Dynamical Test of Cosmic Acceleration: $k$-nearest Neighbor Cross Correlation of Cosmic Microwave Background and Cosmic Infrared Background

Abstract

The physical origin of cosmic acceleration remains one of the central questions in modern cosmology. The integrated Sachs-Wolfe (ISW) and Rees-Sciama (RS) effects, which arise from the evolution of gravitational potentials, provide a dynamical test of cosmic acceleration. We measure the cross correlation between the Planck temperature map of the cosmic microwave background (CMB) and a foreground-free map of the $100\,\mu\mathrm{m}$ cosmic infrared background (CIB) from Y.-K. Chiang (2023), using the $k$-nearest neighbor cumulative distribution function ($k$NN-CDF). As the CIB map is reconstructed from ${\sim}600$ million Wide-field Infrared Survey Explorer galaxies extending to $z\approx2.5$, the measurement is equivalent to a galaxy-CMB cross correlation. We find evidence for a positive cross correlation, rejecting the null hypothesis of no correlation at $p=0.02~(2.3\sigma)$ using the $\chi^2$ test. We further quantify its amplitude with $A_{k\mathrm{NN}}$, defined relative to an assumed cosmological model, and obtain $A_{k\mathrm{NN}}=0.95\pm0.20~(4.8\sigma)$ with respect to $\Lambda\mathrm{CDM}$ mock data including the ISW and RS effects. The $k$NN-CDF analysis improves the detection significance by ${\sim}20\%$ over the two-point correlation function. We also explore evolving dark energy by constructing two tomographic maps from the full CIB map; the results are consistent with $\Lambda$CDM. Finer tomographic reconstruction of the CIB, for example from multiband data of SPHEREx, would further tighten constraints on evolving dark energy.