A Cosmological Bragg Law: Interpreting the CMB as a Diffractogram of Foliated Spacetime

Abstract

Recent work by Ringermacher and Mead has revealed discrete oscillations in the cosmological scale factor, suggesting that spacetime may exhibit vibrational properties akin to those of a crystal. Building on this idea, we propose a novel geometric interpretation of the Cosmic Microwave Background CMB angular power spectrum by treating it as an inverted X-ray diffractogram of early spacetime. In this framework,the acoustic peaks correspond to constructive interference from a stratified, resonant structure of the universe at the time of recombination. We formulate a cosmological analogue of Bragg law, linking angular multipoles to acoustic shell spacing and comoving distance. This model predicts the positions of the first four acoustic peaks observed by the Planck satellite with remarkable accuracy.A global correction factor of near 0.9 needed to align predictions with observations, may reflect the influence of geometric torsion as described in EinsteinCartan theory. While not a replacement for full radiative transfer modeling,this approach offers a complementary geometric framework for understanding the harmonic structure of the CMB and the possible crystalline nature of primordial spacetime.

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