# Geometry of Big Bang

As you look at circle cross-sections around a sphere it's obvious that as you move the circles along the z-axis, the circles get bigger and smaller. When you're at the farthest points on the $z$-axis, the cross-sectional circles shrink to a point, and reach their largest around the middle of the circle.

I'm curious why the third-dimension shouldn't work this way along a fourth-dimensional axis, like time?

Wouldn't it stand that the spatial dimension simply "grow" along the axis of the fourth dimension (time), such that at the beginning of time the three dimensions would be of infinitesimal dimension, a point, but as you move from three dimensional cross-section to three dimensional cross-section along the fourth-axis time away from the first point on that fourth axis that the three dimensions rapidly expand?

Would the big bang and big crunch then, rather than being a surprising quality of our universe, be simple and geometrically provable qualities of a four-dimensional space with a time axis -- the exact thing you'd expect as you move three dimensions along a fourth dimension -- at the beginning of time, point, rapidly expanding to three dimensions, and at the far end of time, collapsing back down to a point?

• You described a version of a closed universe where the "sphere" was your assumption. Another assumption may be a "straight cone" that would describe a closed universe that expands forever (not FLRW). As Javier mentions in his answer, another yet scenario is that the universe has been infinite from the beginning. This model is singular (infinite) on mass and distance (in addition to density) and thus has no physical meaning, but still is accepted by many for some reason. Also note that the spacetime geometry is hyperbolic. Check out the de Sitter and anti deSitter geometries. – safesphere Sep 21 '17 at 4:15