We do not live in the Rh = ct universe

Abstract

We analyse the possibility that our Universe could be described by the model recently proposed by Melia & Shevchuk (2012), where the Hubble scale R_h=c/H is at all times equal to the distance ct that light has travelled since the Big Bang. In such a model, the scale factor is proportional to cosmic time and there is neither acceleration nor deceleration of the expansion. We first point out problems with the very foundations of the model and its consequences for the evolution of the Universe. Next, we compare predictions of the model with observational data. As probes of the expansion we use distance data of supernovae type Ia, as well as Hubble rate data obtained from cosmic chronometers and radial baryon acoustic oscillations. We analyse the redshift evolution of the Hubble parameter and its redshift derivatives, together with the so-called O_m diagnostic and the deceleration parameter. To reliably estimate smooth functions and their derivatives from discrete data, we use the recently developed Gaussian Processes in Python package (GaPP). Our general conclusion is that the discussed model is strongly disfavoured by observations, especially at low redshifts (z<0.5). In particular, it predicts specific constant values for the deceleration parameter and for redshift derivatives of the Hubble parameter, which is ruled out by the data.