Abstract
Recent analysis of the Planck measurements opened a possibility that we live
in a non-flat universe. Given the renewed interest in non-zero spatial
curvature, here we re-visit the light propagation in a non-flat universe and
provide the gauge-invariant expressions for the cosmological probes: the
luminosity distance, galaxy clustering, weak gravitational lensing, and cosmic
microwave background anisotropies. With the positional dependence of the
spatial metric, the light propagation in a non-flat universe is much more
complicated than in a flat universe. Accounting for all the relativistic
effects and including the vector and tensor contributions, we derive the
expressions for the cosmological probes and explicitly verify their gauge
invariance. We compare our results to previous work in a non-flat universe, if
present, but this work represents the first comprehensive investigation of the
cosmological probes in a non-flat universe. Our theoretical formalism in a
non-flat universe will play a crucial role in constraining the spatial
curvature in the upcoming large-scale surveys.
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