Stability of curvature perturbation with new covariant form for energy-momentum transfer in dark sector

TL;DR

This paper proposes a new covariant model for dark matter and dark energy interaction that avoids instabilities in density perturbations on super-Hubble scales, ensuring stable evolution of cosmic structures.

Contribution

The paper introduces a novel covariant formulation for energy-momentum transfer in the dark sector, addressing previous instability issues in perturbation analysis.

Findings

Instabilities are avoided with the new covariant model for constant w_d.

Density perturbations grow regularly in the radiation era.

The model maintains stability on super-Hubble scales.

Abstract

It was found that the model with interaction between cold dark matter (CDM) and dark energy (DE) proportional to the energy density of CDM $\rho_m$ and constant equation of state of DE $w_d$ suffered from instabilities of the density perturbations on the supper-Hubble scales. Here we suggest a new covariant model for the energy-momentum transfer between CDM and DE. Then using the covariant model, we analyze the evolution of density perturbations on the supper-Hubble scale. We find that the instabilities can be avoided in the model with constant $w_d$ and interaction proportional to $\rho_m$. Furthermore, we analyze the dominant non-adiabatic mode in the radiation era and find that the mode grows regularly.