Perturbations of the Quintom Models of Dark Energy and the Effects on Observations

TL;DR

The paper addresses whether dark-energy models can realize a crossing of the equation of state across the boundary $w=-1$ and how perturbations influence observational constraints. It argues that single-fluid or canonical k-essence models cannot achieve stable crossing due to perturbation instabilities, necessitating extra degrees of freedom such as a two-field quintom or a higher-derivative formulation. The authors derive a self-consistent perturbation framework for viable quintom models, show that adiabatic and isocurvature modes can behave regularly across crossing, and demonstrate observable signatures in ISW, CMB, and LSS that differ from a cosmological constant when perturbations are included. They also propose a practical method to include perturbations in parametrized EOS across -1, showing that perturbations generally enlarge the allowed crossing parameter space and affect cosmological inferences, thereby highlighting quintom as a testable alternative to $\\Lambda$CDM.

Abstract

We study in this paper the perturbations of the quintom dark energy model and the effects of quintom perturbations on the current observations. Quintom describes a scenario of dark energy where the equation of state gets across the cosmological constant boundary $w = -1$ during evolution. We present a new method to show that the conventional dark energy models based on single k-essence field and perfect fluid cannot act as quintom due to the singularities and classical instabilities of perturbations around $w = -1$. One needs to add extra degrees of freedom for successful quintom model buildings. There are no singularities or classical instabilities in perturbations of realistic quintom models and they are potentially distinguishable from the cosmological constant. Basing on the realistic quintom models in this paper we provide one way to include the perturbations for dark energy models with parametrized equation of state across -1. Compare with those assuming no dark energy perturbations, we find that the parameter space which allows the equation of state to get across -1 will be enlarged in general when including the perturbations.

Figures (6)

• Figure 1: Effects of the two-field oscillating quintom on the observables. The mass of the phantom field is fixed at $2.0\times10^{-60} m_{pl}$ and the mass of the quintessence field are $10^{-60} m_{pl}$(thicker line) and $4.0\times10^{-60} m_{pl}$(thinner line) respectively. The upper right panel illustrates the evolution of the metric perturbations $\Phi+\Psi$ of the two models when with(solid lines) and without(dashed lines) dark energy perturbations. The scale is $k\sim10^{-3}$ Mpc$^{-1}$. The lower left panel shows the CMB effects and the lower right panel delineates the effects on the matter power spectrum when with(solid lines) and without(dashed lines) dark energy perturbations.
• Figure 2: 3$\sigma$ WMAP and SN constraints on two-field quintom model shown together with the best fit values. $m_Q$ and $m_P$ stand for the mass of quintessence and phantom respectively. We have fixed $m_P\sim 6.2 \times 10^{-61} m_{pl}$ and varied the value of $m_Q$. Left panel: Separate WMAP and SN constraints. The green(shaded) area is WMAP constraints on models where dark energy perturbations have been included and the blue area(contour with solid lines) is without dark energy perturbations. Right panel: Combined WMAP and SN constraints on the two-field quintom model with perturbations(green/shaded region) and without perturbations(red region/contour with solid lines).
• Figure 3: Effects of the two-field quintom model where $w_{eff}=-1$ compared with cosmological constant in CMB(WMAP), the metric perturbations $\Phi+\Psi$(the scale is $k\sim10^{-3}$ Mpc$^{-1}$) and the linear growth factor. The binned error bars in the upper right panel are WMAP TT and TE data Kogut03.
• Figure 4: Reconstructions of the effective adiabatic single field $\chi$ in the framwork of oscillating quintom. The background parameters have been chosen as $m_{\phi 1}= 2\times 10^{-60} m_{pl}, m_{\phi 2}= 10^{-61} m_{pl}$, initial values are $\phi_{1i}=0.09 m_{pl}, \phi_{2i}=0.45 m_{pl}$ and $\dot{\phi_{1i}}= \dot{\phi_{2i}}=0$ early in radiation domination epoch and for this example we have $\Omega_{\phi 1}=0.2, \Omega_{\phi 2}\sim 0.54, h\sim 0.68$. The red lines are the total EOS of dark energy and the blue lines are the total potential. The dashed lines show the cosmological constant boundary. The upper panel delineates the late evolutions of the EOS and potential of dark energy and the lower panel shows the reconstructed values of $\chi$ and its potential, $\chi$ is a quintessence/phantom scalar when $w$ is above/below the dashed line. See the text for details.
• Figure 5: 3$\sigma$ WMAP and SN constraints on the parametrized quintom models $w= -1 + w_0 \cos(w_1 \ln a)$ and $w= -1 + w_0 a \cos(w_1 a)$, shown together with the best fit values. On the left panels the green(shaded) areas are WMAP constraints on models where dark energy perturbations have been included and the blue areas(contours with solid lines) are without dark energy perturbations. On the right panels models with perturbations are delineated in green(shaded) regions and the red regions(contour with solid lines) without perturbations. For illustrations we have fixed $w_1=20$ in the upper panels and $w_1=50$ in the lower panels.