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An Extended WZDR Model with Interacting Scalar Field Dark Matter and Stepped Dark Radiation

Gang Liu

TL;DR

This work extends the WZDR framework by replacing cold dark matter with scalar field dark matter (SFDM) and introducing a pure momentum coupling to stepped dark radiation. The authors derive the coupled background and perturbation dynamics, implement them in CLASS, and perform comprehensive MCMC analyses using Planck 2018, ACT DR4, BAO, SNIa, SH0ES, and DES data, with SFDM mass fixed at $m=10^{-22}$ eV. They find that the extended WZDR+ model yields $H_0$ values around $70$ km s$^{-1}$ Mpc$^{-1}$ and $S_8$ near $0.81$–$0.82$, with an upper bound $\log_{10}(\xi) < 4.56$ indicating a weak coupling; overall, the coupling provides only marginal improvements over the original WZDR model and does not fully resolve the cosmological tensions. The study highlights that while the mechanism can modestly suppress small-scale structure growth and slightly adjust CMB damping, more effective interactions or model refinements are required to achieve a substantial tension alleviation.

Abstract

In this paper, we explore the interaction between scalar field dark matter and stepped dark radiation as an extension of the WZDR model. The supersymmetry-based WZDR framework has demonstrated considerable potential in alleviating the Hubble tension. Previous investigations have examined the interaction between stepped dark radiation and cold dark matter, with the aim of simultaneously addressing both the Hubble and $S_8$ tensions. Given the suppressive effect of scalar field dark matter on small-scale structure growth, we replace cold dark matter with scalar field dark matter in the present work and introduce its interaction with stepped dark radiation via pure momentum coupling, thereby formulating a novel coupling model. We impose constraints on the model parameters using a variety of cosmological datasets, including the Cosmic Microwave Background, Baryon Acoustic Oscillations, Type Ia Supernovae, $H_0$ measurements from SH0ES, $S_8$ data from the Dark Energy Survey Year 3, and data from the Atacama Cosmology Telescope. Our analysis reveals that the performance of the new model is nearly identical to that of the original WZDR model, with only a marginal improvement. When using the full data combination, the best-fit values for $H_0$ in the coupled model and WZDR model are 70.89 km/s/Mpc and 70.68 km/s/Mpc, respectively. For the $S_8$ parameter, the new model results in a decrease from 0.8136 in the original model to 0.8113. Furthermore, the coupling signal remains weak, with the constraint on the coupling parameter being $\log_{10}(ξ)<4.56$. While the coupling model offers some improvement, it does not fully resolve the cosmological tensions, indicating that further investigation is required to address these issues.

An Extended WZDR Model with Interacting Scalar Field Dark Matter and Stepped Dark Radiation

TL;DR

This work extends the WZDR framework by replacing cold dark matter with scalar field dark matter (SFDM) and introducing a pure momentum coupling to stepped dark radiation. The authors derive the coupled background and perturbation dynamics, implement them in CLASS, and perform comprehensive MCMC analyses using Planck 2018, ACT DR4, BAO, SNIa, SH0ES, and DES data, with SFDM mass fixed at eV. They find that the extended WZDR+ model yields values around km s Mpc and near –, with an upper bound indicating a weak coupling; overall, the coupling provides only marginal improvements over the original WZDR model and does not fully resolve the cosmological tensions. The study highlights that while the mechanism can modestly suppress small-scale structure growth and slightly adjust CMB damping, more effective interactions or model refinements are required to achieve a substantial tension alleviation.

Abstract

In this paper, we explore the interaction between scalar field dark matter and stepped dark radiation as an extension of the WZDR model. The supersymmetry-based WZDR framework has demonstrated considerable potential in alleviating the Hubble tension. Previous investigations have examined the interaction between stepped dark radiation and cold dark matter, with the aim of simultaneously addressing both the Hubble and tensions. Given the suppressive effect of scalar field dark matter on small-scale structure growth, we replace cold dark matter with scalar field dark matter in the present work and introduce its interaction with stepped dark radiation via pure momentum coupling, thereby formulating a novel coupling model. We impose constraints on the model parameters using a variety of cosmological datasets, including the Cosmic Microwave Background, Baryon Acoustic Oscillations, Type Ia Supernovae, measurements from SH0ES, data from the Dark Energy Survey Year 3, and data from the Atacama Cosmology Telescope. Our analysis reveals that the performance of the new model is nearly identical to that of the original WZDR model, with only a marginal improvement. When using the full data combination, the best-fit values for in the coupled model and WZDR model are 70.89 km/s/Mpc and 70.68 km/s/Mpc, respectively. For the parameter, the new model results in a decrease from 0.8136 in the original model to 0.8113. Furthermore, the coupling signal remains weak, with the constraint on the coupling parameter being . While the coupling model offers some improvement, it does not fully resolve the cosmological tensions, indicating that further investigation is required to address these issues.

Paper Structure

This paper contains 11 sections, 21 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Coupling dark sector model
  3. Background equations
  4. Perturbation equations
  5. Initial conditions
  6. Numerical results
  7. MCMC analyses
  8. Datasets
  9. Results
  10. Conclusions
  11. The full MCMC posteriors

Figures (6)

  • Figure 1: The impact of varying the SFDM mass on the linear matter power spectrum is investigated. On small scales, the power spectrum for SFDM is suppressed, whereas on large scales, the results are in agreement with those of the $\Lambda$CDM model.
  • Figure 2: The linear matter power spectrum of the WZDR+ model exhibits a reduction on small scales relative to the original WZDR model. This suppression results from the combined effects of the intrinsic property of SFDM and the momentum exchange between dark matter and dark radiation.
  • Figure 3: The differences in the CMB temperature power spectrum between the new model with varying coupling constant and the WZDR model can be attributed to two main factors: the decay of gravitational potentials during acoustic oscillations and the attenuation of gravitational lensing. Together, these effects contribute to the overall reduction in the amplitude of the power spectrum.
  • Figure 4: The posterior distribution contours for the parameter constraints of the $\Lambda$CDM model, WZDR model, and WZDR+ model, obtained using the $\mathcal{DHS}$ data combination, are shown. The results for the coupled model closely resemble those of the WZDR model, with only a slight reduction in the value of $S_8$.
  • Figure 5: The posterior distributions of selected parameters for the WZDR+ model under various data combinations. The inclusion of datasets $\mathcal{H}$ and $\mathcal{S}$ significantly alters the posterior results for the $H_0$ and $S_8$ parameters. Additionally, all data combinations only provide an upper limit for the coupling constant $\xi$.
  • ...and 1 more figures