Because positing the existence of an n+1 dimension complicates the theoretical model without adding to its predictive power. Curvature and expansion can be defi

Because positing the existence of an n+1 dimension complicates the theoretical model without adding to its predictive power. Curvature and expansion can be defined perfectly well using intrinsic measures within n dimensions, without positing another. Further, the n-dimensional manifold might curve in ways that cannot be embedded into n+1 dimensions. For example, a Klein bottle is a logically possible shape of a 2D universe that cannot be embedded into a 3D universe without colliding with itself. Now, if this happens you might say, "Aha! But a Klein bottle can indeed exist embedded in 4D. So perhaps our universe is not in n+1 dimensions, but n+2." But how far does this continue? Adding dimensions every time you find something new out about the curvature of space is like adding epicycles to the geocentric model. You don't need an infinite supply of dimensions to embed the universe in, since everything you know about it can be described without reference to any of these unobservable dimensions that you might suppose exist.