Is there Supernova Evidence for Dark Energy Metamorphosis ?

TL;DR

This work addresses whether dark energy could have an evolving equation of state by performing a model-independent reconstruction from Type Ia supernova data without enforcing priors like $w(z)\ge -1$. It introduces a flexible three-parameter Hubble parameter form, from which the DE equation of state $w(z)$ is derived and marginalized over nuisance parameters, finding that, in the absence of a weak energy condition prior, $w(z)$ evolves rapidly from $w\lesssim 0$ around $z\sim 1$ to $w_0\lesssim -1$ today. The analysis shows a robust metamorphosis of dark energy across various SN samples and analysis choices, though imposing $w(z)\ge -1$ damps the evolution and brings the model closer to ΛCDM. These results suggest that evolving dark energy can be a compelling alternative to a cosmological constant and motivate exploring models such as Chaplygin gas or braneworld scenarios, especially with future high-redshift SN data to sharpen constraints.

Abstract

We reconstruct the equation of state $w(z)$ of dark energy (DE) using a recently released data set containing 172 type Ia supernovae without assuming the prior $w(z) \geq -1$ (in contrast to previous studies). We find that dark energy evolves rapidly and metamorphoses from dust-like behaviour at high $z$ ($w \simeq 0$ at $z \sim 1$) to a strongly negative equation of state at present ($w \lleq -1$ at $z \simeq 0$). Dark energy metamorphosis appears to be a robust phenomenon which manifests for a large variety of SNe data samples provided one does not invoke the weak energy prior $ρ+ p \geq 0$. Invoking this prior considerably weakens the rate of growth of $w(z)$. These results demonstrate that dark energy with an evolving equation of state provides a compelling alternative to a cosmological constant if data are analysed in a prior-free manner and the weak energy condition is not imposed by hand.

Figures (21)

• Figure 1: The fractional deviation $\Delta{\rm log}(d_L H_0)/{\rm log}(d_L H_0)$ between actual value and that calculated using the ansatz (\ref{['eq:taylor']}) over redshift for different models of dark energy with $\Omega_{0 {\rm m}}=0.3$. The solid lines represent quintessence tracker models for potential $V=V_0/\phi^{\alpha}$, with $\alpha=2$ and $4$. The dotted lines show the deviation for Chaplygin Gas models with $\kappa=1$ and $5$ (where $\kappa$ is the ratio between CDM and Chaplygin gas densities at the commencement of the matter dominated epoch). The dot-dashed line represents the SUGRA potential, $V=\left(M^{4+\alpha}/\phi^{\alpha}\right) {\rm exp}[\frac{1}{2}\left(\phi/M_{Pl}\right)^2]$, with $M=1.6\times 10^{-8} M_{Pl}, \alpha=11$. The dashed horizontal line represents zero deviation from model values, which is true for $\Lambda$CDM, and $w=-1/3, w=-2/3$ quiessence models.
• Figure 2: The ($A_1,A_2$) parameter space for the ansatz (\ref{['eq:taylor']}). The light grey shaded area shows the allowed region if dark energy satisfies the weak energy condition both currently and in the past: $w(z) \geq -1, z \geq 0$. The $\chi^2$ surface has two minima, a shallow minimum at $A_1=0.177, A_2=-0.119$ with $\chi^2_{\rm shallow} = 1.0402$ and a deeper minimum at $A_1=-4.360, A_2=1.829$ with $\chi^2_{\rm deep} = 1.0056$. The deeper minimum is marked by a bullet. The solid contours surrounding the deeper minimum are $1\sigma, 2\sigma, 3\sigma$ contours of constant $\Delta\chi^2$ where $\Delta\chi^2 = \chi^2 - \chi^2_{\rm deep}$. Similarly the dashed contours surrounding the shallower minimum are $1\sigma, 2\sigma, 3\sigma$ contours of constant $\Delta\chi^2$ where $\Delta\chi^2 = \chi^2 - \chi^2_{\rm shallow}$. Note that the $\Lambda$CDM model (marked by a solid star) corresponds to $A_1 = A_2 = 0$ which is very close to the shallow minimum.
• Figure 3: The deviation of $H^2/H_0^2$ from corresponding $\Lambda$CDM values over redshift for the ansatz (\ref{['eq:taylor']}). The thick solid line shows the best-fit, the light grey contour represents the $1\sigma$ confidence level, and the dark grey contour represents the $2\sigma$ confidence level around the best-fit. The dashed horizontal line denotes $\Lambda$CDM. $\Omega_{0 {\rm m}} = 0.3$ is assumed.
• Figure 4: The logarithmic variation of dark energy density $\rho_{\rm DE}/\rho_{0{\rm c}}$ (where $\rho_{0{\rm c}}=3 H_0^2/8 \pi G$ is the present day critical density) with redshift for the ansatz (\ref{['eq:taylor']}). The thick solid line shows the best-fit, the light grey contour represents the $1\sigma$ confidence level, and the dark grey contour represents the $2\sigma$ confidence level around the best-fit. The dashed horizontal line denotes $\Lambda$CDM and the dotted line represents matter density $\Omega_{0 {\rm m}} (1+z)^3$, $\Omega_{0 {\rm m}} = 0.3$ is assumed.
• Figure 5: The evolution of $w(z)$ with redshift for different values of $\Omega_{0 {\rm m}}$. The reconstruction is done using the polynomial fit to dark energy, equation (\ref{['eq:taylor']}). In each panel, the thick solid line shows the best-fit, the light grey contour represents the $1\sigma$ confidence level, and the dark grey contour represents the $2\sigma$ confidence level around the best-fit. The dashed line represents $\Lambda$CDM. No priors are assumed on $w(z)$. The $\chi^2$ per degree of freedom for each case is given in Table \ref{['tab:chi']}.