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Accelerating Universes with Scaling Dark Matter

M. Chevallier, D. Polarski

TL;DR

The paper investigates FRW cosmologies with a dominant X-component obeying $-1<w_X<-1/3$, examining how such a component can cause acceleration and how its dynamics can be analyzed via a 1D Hamiltonian framework. It identifies critical points and possible loitering regimes, providing insight into the conditions under which accelerated expansion arises and how flat universes behave asymptotically. Through a toy model with a variable equation of state, it demonstrates that degeneracies with matter/dark-energy densities can hinder distinguishing evolving $w_X$ from constant $w_X$ using $d_L(z)$ data up to $z\sim1$. The work emphasizes the need for precise high-redshift observations ($z>1$–$2$) and independent priors on $\,\Omega_{m,0}$ or $\Omega_{X,0}$ to resolve evolving dark energy from a cosmological constant–like component, guiding future survey design and analysis (e.g., SNAP).

Abstract

Friedmann-Robertson-Walker universes with a presently large fraction of the energy density stored in an $X$-component with $w_X<-1/3$, are considered. We find all the critical points of the system for constant equations of state in that range. We consider further several background quantities that can distinguish the models with different $w_X$ values. Using a simple toy model with a varying equation of state, we show that even a large variation of $w_X$ at small redshifts is very difficult to observe with $d_L(z)$ measurements up to $z\sim 1$. Therefore, it will require accurate measurements in the range $1<z<2$ and independent accurate knowledge of $Ω_{m,0}$ (and/or $Ω_{X,0}$) in order to resolve a variable $w_X$ from a constant $w_X$.

Accelerating Universes with Scaling Dark Matter

TL;DR

The paper investigates FRW cosmologies with a dominant X-component obeying , examining how such a component can cause acceleration and how its dynamics can be analyzed via a 1D Hamiltonian framework. It identifies critical points and possible loitering regimes, providing insight into the conditions under which accelerated expansion arises and how flat universes behave asymptotically. Through a toy model with a variable equation of state, it demonstrates that degeneracies with matter/dark-energy densities can hinder distinguishing evolving from constant using data up to . The work emphasizes the need for precise high-redshift observations (–) and independent priors on or to resolve evolving dark energy from a cosmological constant–like component, guiding future survey design and analysis (e.g., SNAP).

Abstract

Friedmann-Robertson-Walker universes with a presently large fraction of the energy density stored in an -component with , are considered. We find all the critical points of the system for constant equations of state in that range. We consider further several background quantities that can distinguish the models with different values. Using a simple toy model with a varying equation of state, we show that even a large variation of at small redshifts is very difficult to observe with measurements up to . Therefore, it will require accurate measurements in the range and independent accurate knowledge of (and/or ) in order to resolve a variable from a constant .

Paper Structure

This paper contains 3 sections, 24 equations, 6 figures.

Table of Contents

  1. Introduction
  2. FRW cosmologies
  3. Some observational constraints

Figures (6)

  • Figure 1: For $w_X=-2/3$ and $\Omega_{m,0}=2$, two different universes having a quasi-static (loitering) stage are shown. The two universes have different values $\Omega_{X,0}$. The present time is chosen here at $t=0$ and we show for each universe the relevant part, either $t<0$ or $t>0$, containing a quasi-static stage. The quasi-static stages take place in the vicinity of the critical points corresponding to $\Omega_{X,0}=5.8284...$ and $\Omega_{X,0}= 0.17157...$. For an expanding universe with $\Omega_{m,0}=2,~\Omega_{X,0}=5.8284...$ (plain line), loitering is in the past and occurs at $z\approx 0.70$ while it is in the future at $x\approx 3.41$ for an expanding universe with $\Omega_{m,0}=2,~\Omega_{X,0}= 0.17157...$ (dashed line). We could also have a bounce in the past for slightly higher values of $\Omega_{X,0}$; the other loitering stage can be followed either by expansion (this is the case here, but the expansion stage is not shown) or by a recollapse for slightly lower $\Omega_{X,0}$ values.
  • Figure 2: The age of the universe is shown for various cases in function of $w_X=\frac{\rho_X}{p_X}$. The central curve corresponds to a flat universe with ($\Omega_{X,0},~\Omega_{m,0})=(0.72,~0.28)$. For each $\Omega_{X,0}$, the upper, resp. lower, curve corresponds to $\Omega_{m,0}=0.2$, resp., $0.4$. Note that all universes with same $\Omega_{m,0}$ have the same age when the $X$-component scales like the curvature term.
  • Figure 3: The age of the universe at various redshifts $z$ is shown for several universes. The upper curve has $\Omega_{m,0}=0.2$, the lowest dashed curve (with $w_X=-0.6$) has $\Omega_{m,0}=0.4$. The three curves in between all have $\Omega_{m,0}=0.3$. All these universes pass the constraint set by high-redshift objects mentioned in the text for $0.6\le h\le 0.7$. However the lowest dashed curve, is already on the border for h=0.7. We show for comparison $t(z)$ for the Einstein-de Sitter universe (dotted line).
  • Figure 4: The luminosity distance (in $H_0^{-1}$ units) is plotted against redshift for several flat universes. For each constant $w_X$ value, the upper, resp. lower, curve corresponds to $\Omega_{m,0}=0.2$, resp. $0.3$. We see that some combinations conspire to give practically undistinghishable curves up to redshifts $z\sim 1$.
  • Figure 5: The value $w_X(z)$ is shown for our toy model. Note that we display here the cases with $\alpha=0$ which correspond to the present value $w_X(0)=-1.$
  • ...and 1 more figures