Cosmological Dynamics of Relativistic MOND

Abstract: In this paper, we investigate the recently proposed relativistic theory for MOND using the phase space analysis. Unlike its precedent theory, namely TeVeS, this theory is claimed to agree with the observed Cosmic Microwave Background and matter power spectra. We convert the background cosmological equations of the theory to a set of first-order autonomous equations. Then we explore the corresponding critical points and their physical meaning. This method is powerful in the sense that the cosmological behavior of the model is diagnosed independently of the magnitude of the free parameters of the theory. We show that the theory has a viable sequence of cosmological epochs. Although using specific initial conditions, this theory mimics the standard cosmological model; it provides a richer structure as far as the background cosmology is concerned. This implies that further investigations are required to see if this theory contributes to addressing the current cosmological tensions.