Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Toward a solution of the coincidence problem

Sergio del Campo, Ramon Herrera, Diego Pavon

TL;DR

This paper tackles the cosmic coincidence problem by seeking a direct relation between the late-time density ratio $r=\rho_m/\rho_\phi$ and the Hubble rate $H$ within a flat FLRW universe with an energy-transfer term $Q>0$ between dark matter and dark energy. It analyzes two phenomenological interaction forms, $(i)$ $Q=3\alpha H(\rho_m+\rho_\phi)$ and $(ii)$ $Q=3\beta H\rho_m$, deriving $\frac{dr}{dH}=\mathcal{I}/H$ and explicit expressions for $H(r)$ and, via integration, $H(z)$ and $r(z)$. The authors compare the model predictions to model-independent $H(z)$ data from differential ages and SN Ia/radio galaxy distances, finding that current data cannot decisively discriminate the interacting scenarios from each other or from $\Lambda$CDM. They discuss nucleosynthesis constraints (e.g., $\Omega_\phi\lesssim 5\%$ at early times) and emphasize that future, more accurate $H(z)$ measurements over a wider redshift range are needed to assess whether the coincidence problem points to new physics or is merely a coincidence.

Abstract

The coincidence problem of late cosmic acceleration constitutes a serious riddle with regard to our understanding of the evolution of the Universe. Here we argue that this problem may someday be solved -or better understood- by expressing the Hubble expansion rate as a function of the ratio of densities (dark matter/dark energy) and observationally determining the said rate in terms of the redshift.

Toward a solution of the coincidence problem

TL;DR

This paper tackles the cosmic coincidence problem by seeking a direct relation between the late-time density ratio and the Hubble rate within a flat FLRW universe with an energy-transfer term between dark matter and dark energy. It analyzes two phenomenological interaction forms, and , deriving and explicit expressions for and, via integration, and . The authors compare the model predictions to model-independent data from differential ages and SN Ia/radio galaxy distances, finding that current data cannot decisively discriminate the interacting scenarios from each other or from CDM. They discuss nucleosynthesis constraints (e.g., at early times) and emphasize that future, more accurate measurements over a wider redshift range are needed to assess whether the coincidence problem points to new physics or is merely a coincidence.

Abstract

The coincidence problem of late cosmic acceleration constitutes a serious riddle with regard to our understanding of the evolution of the Universe. Here we argue that this problem may someday be solved -or better understood- by expressing the Hubble expansion rate as a function of the ratio of densities (dark matter/dark energy) and observationally determining the said rate in terms of the redshift.

Paper Structure

This paper contains 4 sections, 15 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Basic relations
  3. Two choices for $Q$
  4. Discussion

Figures (5)

  • Figure 1: Evolution of the ratio $r=\rho_{m}/\rho_{\phi}$ with redshift for different values of the parameter $\alpha$. In drawing the curves we have fixed $r_{0}= 3/7 \,$ and $\, w= -0.9$.
  • Figure 2: Evolution $H$ vs the ratio $r=\rho_{m}/\rho_{\phi}$ as given by Eq.(\ref{['HH']}) with $\alpha = 10^{-4}$ for $w= -0.9$ (quintessence, top line) and $w= -1.1$ (phantom, bottom line). Also shown is the prediction of the $\Lambda$CDM model (middle line). In drawing all the curves we have fixed $\, r_{0} = 3/7$.
  • Figure 3: Evolution $H$ vs $z$ with $\alpha = 10^{-4}$ for $w= -0.9$ (quintessence) and $w= -1.1$ (phantom). Also shown is the prediction of the $\Lambda$CDM model (solid line). In all the cases we have fixed $r_{0} = 3/7\,$ and $H_{0} = 71 \, {\rm km/s/Mpc}$. The data points with their $1\sigma$ error bars are borrowed from Simon, Verde, and Jiménez, Ref. simon (full circles) and table 2 of Ref. daly1 (full diamonds).
  • Figure 4: Same as Fig. \ref{['fig:hz1']}. The upper panel shows the combined sample of $132$ SN Ia of Ref. davis and $30$ radio galaxies of Ref. daly2. The bottom panel shows the $30$ radio galaxies only. The data points with their $1\sigma$ error intervals and the best-fit curve (big solid line) in both panels are borrowed from Daly et al., Ref. daly1.
  • Figure 5: Evolution of the ratio $r=\rho_{m}/\rho_{\phi}$ with redshift for different values of the parameter $\beta$. In drawing both curves we have fixed $r_{0}= 3/7 \,$ and $\, w= -0.9$. As it is apparent, $\dot{r}/r \simeq 0$ at late times.