The difference in the shape of the observed paths is visualized in the picture on the right. Here an approximation in 4D space-time is chosen (sufficiently accurate in the neighborhood of ordinary planets) and the curvatures are exaggerated. The object's speed is always c in 4D space-time and only its direction rotates (take note of the labels of the space-time axes!).

The example shows that, in a flat 3D coordinate system, an observer at infinity is indirectly able to perceive the curvature of space-time in the neighborhood of the planet because he observes the acceleration of a falling object.

The ratio between infinitesimal coordinate distance dR and radial distance dr is given in classical general relativity by dR/dr=1/Ö (1-2Gm/rc²). This ratio becomes 1 at infinity, where curvature of space is assumed to be zero as a a result of the absence of mass. But what if the 4D space-time of our universe is closed in the 5th dimension? In that case, curvature on a cosmological scale exists everywhere and at infinity dR/dr will not be equal to 1 (the classical formula will need an extra component to account for this). Just like the curvature increases when approaching a massive object, it will also increase when going a far distance in the universe, i.e., when looking into deep space.
The velocity vector of an object following a geodesic path in that far distance will also gain components in space and the 5th dimension. After all, the object will only appear to be at rest relative to an observer at those places where dR/dr =1. Its absolute spatial speed goes up with increasing distance, both when dR/dr <1 and dR/dr >1.

In a 5D, or even a 4D space, curvature will appear asymmetric to an observer with 3D observational skills as a result of the geometric projection effects. This can be illustrated by using an example of the effect as perceived by a Flatlander, living on a horn torus (see the pictures below).

The conclusion is that in a closed universe, objects in the far distance of that universe should show velocity and acceleration in flat 3D coordinate space, similar to what happens near a massive object. The observer will interpret this as an expanding universe in flat 3D coordinates while the rate of this expansion is accelerating. This is indeed what is observed empirically today, but it is traditionally explained as a physically expanding universe.