AN ALTERNATIVE TO THE ΛCDM MODEL: THE CASE OF SCALE INVARIANCE

Abstract

ABSTRACT The hypothesis is made that, at large scales where general relativity may be applied, empty space is scale invariant. This establishes a relation between the cosmological constant and the scale factor λ of the scale-invariant framework. This relation brings major simplifications in the scale-invariant equations for cosmology, which contain a new term, depending on the derivative of the scale factor, that opposes gravity and produces an accelerated expansion. The displacements due to the acceleration term make a high contribution to the energy density of the universe, satisfying an equation of the form . The models do not demand the existence of unknown particles. There is a family of flat models with different density parameters . Numerical integrations of the cosmological equations for different values of the curvature and density parameter k and are performed. The presence of even tiny amounts of matter in the universe tends to kill scale invariance. The point is that for the effect is not yet completely killed. Models with non-zero density start explosively with a braking phase followed by a continuously accelerating expansion. Several observational properties are examined, in particular the distances, the m–z diagram, and the versus plot. Comparisons with observations are also performed for the Hubble constant H 0 versus , for the expansion history in the plot versus redshift z, and for the transition redshift from braking to acceleration. These first dynamical tests are satisfied by scale-invariant models, which thus deserve further study.