The integrated Sachs–Wolfe effect in interacting dark matter–dark energy models

Abstract

Interacting dark matter-dark energy (IDMDE) models can be considered as one of the present challenges that may affect cosmic structures. The main idea of such models is that the mass of dark matter particles is specified by their interactions with a scalar field whose energy density is characterized by dark energy. In this work, we propose to study the integrated Sachs–Wolfe (ISW) effect in IDMDE models. Regarding this, we initially introduce a theoretical framework for IDMDE models. Moreover, we briefly discuss the stability conditions of IDMDE models, and by specifying a simple functional form for the energy density transfer rate, we calculate the perturbation equations. In the following, we specify the amplitude of the matter power spectrum for IDMDE models and compare it with the corresponding result obtained from the ΛCDM model. Furthermore, we calculate the amplitude of the ISW auto-power spectrum as a function of multipole order l for IDMDE models. The results indicate that the amplitude of the ISW auto-power spectrum in IDMDE models behaves like the one for the ΛCDM model for different values of the phantom dark energy equation of state. While the amplitude of the ISW-auto power spectrum for the IDMDE model should be higher than the one for the ΛCDM model in the case of quintessence dark energy equation of state. Also, it turns out that the corresponding results by different values of the coupling parameter demonstrate that ξ is inversely proportional to the amplitude of the ISW-auto power spectrum in IDMDE models. Finally, by employing four different surveys, we calculate the amplitude of the ISW-cross power spectrum as a function of multipole order l for IDMDE models. The results exhibit that the amplitude of the ISW-cross power spectrum in IDMDE models for all values of ωx is higher than that obtained from the ΛCDM model. Also, it turns out that the amplitude of the ISW-cross power spectrum in IDMDE models changes inversely with the value of coupling parameter ξ.