For decades, the prevailing view in the scientific community has been that our universe is expanding at an accelerating rate. However, a recent experimental study (Junhjuk Son et al., 2025) seems to confirm that our universe shows no signs of acceleration; that is, we might be living in a non-accelerating universe. In this work, we present evidence that this result agrees with the predictions of relativistic theory. To this end, we present a new proof of the zero active mass equation (ρ + 3p = 0) for a universe with FLRW metric and zero spatial curvature (k = 0). We study the expansion of the universe by analyzing two partial models: a classical energy model and a thermodynamic fluid dynamics model. The interrelation between these two models demonstrates that all universes with zero spatial curvature, a Lapse function equal to one, satisfy the zero active mass equation and are necessarily non-accelerating. Their linear expansion is solely a consequence of the pressure of the cosmic fluid and not of any other additional terms in the Friedmann equations.