Clarifying some common misconceptions about the expansion of the universe

Modern cosmology is based on a 6-parameter model, called Lambda-CDM, which provides an accurate description of the expansion of the Universe on the basis of measured parameters. However, there are attempts to give 'phenomenological' descriptions of the dynamics of the Universe that are inconsistent with this model and sometimes lead to misconceptions. They stem from a Newtonian approach that interprets the expansion as due to an 'initial kick' that placed all matter and energy in the Universe on 'inertial trajectories'. These descriptions do not conform to the relativistic approach. Here we show that the Einstein field equations trace the expansion of cosmic space directly to the increase in the energy content of the observable universe caused by the additional space entering it as a consequence of the forward motion of its horizon. We derive here the connection between variations in the scale factor and the corresponding variations in the energy of the observable universe, in the case of the most general cosmological model. We then obtain explicit closed-form expressions of this relationship both in the case of the Universe of any curvature and containing matter and radiation, and in the case of the de Sitter universe, characterized by the cosmological constant only. Some interesting features are pointed out, both in terms of the energy growth rate of the observable universe in the various cosmological models, and in terms of the dynamics of the scale factor. Finally our demonstration is corroborated by an analogy between the expansion of cosmic space and the gravitational stretching of space at the center of a sphere of uniform density whose radius increases with time. This analogy, which allowed us to obtain the novel closed-form expression of the stretching of space at the centre of such a sphere, confirmed that the paradigm that 'gravity expands space' is valid in both systems.