A Lemaitre-Tolman-Friedmann Universe without Dark Energy

Abstract

We build a simple cosmological model by means of a parabolic Lemaître-Tolman-Bondi (LTB) metric up to a redshift $z\simeq 0.4$, an hyperbolic Friedmann metric for $z\sim 0.4$ up to the scale where dimming galaxies are observed ($z\sim 1.4$) and a bulk spatially flat metric up to the last scattering surface. Following Wiltshire, by taking into account the different rate of clocks for an observer at the centre of a parabolic LTB spacetime with respect to a one in the hyperbolic Friedmann metric, an "apparent" negative deceleration parameter is perceived by the observer at the centre of LTB, provided that all the regularity conditions are imposed and the past null sections of the LTB and the hyperbolic Friedmann metrics are identified. As a result, a first order Hubble law emerges at low redshifts. A parameter $K$ arises driving the deceleration parameter perceived by the central LTB observer. Finally, we obtain that a negative value for the deceleration parameter is compatible with the observed energy-density at our present epoch.