Can Geodesics in Extra Dimensions Solve the Cosmological Horizon Problem?

TL;DR

Freese and colleagues address the horizon problem without inflation by allowing signals to travel through extra dimensions via higher dimensional null geodesics that connect distant points on our 3-brane. They construct explicit horizon evading metrics in a 4+1D brane setup with two parallel branes and derive on-brane path lengths $h_{(1,2)}$ that can exceed the standard horizon $h_{(1,3)}$ when $kL$ is large. They also present a pedagogical 2+1D model and a continuous 4+1D generalization to illustrate how extra dimensional shortcuts can relax causal limits, though homogeneous cosmology in the simple continuous case is challenging. The work discusses the physical implications, including nonlocal effective interactions arising from higher dimensional Green functions and the need for appropriate bulk brane boundary conditions, and concludes that such scenarios may be viable if bulk effects are suppressed today.

Abstract

We demonstrate a non-inflationary solution to the cosmological horizon problem in scenarios in which our observable universe is confined to three spatial dimensions (a three-brane) embedded in a higher dimensional space. A signal traveling along an extra-dimensional null geodesic may leave our three-brane, travel into the extra dimensions, and subsequently return to a different place on our three-brane in a shorter time than the time a signal confined to our three-brane would take. Hence, these geodesics may connect distant points which would otherwise be ``outside'' the four dimensional horizon (points not in causal contact with one another).

Figures (2)

• Figure 1: Branes and geodesics for 4+1 dimensional example. Our brane is represented by the left hand vertical line with $u=0$; a second brane is represented by the right hand vertical line with $u=L$. The geodesic in the full metric leaves our brane at point 1, travels along A, B, and C, and reenters our brane at point 2. The distance $h_{(1,3)}$ between points 1 and 3 is the horizon distance usually calculated in cosmology in the absence of extra dimensions. Since $h_{(1,2)} > h_{(1,3)}$, points traditionally "outside the horizon" are here causally connected.
• Figure 2: Brane and geodesics shown in coordinate systems (x,y) and (u,z) in 2+1 dimensional example. The location of our brane (our observable universe) is shown as $y=\xi(x)$ in fig. 1a and as $u=0$ in fig. 1b. The geodesic of the full metric is a straight line between points 1 and 2 in fig. 1a and a curve in fig. 1b. The distance $z_{(1,3)}$ between points 1 and 3 in fig. 1b is the horizon distance usually calculated in cosmology in the absence of extra dimensions. Note that $z_{(1,2)} > z_{(1,3)}$, such that points traditionally "outside the horizon" are here causally connected.