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Crossing the Phantom Divide with Parameterized Post-Friedmann Dark Energy

Wenjuan Fang, Wayne Hu, Antony Lewis

TL;DR

The paper addresses the challenge that dark energy models with a single scalar field cannot cross the phantom divide without instabilities. It proposes a parameterized post-Friedmann (PPF) framework that replaces the dark-energy density and momentum with a single variable Gamma and uses a transition scale to ensure smoothness and energy-momentum conservation, matching metric evolution on both large and small scales. The authors calibrate the transition and demonstrate that PPF accurately reproduces the metric evolution for multi-field crossing dark-energy models and remains a practical approximation for a wide class of smooth models. They implement the method in the CAMB code and discuss its usefulness for horizon-scale probes and future dark-energy constraint analyses.

Abstract

Dark energy models with a single scalar field cannot cross the equation of state divide set by a cosmological constant. More general models that allow crossing require additional degrees of freedom to ensure gravitational stability. We show that a parameterized post-Friedmann description of cosmic acceleration provides a simple but accurate description of multiple scalar field crossing models. Moreover the prescription provides a well controlled approximation for a wide range of "smooth" dark energy models. It conserves energy and momentum and is exact in the metric evolution on scales well above and below the transition scale to relative smoothness. Standard linear perturbation tools have been altered to include this description and made publicly available for studies of the dark energy involving cosmological structure out to the horizon scale.

Crossing the Phantom Divide with Parameterized Post-Friedmann Dark Energy

TL;DR

The paper addresses the challenge that dark energy models with a single scalar field cannot cross the phantom divide without instabilities. It proposes a parameterized post-Friedmann (PPF) framework that replaces the dark-energy density and momentum with a single variable Gamma and uses a transition scale to ensure smoothness and energy-momentum conservation, matching metric evolution on both large and small scales. The authors calibrate the transition and demonstrate that PPF accurately reproduces the metric evolution for multi-field crossing dark-energy models and remains a practical approximation for a wide class of smooth models. They implement the method in the CAMB code and discuss its usefulness for horizon-scale probes and future dark-energy constraint analyses.

Abstract

Dark energy models with a single scalar field cannot cross the equation of state divide set by a cosmological constant. More general models that allow crossing require additional degrees of freedom to ensure gravitational stability. We show that a parameterized post-Friedmann description of cosmic acceleration provides a simple but accurate description of multiple scalar field crossing models. Moreover the prescription provides a well controlled approximation for a wide range of "smooth" dark energy models. It conserves energy and momentum and is exact in the metric evolution on scales well above and below the transition scale to relative smoothness. Standard linear perturbation tools have been altered to include this description and made publicly available for studies of the dark energy involving cosmological structure out to the horizon scale.

Paper Structure

This paper contains 4 sections, 17 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Phantom Divide and Scalar Fields
  3. PPF Description
  4. Discussion

Figures (2)

  • Figure 1: PPF vs scalar field calculation of the evolution of the potential responsible for gravitational redshifts and lensing $(\Phi-\Psi)/2$ for a $w_e=-0.7$ model (flat, with $\Omega_m=0.31$ and $h=0.64$). Curves are normalized to the initial curvature $\zeta_i$.
  • Figure 2: PPF vs scalar field calculation of the CMB anisotropy power spectrum for the $w_e=-0.7$ model of Fig. \ref{['fig:timeplot']} and a two-field crossing model that approximates $w_0=-1.15$ and $w_a=0.5$ (flat, with $\Omega_m=0.26$ and $h=0.74$).