  We propose a heuristic model of the universe as a growing quasicrystal
projected from a higher-dimensional lattice. By extending the Schr\"{o}dinger
equation for a particle in a box with time-dependent boundaries, we derive an
equation that resembles the Friedmann equation, addressing the Hubble tension.
This model incorporates phonons and phasons, providing insights into
cosmic-scale dynamics and the universe's expansion. We outline a pre-inflation
tiling space phase with quantum error correction, a radiation phase dominated
by quasiparticles, and a post-radiation phase with the emergence of matter. Our
hypothesis, which posits that the universe is a growing quasicrystal, suggests
that the necessity for an inflationary period may be obviated. Furthermore,
phonon arising from this quasicrystalline structure could act as dark matter,
influencing the dynamics of ordinary matter while remaining mostly undetectable
by electromagnetic interactions. This hypothesis draws parallels with other
crystalline matter at atomic scales that are fundamentally quantum in nature.
We also explore how the notion of tiling space can support continuous symmetry
atop a discrete structure, providing a novel framework for understanding the
universe's expansion and underlying structure. Consequently, it is logical to
start with quantum mechanics as the foundation of our model. Further
development could enhance our understanding of cosmic expansion and the
underlying structure of the universe.
