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arXiv · 2607.27351

Gauge vs (hidden) physical symmetries of FLRW cosmologies

Andrea Calcinari·Adrià Delhom·Federico Greco·Daniele Oriti·Néstor Rivero
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Abstract

In generally covariant theories evolution in coordinate time is a gauge transformation, so that a symmetry made manifest in a gauge-fixed description need not be a symmetry of the physical dynamics. Deparametrisation, in turn, removes gauge symmetries but may hide physical symmetries, in particular those dependent on the chosen physical clock. We study the relation between gauge and (hidden) physical symmetries in flat FLRW geometry coupled to an arbitrary number $n$ of free massless scalar fields. We show that conformal Killing vectors of the minisuperspace metric generate conserved charges which are Dirac observables--hence gauge-invariant--and whose Poisson algebra is the maximal conformal algebra $\mathfrak{conf}(n,1)\simeq\mathfrak{so}(n+1,2)$, extending previous single-field results to arbitrary $n$. We then revisit the Eisenhart-Duval lift in a family of gauges and show that the manifest symmetry algebra is gauge dependent, enlarging to the Schr\"odinger algebra (which is thus not a physical symmetry) in the distinguished harmonic gauge where the gauge-fixed minisuperspace metric becomes flat. Further, deparametrisation maps the lifted charges to gauge-invariant Dirac observables, which always realise a subalgebra of the conformal algebra and reproduce it in full in the harmonic gauge. These results establish a framework for separating gauge from physical symmetries in minisuperspace models, recovering charges to which reduced phase-space descriptions are structurally blind, and remaining applicable in the presence of potentials.

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Andrea Calcinari, Adrià Delhom, Federico Greco, Daniele Oriti, Néstor Rivero. 2026-07-29. Gauge vs (hidden) physical symmetries of FLRW cosmologies. https://arxiv.org/abs/2607.27351

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