# Why only $\omega=-1$ is taken to explain accelerated expansion of the universe and named dark energy?

From the acceleration equation in cosmology the condition for acceleration comes out if $$\rho+3P\lt0$$,$$P\lt\frac{-1}{3}\rho$$,$$\omega\lt\frac{-1}{3}$$. For $$\omega=-1$$ it gives a constt. energy density & gives an exponential expansion which is quite suitable with the accelerated expansion. My question is why $$\omega=-1$$ is only taken to explain accelerated expansion and named dark energy?? Any $$\omega\lt\frac{-1}{3}$$ will work for accelerated expansion.

Because there are three reasonably-compelling physical models which give $$w=-1$$!
By contrast, I am not aware of arguments as natural as these for another value of $$w$$ that is less than -1/3.