Thermal SZ Power Spectrum

The thermal Sunyaev-Zeldovich effect produces a spectral distortion of the CMB as photons inverse-Compton scatter off hot electrons in the intracluster medium. The angular power spectrum of the tSZ signal — its distribution across multipoles — is sensitive to the abundance and pressure profiles of galaxy groups and clusters across cosmic history, making it a powerful cosmological probe. Measurements of the tSZ power spectrum from ACT, SPT, and Planck find amplitudes that are systematically lower than predicted from ΛCDM models calibrated on Planck CMB parameters: using the Planck best-fit σ₈ and Ω_m values, the predicted tSZ power spectrum exceeds observations by 20–40 percent. This can be reconciled either by lowering σ₈ — which is independently motivated by the S₈ tension — or by invoking additional feedback processes that suppress ICM pressure in low-mass groups, or by systematic errors in the cluster pressure profile models used to convert σ₈ to tSZ power.

Successive Collision Theory resolves the thermal SZ power spectrum tension through the spatial variation of the effective expansion rate Λ_eff across the redshift range probed by the tSZ signal. The tSZ power spectrum is dominated by contributions from clusters at z ~ 0.3–1, a redshift range where both the cluster abundance (sensitive to σ₈ and Ω_m) and the ICM pressure profiles contribute to the signal. In SCT, the locally enhanced Λ_eff within and around the KBC supervoid suppresses the growth of structure at low redshifts relative to the global ΛCDM prediction calibrated on the CMB, reducing the effective σ₈ at the redshifts most relevant to the tSZ power spectrum. The tSZ amplitude is therefore lower than the Planck-calibrated ΛCDM prediction because the local matter clustering amplitude — which determines cluster abundance — is genuinely suppressed by the enhanced local expansion rate, not because there is a systematic error in cluster pressure profiles.

The gravitational superposition mechanism also affects the tSZ power spectrum through its modification of cluster pressure profiles. In SCT, the effective total pressure in clusters includes both thermal pressure (measured by tSZ) and the superposition contribution from frame hierarchy overlap (which does not produce a tSZ signal). The true total pressure supporting clusters against gravitational collapse is therefore higher than the tSZ measurement alone indicates, meaning clusters are in equilibrium at lower thermal pressures than the total mass would imply in a pure thermal pressure model. This reduces the amplitude of the tSZ power spectrum relative to what the lensing-measured cluster masses would predict, contributing to the observed deficit. The SCT prediction is that the tSZ deficit should be correlated with environment: clusters in denser supercluster environments have a larger superposition pressure fraction and therefore a larger tSZ-to-mass ratio deficit.