Kavli Affiliate: Craig Hogan

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| Summary:

We develop a model for correlations of cosmic microwave background anisotropy

on the largest angular scales, based on standard causal geometrical

relationships in slow-roll inflation. Unlike standard models based on quantized

field modes, it describes perturbations with nonlocal directional coherence on

spherical boundaries of causal diamonds. Causal constraints reduce the number

of independent degrees of freedom, impose new angular symmetries, and eliminate

cosmic variance for purely angular 2-point correlations. Distortions of causal

structure from vacuum fluctuations are modeled as gravitational memory from

randomly oriented outgoing and incoming gravitational null shocks, with

nonlocally coherent directional displacements on curved surfaces of causal

diamonds formed by standard inflationary horizons. The angular distribution is

determined by axially symmetric shock displacements on circular intersections

of the comoving sphere that represents the CMB photosphere with other

inflationary horizons. Displacements on thin spheres at the end of inflation

have a unique angular power spectrum $C_ell$ that approximates the standard

expectation on small angular scales, but differs substantially at large angular

scales due to horizon curvature. For a thin sphere, the model predicts a

universal angular correlation function $C(Theta)$ with an exact “causal

shadow” symmetry, $C(pi/4<Theta<3pi/4)= 0$, and significant large-angle

parity violation. We apply a rank statistic to compare models with WMAP and

Planck satellite data, and find that a causally-coherent model with no shape

parameters or cosmic variance agrees with the measured $C(Theta)$ better than

a large fraction ($> 0.9999$) of standard model realizations. Model-independent

tests of holographic causal symmetries are proposed.

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