An alternative to the LCDM model: the case of scale invariance

The hypothesis is made that, at large scales where General Relativity may be applied, the empty space is scale invariant. This establishes a relation between the cosmological constant and the scale factor of the scale invariant framework. This relation brings major simplifications in the scale invariant equations for cosmology, which now contain a new term, depending on the derivative of the scale factor, that opposes to gravity and produces an accelerated expansion. The displacements due to the acceleration term make a high contribution Omega_l to the energy-density of the Universe, satisfying an equation of the form Omega_m+\Omega_k+Omega_l = 1. The models do not demand the existence of unknown particles. There is a family of flat models with different density parameters Omega_m < 1. Numerical integrations of the cosmological equations for different values of the curvature and density parameter k and Omega_m are performed. The presence of even tiny amounts of matter in the Universe tends to kill scale invariance. The point is that for Omega_m = 0.3 the effect is not yet completely killed. The models with non-zero density start explosively with first a braking phase followed by a continuously accelerating expansion. Several observational properties are examined, in particular the distances, the m--z diagram, the Omega_m vs. lambda plot. Comparisons with observations are also performed for the Hubble constant H_0 vs. Omega_m, for the expansion history in the plot H(z)/(z+1) vs. redshift z and for the transition redshift from braking to acceleration. These first dynamical tests are satisfied by the scale invariant models, which thus deserve further studies.