Exploring the Homogeneity of the Hot Observable Universe

[acesuv]

From what I understand, the observable universe began as homogeneous and very hot. if the universe was very hot, doesn't that mean that particles are vibrating at very fast speeds? after all, isn't heat simply kinetic energy of particles? if this is the case, then how could the universe be homogeneous? how could a universe with vibrating particles be homogeneous? this seems analogous to the reasoning behind why the uncertainty principal will turn a homogeneous system non-homogeneous system... because the particles are moving u can't have homogeneous arrangement. so if the universe was hot and moving around, why isn't this enough to turn the universe non-homogeneous?

so where am I wrong? please correct me! thanks I appreciate your replies

 

[mfb]

if the universe was very hot, doesn't that mean that particles are vibrating at very fast speeds?

Vibration needs bound states. There were moving around very fast.

if this is the case, then how could the universe be homogeneous?

The same density of particles everywhere, without any fluctuations as a superposition of all possible particle motions, with the same temperature and velocity distribution everywhere.