A new cosmological model is presented, with characteristics and trends very similar to those of the standard model, but without dark energy.
It differs from the standard one essentially for a constant of integration, which derives from a hypothesis at the centre of this work, which gives rise to an extra spatial distance and an extra fictitious component of matter.
Due to these extra parts, the density parameter of matter is no longer constant but increases from 0.5 to 1 from the beginning of time to the present day, although the universe is homogeneous and isotropic, and although the total amount of energy and matter are constant.
Consequently, the new model, which has one less parameter, satisfies all the constraints arising from the current accurate measurements of the BAO and the angular power spectrum of the CMB with the values of the density parameters of matter which, according to the theory, apply in each context.
Analogously, it solves the Hubble tension and the primordial lithium problem, although it introduces a deuterium problem.
Finally, it shows that it is the pressure of matter due to its variability, not dark energy, that drives the current acceleration phase of the expansion of the universe started by z ≅ 0.5099, when the universe was 7.99 billion years old, about 5 billion years ago.
On a small scale, the same hypothesis has very similar effects to the MOND theory and explains the rotational motion of galaxies.