The cosmological constant and the size of the Physical Universe

Abstract

The cosmological constant $\Lambda$ is a free parameter in Einstein's equations of gravity. We propose to fix its value with a boundary condition: test particles should be free when outside causal contact, e.g. at infinity. Under this condition, we show that constant vacuum energy does not change cosmic expansion and there can not be cosmic acceleration for an infinitely large and uniform Universe. The observed acceleration requires either a large Universe with evolving Dark Energy (DE) and equation of state $\omega>-1$ or a finite causal boundary (that we call Causal Universe) without DE. The former can't explain why $\Omega_\Lambda \simeq 2.3 \Omega_m$ today, something that comes naturally with a finite Causal Universe. This boundary condition, combined with the anomalous lack of correlations observed above 60 degrees in the CMB predicts $\Omega_\Lambda \simeq 0.70$ for a flat universe, with independence of any other measurements. This solution provides new clues and evidence for inflation and removes the need for Dark Energy or Modified Gravity.