CRT is an asymptotic gauge symmetry in flat/AdS quantum gravity, not a true gauge symmetry, and is absent or only spontaneously broken under special untestable conditions in de Sitter cosmologies.
Is Time Reversal in de Sitter Space a Spontaneously Broken Gauge Symmetry?,
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Singularities, Entropy and the Arrow of Time, {\it or} Is CRT a Gauge Symmetry in Quantum Gravity?
CRT is an asymptotic gauge symmetry in flat/AdS quantum gravity, not a true gauge symmetry, and is absent or only spontaneously broken under special untestable conditions in de Sitter cosmologies.