Novel cosmological tests from combining galaxy lensing and the polarized Sunyaev-Zel'dovich effect

Novel cosmological tests from combining galaxy lensing and the polarized Sunyaev-Zel’dovich effect

Oliver H. E. Philcox and Matthew C. Johnson

Phys. Rev. D 106, 083501 – Published 3 October 2022

Abstract

The polarized Sunyaev-Zel’dovich (pSZ) effect is sourced by the Thomson scattering of cosmic microwave background (CMB) photons from distant free electrons and yields a novel view of the CMB quadrupole throughout the observable Universe. Galaxy shear measures the shape distortions of galaxies, probing both their local environment and the intervening matter distribution. Both observables have been shown to give interesting constraints on the cosmological model; in this work we ask: what can be learnt from their combination? The pSZ-shear cross-spectrum measures the shear-galaxy-polarization bispectrum [i.e., $⟨ γ δ_{g} (Q \pm i U) ⟩$ ] and contains contributions from three main phenomena: (1) the Sachs-Wolfe (SW) effect, (2) the integrated Sachs-Wolfe (ISW) effect, and (3) inflationary gravitational waves. Since the modes contributing to the pSZ signal are not restricted to the Earth’s past light cone, the low-redshift cross-spectra could provide a novel constraint on dark energy properties via the ISW effect, whilst the SW signal is sourced by a coupling of scalar modes at very different times (recombination and the lensing redshift), but at similar positions; this provides a unique probe of the Universe’s homogeneous time evolution. We give expressions for all major contributions to the galaxy shear, galaxy density, and pSZ auto- and cross-spectra, and evaluate their detectability via Fisher forecasts. Despite significant theoretical utility, the shear cross-spectra will be challenging to detect: combining CMB-S4 with the Rubin observatory yields a $1.6 σ$ detection of the ISW contribution, though this increases to $5.2 σ$ for a futuristic experiment involving CMB-HD and a higher galaxy sample density. For parity-even (parity-odd) tensors, we predict a $1 σ$ limit of $σ (r) = 0.9$ (0.2) for CMB-S4 and Rubin, or 0.3 (0.06) for the more futuristic setup. Whilst this is significantly better than the constraints from galaxy shear alone (and contains fewer systematics than most auto-spectra), it is unlikely to be competitive, but may serve as a useful cross-check.

Received 24 June 2022
Accepted 19 September 2022

DOI:https://doi.org/10.1103/PhysRevD.106.083501

Physics Subject Headings (PhySH)

Cosmic microwave background Cosmological parameters Dark energy Gravitational waves Large scale structure of the Universe

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Oliver H. E. Philcox ^1,2,3,4,* and Matthew C. Johnson^5,6,†

¹Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08540, USA
²School of Natural Sciences, Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540, USA
³Center for Theoretical Physics, Department of Physics, Columbia University, New York, New York 10027, USA
⁴Simons Society of Fellows, Simons Foundation, New York, New York 10010, USA
⁵Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo ON N2L 2Y5, Canada
⁶Department of Physics and Astronomy, York University, Toronto ON M3J 1P3, Canada

^*ohep2@cantab.ac.uk
^†mjohnson@perimeterinstitute.ca

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 106, Iss. 8 — 15 October 2022

