The Physical Origin of Dark Energy Constraints from Rubin Observatory and CMB-S4 Lensing Tomography

Abstract

We seek to clarify the origin of constraints on the dark energy equation of state parameter from CMB lensing tomography, that is the combination of galaxy clustering and the cross-correlation of galaxies with CMB lensing in a number of redshift bins. In particular, we consider the two-point correlation functions which can be formed with a catalog of galaxy locations and photometric redshifts from the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and CMB lensing maps from the CMB-S4 experiment. We focus on the analytic understanding of the origin of the constraints. Dark energy information in these data arises from the influence of three primary relationships: distance as a function of redshift (geometry), the amplitude of the power spectrum as a function of redshift (growth), and the power spectrum as a function of wavenumber (shape). We find that the effects from geometry and growth play a significant role and partially cancel each other out, while the shape effect is unimportant. We also show that Dark Energy Task Force (DETF) Figure of Merit (FoM) forecasts from the combination of LSST galaxies and CMB-S4 lensing are comparable to the forecasts from cosmic shear in the absence of the CMB lensing map, thus providing an important independent check. Compared to the forecasts with the LSST galaxies alone, combining CMB lensing and LSST clustering information (together with the primary CMB spectra) increases the FoM by roughly a factor of 3-4 in the optimistic scenario where systematics are fully under control. We caution that achieving these forecasts will likely require a full analysis of higher-order biasing, photometric redshift uncertainties, and stringent control of other systematic limitations, which are outside the scope of this work, whose primary purpose is to elucidate the physical origin of the constraints.

Cosmological Implications of a Neutrino Mass Detection

“…For photometric galaxy surveys it is useful to analyze the angular power spectra of galaxy densities divided into redshift bins (see e.g. [25,[62][63][64]). These power spectra can be calculated using the Limber approximation shown in Equation (3.1).…”

Skewing the CMB$\times$LSS: a Fast Method for Bispectrum Analysis

“…In preparation for the application of our formalism to real data, we test it on the MassiveNuS simulation suite 7 [25]. These simulations contain 1024 3 CDM particles with 6 While more precise fitting functions for the bispectrum are available [49], we choose to use this one for simplicity. In the biases, we show only the last bin to be concise, but the rest show a relative difference of less than 17%.…”

“…A cross-correlation analysis is a useful complementary probe of the redshift evolution of LSS. Since the CMB lensing window peaks around z ≈ 1 − 3, correlation with galaxy samples in this range can provide, for example, constraints on the nature of dark energy [6] or tests of general relativity at the largest scales [7]. Moreover, it is a powerful tool to break degeneracies between cosmological parameters, such as the one between the matter fraction Ω m and the amplitude of galaxy clustering measured on spheres of comoving radius R = 8/h Mpc, namely σ 8 , and also bypass the cosmic variance limited by the survey volume [8].…”

The Benefits of CMB Delensing

“…structure at late times, including neutrino mass [9][10][11][12][13] and dark energy [14]. The value of CMB lensing maps are enhanced by the opportunities presented by cross-correlations with large scale galaxy surveys [15][16][17][18][19].…”