A FLRW-Metric Universe with Zero Spatial Curvature is Incompatible with Dark Energy as a Cosmological Constant

We have obtained a theoretical result that leads us to believe that a universe FLRW with zero spatial curvature and dark energy as cosmological constant is incompatible with the results corresponding to the acceleration of our universe over the last 6 billion years, a phenomenon attributed in the 𝚲CDM model to the existence of dark energy. To this end, we calculated, in the FLRW metric, the equation for the derivative of the Hubble parameter and studied its sign during the three eras of the universe: the radiation era, the matter era, and the dark energy era. We were able to verify that for zero spatial curvature and dark energy as the cosmological constant, a positive value for the derivative of the Hubble parameter will never occur; that is, the Hubble parameter, H, will never be increasing, which makes a period like the one occurring for the last 6 billion years, caused by dark energy, impossible.

Keywords: Dark Energy, Spatial Curvature, Friedmann Equations, Cosmology.