Dipole-independent measurements of nearly-zero CMB correlation: a possible symmetry of primordial causal quantum coherence

Anisotropy of space-time is measured on the scale of the cosmic horizon, using the angular correlation function $C(Θ)$ of cosmic microwave background (CMB) temperature at large angular separation $Θ$. Even-parity correlation $C_{\rm even}(Θ)$ is introduced to obtain a direct, precise measure of horizon-scale curvature anisotropy independent of the unknown dipole, with uncertainty dominated by models of Galactic emission. In maps from WMAP and Planck, $C_{\rm even}(Θ)$ at $Θ\simeq 90^\circ\pm 15^\circ$ is found to be much closer to zero than in previously documented measurements. Variation from zero as small as that in the {\sl Planck} maps is estimated to occur by chance in a fraction $\simeq 10^{-4.3}$ to $\simeq 10^{-2.8}$ of standard realizations. Measurements are found to be consistent with zero correlation in a range of angles expected from quantum fluctuations during inflation whose spacelike coherence is bounded by inflationary horizons around every location at every epoch. This scale-invariant symmetry of cosmological initial conditions is incompatible with the standard quantum theory of initial conditions, but is broadly consistent with other cosmological measurements, and is subject to further tests.