Do the cosmological observational data prefer phantom dark energy?

The dynamics of expansion and large-scale structure formation of the Universe are analyzed for models with dark energy in the form of a phantom scalar field which initially mimics a $\Lambda$-term and evolves slowly to the Big Rip singularity. The discussed model of dark energy has three parameters—the density and the equation of state parameter at the current epoch, ${\Omega }_{\mathrm{de}}$ and $w_0$, and the asymptotic value of the equation of state parameter at $a\to \infty$, $c_a^2$. Their best-fit values are determined jointly with all other cosmological parameters by the Markov chain Monte Carlo method using observational data on cosmic microwave background anisotropies and polarization, supernovae type Ia luminosity distances, baryon acoustic oscillations measurements, and more. Similar computations are carried out for $\Lambda \mathrm{CDM}$ and a quintessence scalar field model of dark energy. It is shown that the current data slightly prefer the phantom model, but the differences in the maximum likelihoods are not statistically significant. It is also shown that the phantom dark energy with monotonically increasing density in the future will cause the decay of large-scale linear matter density perturbations due to the gravitational domination of dark energy perturbations long before the Big Rip singularity.

Figure 1

Left column: top panel—the dependence of EoS parameter on the scale factor for barotropic phantom scalar field with $w_0=-1.2$ and different $c_a^2$ ($-2.0$, $-1.3$, $-1.2$, $-1.1$); bottom panel—the dependence of the dark energy density (in the units of critical one at the current epoch) on the scale factor with the same EoS parameters. Right column: top panel—the dynamics of the expansion of the Universe with barotropic phantom scalar field: $H^2(a)$ (top panel) and $q(a)$ (bottom panel) for the same models as in the left panels.

Figure 2

Left panel: The dependences of potentials $U$ (solid line), field variable $\varphi -{\varphi }_i$ (dotted), and the kinetic term $X$ (dashed) as functions of the scale factor $a$ for PSF with Lagrangian (1) and barotropic EoS (5) with different relations between $w_0$ and $c_a^2$ ($c_a^2=-2.0$, $-1.2$, $-1.1$ from top to bottom, $w_0=-1.2$ for all). Right panel: The dependences of potentials $U$ on ($\varphi -{\varphi }_i$) for the same PSF models. In all except the bottom right panels the dependences are in log-log scales, in the right bottom panel we use log-lin scales. The potential and the kinetic term are in the units of current critical energy density, $3c^2{H}_0^2/8\pi G$, the field variable is in units of $\sqrt{3c^2/8\pi G}$. In the right panels, field evolves from left to right.

Figure 3

Dependences of the scale factor on time, $a(t)$, for cosmological models with quintessence/phantom scalar fields with $w_0=-1\pm 0.2$ and $c_a^2=-1\pm 1$ (dotted line), $-1\pm 0.3$ (dashed one), $-1\pm 0.2$ (dash-dotted), $-1\pm 0.1$ (dash-three-dotted). The upper sign is for QSF, the lower one for PSF. For the $\Lambda \mathrm{CDM}$ model $a(t)$ is shown by thick solid line. Note also that the limiting behavior for PSF with $1+c_a^2\nearrow 0$ does tend to the cosmological constant behavior, while $1+c_a^2\nearrow 0$ does not. In all models ${\Omega }_m=0.3$, ${\Omega }_{\mathrm{de}}=0.7$, $H_0=70\mathrm{km}/\mathrm{s}·\mathrm{Mpc}$.

Figure 4

The evolution of the Fourier amplitude ($k=0.05{\mathrm{Mpc}}^{-1}$) of density perturbations for cold dark matter (dashed line), baryonic matter (dotted), and PSF (solid) for $c_a^2<w_0$ (top panel) and for $c_a^2=w_0$ (bottom panel).

Figure 5

The evolution of matter density perturbations from the Dark Ages to the present in sCDM, $\Lambda \mathrm{CDM}$, $\mathrm{QSF}+\mathrm{CDM}$ (1: $w_0=-0.8$, $c_a^2=-0.8$; 2: $w_0=-0.8$, $c_a^2=-0.5$), and $\mathrm{PSF}+\mathrm{CDM}$ (1: $w_0=-1.2$, $c_a^2=-1.2$; 2: $w_0=-1.2$, $c_a^2=-1.5$) models. Amplitudes are normalized to 0.1 at $z=10$ ($a=0.1$). In models with dark energy, ${\Omega }_m=0.3$, ${\Omega }_{\mathrm{de}}=0.7$.

Figure 6

The evolution of different Fourier amplitudes of PSF (left column) and matter (right column) density perturbations from $a=0.1$ to $a=200$ for models with $w_0=-1.2$, $c_a^2=-1.5$ (top panels) and $w_0=-1.2$, $c_a^2=-1.2$ (bottom panels). The rest of parameters are the same as in Figs. 4, 5. The different lines correspond to different wave numbers $k$ (in ${\mathrm{Mpc}}^{-1}$) as follows: $1-0.0005$, $2-0.001$, $3-0.0015$, $4-0.002$, $5-0.0025$, $6-0.005$, $7-0.01$, $8-0.05$, $9-0.1{\mathrm{Mpc}}^{-1}$. The amplitudes of all $k$-modes of ${\delta }_{\mathrm{de}}$ are normalized to ${\delta }_{\mathrm{de}}(k,a=0.1)={\delta }_m(k,a=0.1)=0.1$ at $a=0.1$, for all $k$-modes.

Figure 7

One-dimensional marginalized posteriors (solid lines) and mean likelihoods (dotted lines) for $w_0$ (top panels) and $c_a^2$ (middle panels). From left to right: PSF and $\mathrm{WMAP}7+\mathrm{HST}+\mathrm{BBN}+\mathrm{BAO}+\mathrm{SN}$ SDSS MLCS2k2, QSF and $\mathrm{WMAP}7+\mathrm{HST}+\mathrm{BBN}+\mathrm{BAO}+\mathrm{SN}$ SDSS MLCS2k2, PSF and $\mathrm{WMAP}7+\mathrm{HST}+\mathrm{BBN}+\mathrm{BAO}+\mathrm{SN}$ SDSS SALT2, QSF and $\mathrm{WMAP}7+\mathrm{HST}+\mathrm{BBN}+\mathrm{BAO}+\mathrm{SN}$ SDSS SALT2. Bottom: the corresponding two-dimensional mean likelihood distributions in the plane $c_a^2—w_0$. Solid lines show the $1\sigma$ and $2\sigma$ confidence contours.

Figure 8

One-dimensional marginalized posteriors (solid lines) and mean likelihoods (dotted lines) for $w_0$ (top panels) and $c_a^2$ (middle panels). From left to right: PSF and $\mathrm{WMAP}7+\mathrm{HST}+\mathrm{BBN}+\mathrm{BAO}+\mathrm{WiggleZ}+\mathrm{SNLS}3$, QSF and $\mathrm{WMAP}7+\mathrm{HST}+\mathrm{BBN}+\mathrm{BAO}+\mathrm{WiggleZ}+\mathrm{SNLS}3$, PSF and $\mathrm{WMAP}7+\mathrm{HST}+\mathrm{BBN}+\mathrm{BAO}+\mathrm{WiggleZ}+\mathrm{Union}2.1$, QSF and $\mathrm{WMAP}7+\mathrm{HST}+\mathrm{BBN}+\mathrm{BAO}+\mathrm{WiggleZ}+\mathrm{Union}2.1$. Bottom: the corresponding two-dimensional mean likelihood distributions in the plane $c_a^2\mathrm{a}—w_0$. Solid lines show the $1\sigma$ and $2\sigma$ confidence contours.