;DR

The study addresses whether cosmic acceleration is due to dark energy within General Relativity or to a modification of gravity such as the DGP brane-world scenario. By analyzing linear perturbations in the Newtonian gauge and introducing the comoving density perturbation $\Delta$, the authors show that the growth factor $g$ is not uniquely determined by the expansion history and can be altered by dark energy perturbations. They demonstrate that anisotropic stress $\sigma$ and pressure perturbations $\delta p$ in a generalized dark energy fluid can reproduce the DGP metric perturbations $\phi$ and $\psi$, effectively matching both the growth of matter perturbations and the 3+1D metric perturbations, thus creating a cosmological degeneracy. The key implication is that, without measuring the full set of metric perturbations, cosmological observations of growth may fail to distinguish between dark energy and modified gravity, especially as observations favor $w_{DE} \approx -1$.

Abstract

There is now strong observational evidence that the expansion of the universe is accelerating. The standard explanation invokes an unknown "dark energy" component. But such scenarios are faced with serious theoretical problems, which has led to increased interest in models where instead General Relativity is modified in a way that leads to the observed accelerated expansion. The question then arises whether the two scenarios can be distinguished. Here we show that this may not be so easy, demonstrating explicitely that a generalised dark energy model can match the growth rate of the DGP model and reproduce the 3+1 dimensional metric perturbations. Cosmological observations are then unable to distinguish the two cases.

Figures (2)

• Figure 1: This figure shows how the growth of the matter perturbations depends on the clustering properties of the dark energy. From the top downward the sound speed is $c_s^2=-2\times10^{-4}$ (cyan dash-dotted line), $c_s^2=-10^{-4}$ (magenta long dashed line), $c_s^2=0$ (blue dotted line) and $c_s^2=1$ (red dashed line). For comparison we also plot the growth factor of the DGP model (black solid line).
• Figure 2: In this figure we show how the anisotropic stress of the dark energy affects the growth of the dark matter perturbations. The red dashed line corresponds to scalar field dark energy with $c_s^2=1$ and $\sigma=0$. The dotted blue line shows how the dark matter growth factor decreases for a constant $\sigma_\mathrm{DE}=-0.1$. The long-dashed magenta line uses the theoretical anisotropic stress of Eq. (\ref{['eq:sigma_theo']}) with $c_s^2=1$, which suppresses the growth of the matter perturbations too much. Finally, the dash-dotted cyan line (nearly on top of black solid DGP line) uses the same $\sigma_\mathrm{DE}$ but sets the pressure perturbation of the dark energy to $\delta p = (1+w)\rho \sigma$ in its rest frame.