Rapidity Asymmetry in Cosmology and the Observable Cosmological Arrow

On background cosmological scales, after subtraction of peculiar velocities and local bound-system motions, observed cosmological signals are redshifted rather than blueshifted. Yet, redshift alone does not distinguish the past lightcone of an expanding Universe from the future lightcone of a contracting one. In practice, the identification of the observed redshifted branch with the observational past is set primarily by electromagnetic radiation, whose retarded character is independently established in controlled physics, albeit over non-cosmological scales. From that perspective, the observed cosmological arrow is not separable from the causal/radiative prescription used to interpret the signals. This effective entanglement between the cosmological and the radiative arrows should nevertheless be distinguished from the notion of arrow used in the present work. Here instead, the relevant arrow is not thermodynamic but kinematic; it is defined by the symmetry or asymmetry of background lightcone observables under ξ↔−ξ, where ξ≡ln(1+z) and z is the redshift—a criterion motivated directly by the time-reversal-symmetric special-relativistic longitudinal Doppler shift. Equivalently, the arrow considered here is the observed redshift/blueshift asymmetry of cosmological lightcone signals; retarded observations of an expanding FRW Universe are in the redshifted branch, whereas the opposite rapidity orientation would correspond to the blueshifted branch. This naturally suggests using rapidity-reversal symmetry as the redshift-space no-arrow condition when passing from special relativity (SR) to Friedmann–Robertson–Walker (FRW) cosmology, where the empty Milne Universe is a bridging borderline case. In fact, the viewpoint advocated here is that ξ-symmetry/asymmetry is practically more fundamental than t-symmetry/asymmetry simply because the former is more readily related to cosmological observables. It is shown here that generic non-empty FRW Universes possess an intrinsic ξ-asymmetry already at the background level, independently of entropy, coarse-graining, structure growth, or a Past Hypothesis.