Conceptual Problems of the Standard Cosmological Model

The physics of the expansion of the universe is still a poorly studied subject of the standard cosmological model. This because the concept of expanding space can not be tested in the laboratory and because ``expansion'' means continuous creation of space, something that leads to several paradoxes. We re-consider and expand here the discussion of conceptual problems, already noted in the literature, linked to the expansion of space. In particular we discuss the problem of the violation of energy conservation for local comoving volumes, the exact Newtonian form of the Friedmann equations, the receding velocity of galaxies being greater than the speed of light, and the Hubble law inside inhomogeneous galaxy distribution. Recent discussion by Kiang, Davis \& Lineweaver, and Whiting of the non-Doppler nature of the Lemaitre cosmological redshift in the standard model is just a particular consequence of the paradoxes mentioned above. The common cause of these paradoxes is the geometrical description of gravity (general relativity), where there is not a well defined concept of the energy-momentum tensor for the gravitational field and hence no energy-momentum conservation for matter plus gravity.