Scale Invariance, Horizons, and Inflation

TL;DR

This paper explores how scale invariance in cosmology is affected by matter presence, linking it to inflation and the cosmological constant problem, and predicts observable differences from LCDM models at high redshift.

Contribution

It demonstrates that scale invariance is suppressed by matter above a critical density and connects the scalar field in scale invariant models to inflation, addressing the cosmological constant problem.

Findings

Scale invariance declines rapidly with increasing matter density.

Inflation with many e-foldings is predicted in the scale invariant framework.

Differences from LCDM models may be observable at high redshift.

Abstract

Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises on how much matter within the horizon is necessary to kill scale invariance. The scale invariant field equation, first written by Dirac in 1973 and then revisited by Canuto et al. in 1977, provides the starting point to address this question. The resulting cosmological models show that, as soon as matter is present, the effects of scale invariance rapidly decline from \rho=0 to \rho_c and are forbidden for densities above \rho_c. The absence of scale invariance in this case is consistent with considerations about causal connection. Below \rho_c, scale invariance appears as an open possibility, which also depends on the occurrence of inflation in the scale invariant context. In the present approach, we identify the scalar field of the empty space in the Scale Invariant Vacuum (SIV) context to the scalar field \phi in the energy density expression of the vacuum at inflation. This leads to some constraints on the potential. This identification also solves the so-called ``cosmological constant problem''. In the framework of scale invariance,an inflation with a large number of e-foldings is also predicted. We conclude that scale invariance for models with densities below \rho_c is an open possibility; the final answer may come from high redshift observations, where differences from the LCDM models appear.