What if the singular point is just a time horizon?

In a very loose sense you can think of spacetime as a 4 dimensional hypersphere. However we are not on its surface, we are inside of it. There are a couple of things in your explanation that I want to touch upon. In this model, our current universe space-time coordinate is like a point on the surface of a space-time sphere. In this vision the spacetime is a closed surface. Think of it. The surface of the sphere is a closed 2D surface which exists in a 3D space. A point on that surface will then have a 3D coordinate in the overall 3D space but there is a constraint of being on the surface. To remove that constraint you just express the point as a 2D coordinate in a coordinate system which is itself on the surface (like longitude/latitude). Switch to more dimensions and you can imagine a model with a 4D spacetime as being the surface of a 5D sphere. So far so good: we have described almost exactly one of the hypotheses which have been debated for a long time: is spacetime closed or not? If it is closed, than it is, in fact, very much like our closed (potentially spherical in a 5th dimensional sense) surface. In this sense your idea is not new. However, if you able to time travel back to the coordinate we thought where and when universe begin There is a misunderstanding here. There is no such a thing as "the coordinate we thought where and when universe begin". The BB was not a point on the surface of the sphere. It's the whole surface. Our universe is 4D (3 dimensions are space and one is time). But to stay with our simplified model let's pretend we live in an hypothetical 2D universe. We can now picture this 2D universe as being a spherical surface embedded in a 3D space (of course the 3rd dimension is not really part of the 2D universe: the universe is simply the surface of the sphere). What happens is that no point in that universe (or 2D surface of the sphere) is the point where the BB happened. In fact the whole surface is where it happened. The BB theory in that model is that the sphere is inflating (diameter is growing). The BB was the singularity when the diameter of the sphere was zero: the whole surface was a point. In fact both the dimensions of this surface were no more dimensions at all: they were "collapsed" into a point. When the sphere started "inflating" and stopped being a point to become an actual sphere both the dimensions of its surface "emerged" from that singularity point. This is very close to how the BB theory explains things if the universe is closed. What would be the "horizon" in this model? Suppose that, due to the limited speed of light, any point on that surface can only observe the surface itself up to a limited distance. Living in such a universe, no matter where you are on that surface all you see is effectively a dome, except that you see it flat and it looks like a disk to you. Since the sphere is expanding, points on the surface are coming apart. This happens everywhere uniformly on the whole surface. From your point of view, if you look around, you see all points as drifting away from you. Also the further the point is, the faster it drifts away. No matter where you are in that surface, what you observe is a "disk" with you at the center and objects around you drifting away in such a way that the ones further away are drifting faster. This is what you would observe no matter where you are. Anyone anywhere on that surface will see the same phenomenon. And we see exactly that, except it happens in 4 dimensions, not in 2. The next observation is that there really is no need for that surface to be spherical. Think of a deflated party balloon (ignore the hole we use to inflate it, imagine it closed). We can bend it however we want, it does not need to be a sphere. We need a little leap of imagination to take the next step. You can bend the ballon without stretching it (without dilating the surface) or you can stretch it (dilating the surface as would happen if you inflated it). These are separate things. Dilation (stretching) can be done uniformly (not with fingers, but just imagine it's being done) and it's independent of the bending. It turns out that the 3d bending is totally inessential for anyone living on that surface: only the stretching is really observable. With a leap of imagination you should now think that the balloon does not exist in a 3D space at all. It is just 2D and expanding, there is no third dimension, the stretching still makes sense and is relevant but the bending is not: there is no 3rd dimension therefore there is not even any bending, which would be totally irrelevant to begin with. Any mathematic or 2D geometry you do on that surface need no 3rd dimension to exist at all: it's all 2d (in a "stretching" 2d space). If you can make that leap of imagination, you have exactly the picture of a closed universe with a BB. There is no extra dimension and the BB was when the 2D space was de-stretched all the way to a point (which is not a 2D thing, therefore you can only describe it as a degeneration due to a singularity in the 2d geometry). At the BB your 2d universe was a point. The very moment the universe was no more a point you get out of the degenerate/singularity condition and already have a full fledged 2d (closed) coordinate system. Since it's a closed model it's both finite and infinite: in a sense it's infinite modulo "roundtrip".

Your horizon analogy does not apply. When observing the horizon on earth, you cannot see around the planet's curvature because the photons observable travel in straight lines and not along the earth's curvature. When observing light within our universe the photons you see curve right along the presumed round or elliptical curvature of space, so there would be no illusion of horizon. If the universe is a closed system one can look all the way around to the viewer's own location, but will see photons that were emitted far back in time because of the maximum speed light travels through space until seen by the viewer. Of course, our universe may not be a closed sphere or ellipse, but could be instead an open shape, if you imagine you could view it from a point outside of our space and time (from another dimension). Either way, there is theoretically nothing stopping us from seeing back in time as far as there was light in the universe, with instruments sensitive enough to look that far. P.S.: Since the calculations seem to indicate that the force of gravity everywhere emanates from a dimension outside our 3D/4D universe, and since we understand (to some extent) the role of gravity in creating a singularity within a black hole, it seems reasonable to accept that gravity maintained or created the condition from which our universe sprang as it did when the event we refer to as "the big bang" occurred. In that dimension where gravity is the ruling force, a singularity (as described by application of our universe's known physical laws) must exist or have existed and something happened to spit out our universe into our dimension. At present, humans lack any scientific observations from which mathematical extensions can be performed to postulate what caused the start of our big bang. That's at least so far as anyone I know of can say, without spouting bullshit. If our entire universe was held in a singularity-sized point by gravity, its not surprising the big bang started with the intense heat and pre-atomic plasma conditions which have been calculated to have existed when the universe began.

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the universe is a hyper-torus, so not too sure what you mean.  The Big Bang, is just the point from which a bunch of parallel lines started to diverge from.  It's the start point on the line, in which our particular line segment of time started.