The theory of the four dimensional universe claim that the inverse is curved ever so slightly but it is invisible to the human eye, and comes back to an initial spot once one has travelled a significant enough distance. It represents the universe as a balloon – constantly expanding.
The theory also claims that because the universe is four dimensional and humans cannot perceive the fourth dimensional, that the universe appears flat, or is curve d ever so slightly. However, in graphs depicting redshift of the stars over large distances – in other words, how fast objects are moving away from Earth far away, one finds that velocity increase with distance.
The graph above clearly shows that the objects in the universe are moving exponentially faster away from earth as they are further away. By the principle of ergodicity, which states that over a large space, space and properties will naturally average out, it makes little sense that objects that are further away are moving faster away from us than objects that are closer. Even if one scales this for the squared effect of there being more distance between the Earth and faraway objects (and therefore more dark energy by the current theory of the expanding universe), the speed increase seems far too high to be explained by space differences alone.
This leads to the conclusion that space time itself is curve in a way we can only perceive by travelling or seeing large distances. On an expanding balloon, if Earth were at point A, and another system were at point B, the constant expansion over a curved surface would create more surface (angular) distance than if the same force per square inch of balloon were used to stretch earth and that object over a flat balloon.
These ideas provide an interesting commentary on how humans perceive space time and the fourth dimension. While we are unable to see or perceive the fourth dimension visibly, its effects are evident in the changing speeds of objects as we get further and further away from them.