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The Tensor to Scalar Ratio of Phantom Dark Energy Models

A. E. Schulz, Martin White

TL;DR

This work investigates phantom dark energy with a constant equation of state $w< -1$ and its impact on CMB anisotropies, including tensor modes. By extending CMBfast to evolve the phantom background and its perturbations, the authors compute both scalar and tensor spectra across a range of $w$, $$, and spectral indices, and they derive cosmology-dependent transfer functions $f_S$ and $f_T$ to relate primordial perturbations to CMB normalizations. A key finding is that the tensor normalization is largely insensitive to $w$, so the tensor-to-scalar ratio is driven primarily by the $w$-dependence of scalar perturbations and the late ISW effect. The study provides percent-level fits for the transfer functions and discusses how the angular-diameter distance to the last scattering surface shifts spectral features with $w$, offering a framework to interpret potential future detections of long-wavelength gravitational waves in terms of the inflation scale and the phantom dark-energy model.

Abstract

We investigate the anisotropies in the cosmic microwave background in a class of models which possess a positive cosmic energy density but negative pressure, with a constant equation of state w = p/rho < -1. We calculate the temperature and polarization anisotropy spectra for both scalar and tensor perturbations by modifying the publicly available code CMBfast. For a constant initial curvature perturbation or tensor normalization, we have calculated the final anisotropy spectra as a function of the dark energy density and equation of state w and of the scalar and tensor spectral indices. This allows us to calculate the dependence of the tensor-to-scalar ratio on w in a model with phantom dark energy, which may be important for interpreting any future detection of long-wavelength gravitational waves.

The Tensor to Scalar Ratio of Phantom Dark Energy Models

TL;DR

This work investigates phantom dark energy with a constant equation of state and its impact on CMB anisotropies, including tensor modes. By extending CMBfast to evolve the phantom background and its perturbations, the authors compute both scalar and tensor spectra across a range of , , and spectral indices, and they derive cosmology-dependent transfer functions and to relate primordial perturbations to CMB normalizations. A key finding is that the tensor normalization is largely insensitive to , so the tensor-to-scalar ratio is driven primarily by the -dependence of scalar perturbations and the late ISW effect. The study provides percent-level fits for the transfer functions and discusses how the angular-diameter distance to the last scattering surface shifts spectral features with , offering a framework to interpret potential future detections of long-wavelength gravitational waves in terms of the inflation scale and the phantom dark-energy model.

Abstract

We investigate the anisotropies in the cosmic microwave background in a class of models which possess a positive cosmic energy density but negative pressure, with a constant equation of state w = p/rho < -1. We calculate the temperature and polarization anisotropy spectra for both scalar and tensor perturbations by modifying the publicly available code CMBfast. For a constant initial curvature perturbation or tensor normalization, we have calculated the final anisotropy spectra as a function of the dark energy density and equation of state w and of the scalar and tensor spectral indices. This allows us to calculate the dependence of the tensor-to-scalar ratio on w in a model with phantom dark energy, which may be important for interpreting any future detection of long-wavelength gravitational waves.

Paper Structure

This paper contains 5 sections, 17 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The Model
  3. CMB Anisotropy Spectra
  4. dependence of $T/S$ on $w$ and $n_S$
  5. Discussion

Figures (4)

  • Figure 1: The scalar CMB temperature anisotropy spectra, $\ell(\ell+1)C_{\ell}/2(\pi)$ vs.$\ell$ for several values of $w$. The solid lines are $w=-1.1$, dashed are $w=-3$, dot-dash are $w=-10$, and dash-dash are $w=-0.4$. The spectra have been normalized at $C_{10}$ to fit the COBE data.
  • Figure 2: The tensor CMB temperature anisotropy spectra as a function of $w$. As in Fig. \ref{['fig:scalar']}, the solid lines are $w=-1.1$, dashed are $w=-3$, dot-dash are $w=-10$, and dash-dash are $w=-0.4$. Notice that the curves are almost degenerate for the first 40 multipoles. There appears to be negligible dependence of the tensor normalization on the equation of state $w$.
  • Figure 3: The polarization anisotropy spectra. For the scalar modes, the E-E polarizations anisotropies are shown (top), and for the tensor modes the E-E and B-B polarization anisotropies are presented (middle and bottom). The scale is arbitrary, depending on our particular choice of normalization.
  • Figure 4: The normalization of the tensor and scalar spectra at the 10th multipole for an initial perturbation $\zeta=1$ and $h=1$.