Einstein-like field equations with conserved source and decreasing ∧ term; Their cosmological consequences

Abstract

The consequences of a cosmological ∧ term varying asS ⁻² in a spatially isotropic universe with scale factorS and conserved matter tensor are investigated. One finds a perpetually expanding universe with positive ∧ and gravitational ‘constant’G that increases with time. The ‘hard’ equation of state 3P>U (U mass-energy density,P scalar pressure) applied to the early universe leads to the expansion lawS∝t (t cosmic time) which solves the horizon problem with no need of inflation. Also the flatness problem is resolved without inflation. The model does not affect the well known predictions on the cosmic light elements abundance which come from standard big bang cosmology.

In the present, matter dominated universe one findsdG/dt=2∧H/U (H is the Hubble parameter) which is consistent with observations provided ∧<10⁻⁵⁷ cm⁻². Asymptotically (S→∞) the ∧ term equalsGU/2, in agreement with other studies.