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Tensors and the Integrated Sachs-Wolfe effect and (b) Unequal Time Sachs-Wolfe effect. Cartoon of the pSZ-shear cross-correlations considered in this work. The pSZ effect is sourced by the CMB observed at some distant galaxy (brown arrows), whose quadrupole moment, $Θ_{2}$ , is anisotropically scattered (blue arrow) and reaches the Earth. This is sensitive to physics on the light cone of the distant galaxy, and that between the distant galaxy and the Earth. In contrast, shear is sourced by the perturbations to a photon geodesic imprinted by scalars, $Ψ$ , and tensors, $h_{i j}$ , as it traverses its worldline on the Earth’s light cone (shown in black dotted lines). If the lens (green region) lies close to the scattering galaxy, a correlation will be induced due to both sets of photons (scattered CMB and weak lensing) experiencing the same scalar (through the integrated Sachs-Wolfe effect) and tensor modes. If the lens lies further than the pSZ source, other correlations can arise, such as one between the scalar potential at last scattering, $Ψ (χ_{dec})$ and that sourcing gravitational lensing. Unlike most physics observables, this correlates two effects at very different times but at the same physical location.
Reuse & Permissions
Figure 2
Contributions of scalar and tensor modes to the shear and pSZ angular power spectrum. We show a single redshift bin centered at $z = 1$ , and plot scalar (tensor) contributions to the spectra in blue (red, assuming $r = 1$ ). The first, second, and third plots show the shear-auto, pSZ-auto and shear-pSZ spectra for $E$ modes (left) and $B$ modes (right), with all spectra multiplied by $ℓ (ℓ + 1) / (2 π)$ . We additionally convert the CMB based measurements into micro-Kelvin units by multiplying by $T_{CMB}$ . The black curves show noise contributions, and the gray regions give $1 σ$ errors around the total tensor-free signal, relevant for both CMB-S4/VRO and CMB-HD/VRO experiments. Clearly, the pSZ-shear cross-spectra has much reduced signal to noise compared to the pSZ-pSZ spectra, though some detection of gravitational waves may be possible in the $B$ mode, particularly at larger $z$ .
Reuse & Permissions
Figure 3
Contributions to the $E$ -mode pSZ-shear cross-spectrum in two redshift bins, with centers indicated by the titles. We show scalar contributions from the Sachs-Wolfe (green, SW), integrated Sachs-Wolfe (red, ISW) and Doppler (blue) effect and $r = 1$ tensors (black, as in Fig. 2). The dotted lines show the same contributions but only including the effects of gravitational lensing (omitting intrinsic alignments). The shaded region shows the $1 σ$ error for VRO/CMB-S4 as in Fig. 2. We note that the ISW effect dominated the scalar signal at low- $z$ , but there is significant contribution from the SW effect at high $z$ . Furthermore, intrinsic alignments are seen to be a key contribution to the tensor signal in both bins, though the high- $z$ scalar signals are sourced almost entirely by lensing shear modes.
Reuse & Permissions
Figure 4
Signal-to-noise ( $S / N$ ) ratio for the pSZ auto- and cross-spectra. We give the significance of a detection in each $ℓ$ bin [equivalent to the $S / N$ per ${ℓ, m}$ mode multiplied by $(2 ℓ + 1)$ )] the total $S / N$ is the sum over all bins and given in Table 1. We show detection significances for the total pSZ effect (black) and split into the SW, ISW and Doppler subcomponents (green, red, and blue), always assuming the CMB-S4/VRO noise parameters. The overall signal is strongest in the auto-spectrum; however, this is more susceptible to systematic effects than cross-spectra. The auto-spectra are dominated by the SW signal, whilst cross-spectra are a probe instead of the ISW. Whilst all curves are a strong function of $ℓ$ , the falloff is slower for the cross-spectra, indicating the utility of measuring smaller scales.
Reuse & Permissions
Figure 5
Contributions to the tensor Fisher matrix from shear and pSZ auto- and cross-spectra, assuming CMB-S4/VRO noise parameters. We show results for the parity-even and parity-odd components (constraining $r$ and $r Δ_{h}$ respectively) in red and blue, plotting the contribution to $\sqrt{F} = σ^{- 1}$ from each set of $ℓ$ modes. The dashed curves give the results with only lensing shear modes; we find that lensing dominates the shear constraints, but intrinsic alignments are also important for the cross-spectra with pSZ. $1 σ$ detection limits are given in Table 2; briefly, we find that the cross-spectrum has some (albeit weak) sensitivity to tensors, particularly parity-odd tensors, and, suffers less from from systematic effects than auto-spectra.
Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology