CIBER 4th flight fluctuation analysis: Measurements of near-IR auto- and cross-power spectra on arcminute to sub-degree scales

We present new anisotropy measurements in the near-infrared (NIR) for angular multipoles $300<\ell<10^5$ using imaging data at 1.1 $\mu$m and 1.8 $\mu$m from the fourth flight of the Cosmic Infrared Background ExpeRiment (CIBER). Using improved analysis methods and higher quality fourth flight data, we detect surface brightness fluctuations on scales $\ell<2000$ with CIBER auto-power spectra at $\sim14\sigma$ and 18$\sigma$ for 1.1 and 1.8 $\mu$m, respectively, and at $\sim10\sigma$ in cross-power spectra. The CIBER measurements pass internal consistency tests and represent a $5-10\times$ improvement in power spectrum sensitivity on several-arcminute scales relative to that of existing studies. Through cross-correlations with tracers of diffuse galactic light (DGL), we determine that scattered DGL contributes $<10\%$ to the observed fluctuation power at high confidence. On scales $\theta > 5'$, the CIBER auto- and cross-power spectra exceed predictions for integrated galactic light (IGL) and integrated stellar light (ISL) by over an order of magnitude, and are inconsistent with our baseline IGL+ISL+DGL model at high significance. We cross-correlate two of the CIBER fields with 3.6 $\mu$m and 4.5 $\mu$m mosaics from the Spitzer Deep Wide-Field Survey and find similar evidence for departures from Poisson noise in Spitzer-internal power spectra and CIBER $\times$ Spitzer cross-power spectra. A multi-wavelength analysis indicates that the auto-power of the fluctuations at low-$\ell$ is bluer than the Poisson noise from IGL and ISL; however, for $1' <\theta < 10'$, the cross-correlation coefficient $r_{\ell}$ of nearly all band combinations decreases with increasing $\theta$, disfavoring astrophysical explanations that invoke a single correlated sky component.