Dark Energy Tomography

TL;DR

Dark Energy Tomography assesses forecasted constraints on the dark energy equation-of-state history from tomographic cosmic shear combined with CMB data, exploring sky coverage, source density, and small-scale information through a ratio statistic. It compares a two-parameter history $w(z)=w_0+ w_a (1-a(z))$ with a five-bin discretization, using a Fisher-matrix approach that marginalizes over an 11-parameter cosmology and includes unlensed CMB spectra; results depend on survey configuration and which parameters are fixed by CMB priors. The study finds that all-sky weak-lensing with Planck (and especially CMBpol) can constrain $w_0$ and $w_a$ to about $oldsymbol{ m σ}(w_0)\sim ext{0.06}$ and $oldsymbol{ m σ}(w_a)\sim ext{0.09}$, with significantly tighter limits for the $w(z)$ bins when the ratio statistic is used; this also yields strong neutrino-mass and primordial-spectrum constraints. Overall, the work demonstrates the strong synergy between cosmic shear and CMB data for robust dark-energy tomography, enabling meaningful constraints on $m_ u$, $n_s$, and $n_s'$ while offering a path to reconstruct the redshift evolution of dark energy up to $z oughly 2$.

Abstract

We study how parameter error forecasts for tomographic cosmic shear observations are affected by sky coverage, density of source galaxies, inclusion of CMB experiments, simultaneou fitting of non--dark energy parameters, and the parametrization of the history of the dark energy equation-of-state parameter w(z). We find tomographic shear-shear power spectra on large angular scales (l<1000) inferred from all-sky observations, in combination with Planck, can achieve sigma(w0)=0.06 and sigma(wa)=0.09 assuming the equation-of-state parameter is given by w(z)=w0+wa(1-a(z)) and that nine other matter content and primordial power spectrum parameters are simultaneously fit. Taking parameters other than w0, wa and Omegam to be completely fixed by the CMB we find errors on w0 and wa that are only 10% and 30% better respectively, justifying this common simplifying assumption. We also study `dark energy tomography': reconstuction of w(z) assumed to be constant within each of five independent redshift bins. With smaller-scale information included by use of the Jain & Taylor ratio statistic we find sigma(wi)<0.1 for all five redshift bins and sigma(wi)<0.02 for both bins at z<0.8. Finally, addition of cosmic shear can also reduce errors on quantities already determined well by the CMB. We find the sum of neutrino masses can be determined to +-0.013eV and that the primordial power specrum power-law index, ns, as well as dns/dlnk, can be determined more than a factor of two better than by Planck alone. These improvements may be highly valuable since the lower bound on the sum of neutrino masses is 0.06eV as inferred from atmospheric neutrino oscillations, and slow-roll models of inflation predict non-zero dns/dlnk at the forecasted error levels when |n_S-1|>0.04.

Figures (6)

• Figure 1: The shear-shear auto power spectra. The 8 solid curves are the shear power spectra from each of the galaxy source planes, $B_1$ to $B_8$. Dotted curves are the linear perturbation theory approximation. From bottom to top the source plane redshift ranges are $B_1$: $z\in[0.0,0.4]$, $B_2$: $z\in[0.4,0.8]$, $B_3$: $z\in[0.8,1.2]$, $B_4$: $z\in[1.2,1.6]$, $B_5$: $z\in[1.6,2.0]$, $B_6$: $z\in[2.0,2.4]$, $B_7$: $z\in[2.4,2.8]$ and $B_8$: $z\in[2.8,3.2]$. The error boxes are forecasts for G4$\pi$ (see Table I). The top dashed curve is the shear power spectrum for the CMB source plane. The error boxes are forecasts for CMBpol (see Table II).
• Figure 2: Contours of constant error in $w_0$ (top panels) and $w_a$ (bottom panels) for cosmic shear observations of $f_{\rm sky}$ of the sky and shear weight per solid angle $\bar{n}_{\rm tot}/\gamma_{\rm rms}^2$. The left panels are for $l_{\rm max}=1000$ and the right panels are for $l_{\rm max}=2000$. These parameter error forecasts also include constraints from Planck.
• Figure 3: Error boxes indicate expected 1-$\sigma$ error in each $w_i$ for G$4\pi$ combined with either Planck (left panels) or CMBpol (right panels) for $w_{\rm fid}=-1$ (top panels) or -0.8 (bottom panels).
• Figure 4: Error boxes indicate expected 1-$\sigma$ error in each $w_i$ for the combination of experiments specified in each panel.
• Figure 5: Forecasts of 1-$\sigma$ error contours for pairs of $w_i$ assuming G$4\pi$ and CMBpol. The thin solid contour is for shear-shear correlations alone, the dashed contour is for the ratio statistic alone and the thick contour is for their combination.