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Exploring a new interaction between dark matter and dark energy using the growth rate of structure

Martín G. Richarte, Lixin Xu

TL;DR

The paper investigates a new interaction between dark energy and dark matter parameterized by a scale-factor power-law coupling via $Q_{x}= H\\bar{Q}_{x}$ with $\\bar{Q}_{x}= -\\xi_{c}\\rho_{c0}a^{\\beta}$ and analyzes its impact on both background evolution and linear perturbations. To avoid instabilities in the perturbations, the authors implement the interacting PPF (IPPF) framework, deriving how the coupling modifies the growth of structure and the evolution of the gravitational potential. They perform a comprehensive MCMC analysis using CosmoMC/CAMB, combining geometric probes (Planck, WMAP9, JLA, BAO, HST) with dynamical data (RSD), and obtain tight constraints on $w_x$, $\\xi_c$, and $\\beta$, finding a phantom-like $w_x$ and a nonzero, potentially sizable coupling when growth data are included. The results show that a large coupling, while consistent with the full data set, is driven by the perturbation sector and the perturbed Hubble term; the model also predicts shifts in the CMB acoustic peaks and a modified turnover in the matter power spectrum due to an earlier matter–radiation equality, offering observable tests for future surveys and cross-correlations.

Abstract

We present a phenomenological interaction with a scale factor power law form which leads to the appearance of two kinds of perturbed terms, a scale factor spatial variation along with perturbed Hubble expansion rate. We study both the background and the perturbation evolution within the parametrized post-Friedmann scheme, obtaining that the exchange of energy-momentum can flow from dark energy to dark matter in order to keep dark energy and dark matter densities well defined at all times. We combine several measures of the cosmic microwave background (WMAP9+Planck) data, baryon acoustic oscillation measurements, redshift-space distortion data, JLA sample of supernovae, and Hubble constant for constraining the coupling constant and the exponent provided both parametrized the interaction itself. The joint analysis of ${\rm Planck+WMAP9+BAO}$ ${\rm +RSD+JLA+HST}$ data seems to favor large coupling constant, $ξ_c = 0.34403427_{- 0.18907353}^{+ 0.14430125}$ at 1 $σ$ level, and prefers a power law interaction with a negative exponent, thus $β= -0.50863232_{- 0.40923857}^{+ 0.48424166}$ at 1 $σ$ level. The CMB temperature power spectrum indicates that a large coupling constant produces a shift of the acoustic peaks and affects their amplitudes at lower multipoles. In addition, a larger $β$ exponent generates a shift of the acoustic peaks, pointing a clear deviation with respect to the concordance model. The matter power spectrum are sensitive to the variation of the coupling constant and the $β$ exponent. In this context, the interaction alters the scale of matter and radiation equality and pushes it away from the present era, which in turn generates a shift of the turnover point toward to smaller scale.

Exploring a new interaction between dark matter and dark energy using the growth rate of structure

TL;DR

The paper investigates a new interaction between dark energy and dark matter parameterized by a scale-factor power-law coupling via with and analyzes its impact on both background evolution and linear perturbations. To avoid instabilities in the perturbations, the authors implement the interacting PPF (IPPF) framework, deriving how the coupling modifies the growth of structure and the evolution of the gravitational potential. They perform a comprehensive MCMC analysis using CosmoMC/CAMB, combining geometric probes (Planck, WMAP9, JLA, BAO, HST) with dynamical data (RSD), and obtain tight constraints on , , and , finding a phantom-like and a nonzero, potentially sizable coupling when growth data are included. The results show that a large coupling, while consistent with the full data set, is driven by the perturbation sector and the perturbed Hubble term; the model also predicts shifts in the CMB acoustic peaks and a modified turnover in the matter power spectrum due to an earlier matter–radiation equality, offering observable tests for future surveys and cross-correlations.

Abstract

We present a phenomenological interaction with a scale factor power law form which leads to the appearance of two kinds of perturbed terms, a scale factor spatial variation along with perturbed Hubble expansion rate. We study both the background and the perturbation evolution within the parametrized post-Friedmann scheme, obtaining that the exchange of energy-momentum can flow from dark energy to dark matter in order to keep dark energy and dark matter densities well defined at all times. We combine several measures of the cosmic microwave background (WMAP9+Planck) data, baryon acoustic oscillation measurements, redshift-space distortion data, JLA sample of supernovae, and Hubble constant for constraining the coupling constant and the exponent provided both parametrized the interaction itself. The joint analysis of data seems to favor large coupling constant, at 1 level, and prefers a power law interaction with a negative exponent, thus at 1 level. The CMB temperature power spectrum indicates that a large coupling constant produces a shift of the acoustic peaks and affects their amplitudes at lower multipoles. In addition, a larger exponent generates a shift of the acoustic peaks, pointing a clear deviation with respect to the concordance model. The matter power spectrum are sensitive to the variation of the coupling constant and the exponent. In this context, the interaction alters the scale of matter and radiation equality and pushes it away from the present era, which in turn generates a shift of the turnover point toward to smaller scale.

Paper Structure

This paper contains 8 sections, 32 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background and Perturbation Equations
  3. Background
  4. Perturbation
  5. Perturbation
  6. The PPF method
  7. Constraint and Results
  8. summary

Figures (5)

  • Figure 1: 68 $\%$ and 95 $\%$ constraints on $w_x$, $\xi_c$, and $\beta$ from the combined analysis made with the Planck 2013+WMAP9+JLA+BAO+RSD+HST data. The 1D marginalized posterior distribution of $w_x$, $\xi_c$, and $\beta$ are also shown.
  • Figure 2: Typical effects of the coupling constant on the theoretical CMB temperature power spectrum. We exhibit $C^{\rm TT}_{\rm l}$ versus multipole for different values of the coupling constant.
  • Figure 3: Typical effects of the $\beta$ exponent on the theoretical CMB temperature power spectrum. We show $C^{\rm TT}_{\rm l}$ versus multipole for different power-law interactions.
  • Figure 4: The total matter power spectrum at $z=0$ as the coupling constant varies from 0 to 0.9. Baryon acoustic oscillations generate wiggles in the matter power spectrum.
  • Figure 5: The total matter power spectrum at $z=0$ as the $\beta$ exponent varies from 0 to -1. Baryon acoustic oscillations generate wiggles in the matter power spectrum.