This paper investigates the possibility of accelerating universes with a large fraction of energy density stored in a component with an equation of state $ w_X < -1/3 $. The authors analyze the critical points of such universes and compare them with those dominated by a cosmological constant $ \Lambda $. They show that even a significant variation of $ w_X $ at small redshifts is difficult to observe with luminosity distance measurements up to $ z \sim 1 $. Therefore, accurate measurements in the range $ 1 < z < 2 $ and independent knowledge of $ \Omega_{m,0} $ (and/or $ \Omega_{X,0} $) are needed to distinguish between models with variable and constant $ w_X $. The paper discusses the Friedmann-Robertson-Walker (FRW) cosmologies and the equations governing their dynamics. It considers a universe filled with dust-like matter and an unknown component with negative pressure, $ -1 \leq w_X < -1/3 $. The authors derive the equations for the evolution of the scale factor $ x $ and show that the universe is currently accelerating if $ w_X < -1/3 (1 + \Omega_{m,0}/\Omega_{X,0}) $. They also analyze the critical points of the system and find that the existence of a critical point depends on the parameters $ \Omega_{X,0} $ and $ \Omega_{m,0} $. The paper then considers observational constraints, such as the age of the universe, the age in function of redshift, and the luminosity distance $ d_L(z) $. It shows that these quantities can be used to distinguish between different models of the universe. However, the authors argue that accurate measurements in the range $ 1 < z < 2 $ and independent knowledge of $ \Omega_{m,0} $ are needed to resolve the differences between models with variable and constant $ w_X $. The paper also presents a toy model with a variable equation of state and shows that even a strongly varying $ w_X $ does not yield a significant difference compared to a constant $ w_X $ at redshifts $ z \sim 1 $. However, at redshifts $ z \sim 1-2 $, a measurement with an accuracy at the percentage level might be able to distinguish between models with variable and constant $ w_X $. The authors conclude that independent accurate knowledge of $ \Omega_{m,0} $ is crucial for resolving the various curves and distinguishing between different models.This paper investigates the possibility of accelerating universes with a large fraction of energy density stored in a component with an equation of state $ w_X < -1/3 $. The authors analyze the critical points of such universes and compare them with those dominated by a cosmological constant $ \Lambda $. They show that even a significant variation of $ w_X $ at small redshifts is difficult to observe with luminosity distance measurements up to $ z \sim 1 $. Therefore, accurate measurements in the range $ 1 < z < 2 $ and independent knowledge of $ \Omega_{m,0} $ (and/or $ \Omega_{X,0} $) are needed to distinguish between models with variable and constant $ w_X $. The paper discusses the Friedmann-Robertson-Walker (FRW) cosmologies and the equations governing their dynamics. It considers a universe filled with dust-like matter and an unknown component with negative pressure, $ -1 \leq w_X < -1/3 $. The authors derive the equations for the evolution of the scale factor $ x $ and show that the universe is currently accelerating if $ w_X < -1/3 (1 + \Omega_{m,0}/\Omega_{X,0}) $. They also analyze the critical points of the system and find that the existence of a critical point depends on the parameters $ \Omega_{X,0} $ and $ \Omega_{m,0} $. The paper then considers observational constraints, such as the age of the universe, the age in function of redshift, and the luminosity distance $ d_L(z) $. It shows that these quantities can be used to distinguish between different models of the universe. However, the authors argue that accurate measurements in the range $ 1 < z < 2 $ and independent knowledge of $ \Omega_{m,0} $ are needed to resolve the differences between models with variable and constant $ w_X $. The paper also presents a toy model with a variable equation of state and shows that even a strongly varying $ w_X $ does not yield a significant difference compared to a constant $ w_X $ at redshifts $ z \sim 1 $. However, at redshifts $ z \sim 1-2 $, a measurement with an accuracy at the percentage level might be able to distinguish between models with variable and constant $ w_X $. The authors conclude that independent accurate knowledge of $ \Omega_{m,0} $ is crucial for resolving the various curves and distinguishing between different models.