The big bang is the only naked singularity allowed to exist in the cosmic censorship hypothesis, which otherwise conjectures that all singualarities in nature must be behind an event horizon. (Also, just to clarify, modern physics is incapable of describing the universe before the big bang. Classical GR predicts that the universe has existed for a finite amount of time. Specifically, the universe has existed for all time t>0 and that there is a spacelike singularity everywhere in space corresponding to the limit as t-->0. It is meaningless to talk about what happens at or before t=0.)
In general, there are two very important horizons in cosmology, the particle horizon and the cosmic event horizon, which both exist for each point in space. (Each point in space has its own pair of horizons.) Implicit in the definitions of either horizon is that we are describing spacetime in cosmological coordinates. The particle horizon for a point P is the surface beyond which any signal emitted at the big bang could not have reached P yet. In other words, the particle horizon defines the boundary of the observable universe about point P. The cosmic event horizon is the surface beyond which any signal emitted now will never reach point P. In other words, the cosmic event horizon roughly describes the points in space we can still communicate with today.
The evolution of both horizons is very important in cosmology and intrinsically linked to the matter distribution of the universe and the density of dark energy. The distance to the particle horizon is always increasing over time in comoving coordinates but current evidence shows that the distance will asymptote to some finite number. In other words, there are galaxies we will never see at all. The distance to the cosmic event horizon, on the other hand, is decreasing over time in comoving coordinates. That means that eventually all we will see in the sky are stars in our own galaxy.
Note that these horizons are unlike the event horizon of a black hole. For a black hole, the horizon is a single surface in space and a universal and eternal feature of that spacetime. That is, every observer has the same horizon. The cosmological horizons are different at each point in space.