Kinemaitcs in spatially flat FLRW spacetimes

The kinematics on spatially flat FLRW space-times is presented for the first time in co-moving local charts with physical coordinates, i. e. cosmic and Painlev\' e-type Cartesian space coordinates. It shown that there exists a conserved momentum which determines form of covariant four-momentum geodesics terms Moreover, help one identifies peculiar separating recessional motions without ambiguities. energy satisfy mass-shell condition special relativity while does not produce energy. In this framework, measurements kinetic quantities along geodesic performed by different observers are analysed pointing out an loss massive particles similar to giving photon redshift. examples de Sitter expanding universe new Milne-type space-time extensively analysed.