Space and Observers in Cosmology
M. Lachi\`eze-Rey (Centre d'Etudes de Saclay, France)

TL;DR
The paper proposes a method to define space for any observer in curved space-time, clarifying observer-dependent notions of space and time, with applications to Minkowski, Rindler, and cosmological models, impacting quantum and relativistic theories.
Contribution
It introduces a novel prescription based on simultaneity to define space for arbitrary observers in curved space-time, aiding in quantization and understanding observer-dependent phenomena.
Findings
Different observers perceive different spaces in curved space-time.
The method justifies Rindler coordinates and the Unruh effect.
Applied to cosmology, space differs from hypersurfaces of homogeneity.
Abstract
I provide a prescription to define space, at a given moment, for an arbitrary observer in an arbitrary (sufficiently regular) curved space-time. This prescription, based on synchronicity (simultaneity) arguments, defines a foliation of space-time, which corresponds to a family of canonically associated observers. It provides also a natural global reference frame (with space and time coordinates) for the observer, in space-time (or rather in the part of it which is causally connected to him), which remains Minkowskian along his world-line. This definition intends to provide a basis for the problem of quantization in curved space-time, and/or for non inertial observers. Application to Mikowski space-time illustrates clearly the fact that different observers see different spaces. It allows, for instance, to define space everywhere without ambiguity, for the Langevin observer (involved in…
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