## Models of the Converging Universe For a while now, I have been puzzled by a subtle contradiction between the image of the “expanding universe” and that of the Big Bang. If the universe is expanding, the density of the cosmic objects (galaxies) should decrease proportionally to the distance. The further in space we are from here, the less dense the universe should be. On the other hand, because of the speed of light limit, the deeper into space we look, the younger universe we see. According to the Big Bang, the younger the universe is, the smaller it is, and the density of the cosmic objects should therefore increase with distance. In other words, our universe is expanding in all directions proportionally to the space-distance from “here” and at the same time it is shrinking proportionally to the time-distance from “now”. Clearly, this contradiction between the “distant” and the “young” universe is not in the universe itself but in our way of looking at it. Usually we place ourselves, as observes, inside the universe (at its center) while the space/time continuum unfolds in all directions ad infinitum. But this is only one way to observe the universe. What if we invert the configuration and place the observer on the “periphery” or “outside” of the universe? A simple model of this would be a spherical mirror. If we place such a mirror(r=1m) somewhere in space not very far from the solar system, the entire visible universe would be contained within it. The closer objects would appear nearer to the surface of the mirror, while the more distant objects would group toward its interior, with the farthest objects converging toward the virtual center of the mirror. Here, instead of expanding in all directions, we would observe the universe converging toward a single point (Fig.1). This point would be the virtual center of the mirror and would coincide with the geometric center of the sphere. We could now imagine an observer that actually sees the universe in an analogous way. An observer with spherical shape having sensors(eyes) all over its surface(Fig.2) may “see” the universe in two different ways(Fig3): either the universe surrounds the observer(model A), or the universe is inside the observer(model B). Although these two cases are topologically indistinguishable, they have some important geometric differences. Universe A is spreading from the observer in all directions toward the countless points in the infinitum, while the universe B is converging toward a single point in the center, which we assume to be in the infinitum. Since these two models of the universe are complementary, we may consider the possibility that universe A is not spreading without limits, but in fact “converging” too, in this case asymptotically toward countless points(sphere) on the “edge” of the universe, which we would consider to be in the infinitum(Fig.4). These points at the limits of the universe would form a sphere with the observer in its center. We could consider this sphere to be the horizon of the universe A, while the single point in the center of universe B would be its vanishing point. These are just suggestions for possible models of the converging universe that could question some basic concepts of contemporary cosmology such as Big Bang and the expanding universe. They might also lead us toward the new understanding of the nature of those phenomena we call “space” and “time”. Whatever the answers may be, it is worth bearing in mind that what the universe is would depend on who the observer is.

Argos Panopty, New York 1999  argos.panopty@gmail.com