# What happens physically in the horizon distance in predominant matter universe?

Setting constant curvature $k = 0$, the Friedmann equation takes the simple form: $\dot{a}^{2} = \dfrac{8 \pi G \epsilon_o}{3 c^2}a^{-(1+3\omega)}$ If We suppose: $a \propto t^q$. We have $a(t) = (\dfrac{t}{t_o})^{2/(3+3\omega)}$. Then the horizon distance take the form: $d_{hor}(t_o) = c \int_{0}^{t_o} \dfrac{dt}{a(t)} \ = \ \dfrac{c}{H_o} \dfrac{2}{1+ 3\omega}$.

If we consider a universe with only non-relativistic matter, then $\omega = 0$ and $d_{hor}(t_o) = 3ct_o$.

MY doubt is: What is the physical meaning of the horizontal distance in the universe with only matter being greater than the distance that light travels?

Hence, whereas in a static universe the horizon distance would be $ct_0$, in an expanding universe it will be larger.