Dark Energy and Neutrino Masses from Future Measurements of the Expansion History and Growth of Structure

TL;DR

This work forecasts cosmological constraints on early dark energy ($\Omega_e$), curvature ($\Omega_k$), and the sum of neutrino masses ($\sum m_\nu$) by combining expansion-history and growth probes (weak lensing, galaxy tomography, SN, and CMB) with full cross-correlations. It employs a Fisher-matrix framework and a tracker-like EDE parameterization with fiducial $\Omega_e=0.01$, evaluating Planck/EPIC-like CMB data alongside LSST/JDEM-like surveys. The key finding is that $\Omega_e$ can be constrained to about 0.2% of the critical density, $\Omega_k$ to ~0.06%, and $\sum m_\nu$ to ~0.04 eV, with $w_0$ at ~0.01, and that cross-correlations can boost neutrino and EDE constraints by up to a factor of 2 while reducing the impact of nonlinear scales. The study also highlights potential biases if EDE is neglected (up to ~2σ) and shows that a multi-probe approach is essential to breaking parameter degeneracies and achieving robust inferences about high-redshift dark energy and neutrino physics.

Abstract

We forecast the expected cosmological constraints from a combination of probes of both the universal expansion rate and matter perturbation growth, in the form of weak lensing tomography, galaxy tomography, supernovae, and the cosmic microwave background incorporating all cross-correlations between the observables for an extensive cosmological parameter set. We allow for non-zero curvature and parameterize our ignorance of the early universe by allowing for a non-negligible fraction of dark energy (DE) at high redshifts. We find that early DE density can be constrained to 0.2% of the critical density of the universe with Planck combined with a ground-based LSST-like survey, while curvature can be constrained to 0.06%. However, these additional degrees of freedom degrade our ability to measure late-time dark energy and the sum of neutrino masses. We find that the combination of cosmological probes can break degeneracies and constrain the sum of neutrino masses to 0.04 eV, present DE density also to 0.2% of the critical density, and the equation of state to 0.01 - roughly a factor of two degradation in the constraints overall compared to the case without allowing for early DE. The constraints for a space-based mission are similar. Even a modest 1% dark energy fraction of the critical density at high redshift, if not accounted for in future analyses, biases the cosmological parameters by up to 2 sigma. Our analysis suggests that throwing out nonlinear scales (multipoles > 1000) may not result in significant degradation in future parameter measurements when multiple cosmological probes are combined. We find that including cross-correlations between the different probes can result in improved constraints by up to a factor of 2 for the sum of neutrino masses and early dark energy density.

Figures (12)

• Figure 1: Energy density (top) and equation of state (bottom) of early dark energy and a cosmological constant. At low redshifts the EDE mimics a dark energy component with the same density and EOS at present, and decouples after redshifts of a few, the exact redshift depending on the size of the EDE fraction $\Omega_e$.
• Figure 2: Matter power spectrum $P(k)~(({\rm Mpc}/h)^3)$ against wavenumber $k~(h/{\rm Mpc})$ at $z = [0,1,5,10]$ (high to low) in four distinct cosmologies: $\Lambda$CDM (dotted black), wCDM (dashed red, $w_0 = -0.9$ and $\Omega_e=0$), $\Lambda$CDM with massive neutrinos (solid green, $\sum m_\nu = 0.3$ eV), and a CDM universe with EDE (dot-dashed blue, $\Omega_e = 0.05$, $w_0=-1$).
• Figure 3: Redshift dependent geometric weight $W_{ij}(z) = {{9 \over 16}{(\Omega_m H_0^2)^2}H(z)\chi^{7/2}(z){\zeta}^{\kappa}_{i}(z){\zeta}^{\kappa}_{j}(z)}$ (see text following Eqn. \ref{['eqkappa']}) of CMB weak lensing (CMBL) and tomographic low redshift weak lensing bins for a flat CDM model with $\Omega_e = 0.1$ and $w_0=-1.0$. For CMB lensing and the fifth tomographic bin we also plot the kernel for $\Omega_e=0$. The lensing kernel captures approximately the redshift dependence of the integrand for the lensing power spectrum (including that from the matter power spectrum). The diminishment of the kernels for $\Omega_e>0$ stems from the increase of $H(z)$ with increasing $\Omega_e$.
• Figure 4: Left: Top: Convergence power spectra $\ell(\ell+1)C^{\kappa\kappa}_{ij}/{2\pi}$ for the case of five tomographic bins in the fiducial cosmology. We include the expected noise for LSST as a band about the curve. Mid: Logarithmic derivative $d\ln{C^{\kappa\kappa}_{ij}}/d\ln{p_k}$ of the convergence power spectrum with cosmological parameters $p_k$ for the third tomographic bin ($i = j = 3$). The derivatives of the other tomographic bins have similar shapes. Bottom: The sub-window zooms in on the logarithmic derivatives with sum of neutrino masses (dotted blue) and EDE density (dot-dot-dashed red). Right: Same as Left but for galaxy power spectra. The noise contribution (both LSST and JDEM) is at most on sub-percent level and decreases towards smaller scales, as the noise is constant with scale whereas $C_\ell^{gg}$ increases with scale. This is to be contrasted with lensing tomography where $C_\ell^{\kappa\kappa}$ peaks at around $\ell = 10$ and thereafter decreases continuously.
• Figure 5: Left: Top: Tomographic galaxy-lensing correlations $\ell(\ell+1)C^{{\kappa}g}_{ij}/{2\pi}$. Here we only illustrate a subset of cases where galaxy and lensing bins fully overlap. Mid: Logarithmic derivatives of the power spectra $d\ln{C^{{\kappa}g}_{ij}}/d\ln{p_k}$ with parameters $p_k$ for the third tomographic bin in both galaxy and lensing (similar characteristics for other bins). Bottom: Zooming in on the derivatives with EDE density and sum of neutrino masses. Right: Logarithmic derivatives of the CMB temperature (solid black), E-mode (dashed blue), and lensing potential (dotted red) power spectra with cosmology.