Expanding Space Obviated (Solves the Flatness Problem)

Cosmologists today generally accept the expanding space paradigm, the notion that space itself is expanding, to explain how most of the galaxies we see are receding from one another. They believe that space must expand in a universe in which most of the galaxies recede from one another, or else the universe would have a center and an edge, violating the cosmological principle. They believe that sufficiently large objects stretch or break apart, and proffer explanations as to why smaller objects, like galaxies, don’t do likewise.1 The argument below shows that the expanding space paradigm is superfluous. It shows that space need not expand to explain how most of the galaxies we see are receding from one another. It shows that our universe needn’t have a center or edge when space doesn’t expand. The argument introduces a feature predicted by general relativity, relative expansion, which is ignored by our cosmology and explains observations that purport to confirm the expanding space paradigm, including the observation that galaxies are receding from us faster than c, the speed of light.

Let an infinitely large universe whose space neither expands nor contracts be sprinkled with an infinity of galaxies. Let S be a section of this universe, and let S have the property that all of the galaxies within it approach one another. Nothing prevents this in principle. The galaxies in S can approach one another even though the space of S doesn’t contract. The size of S is arbitrary; it can have any size. Make S infinitely large, unbounded. Now all of the galaxies in this universe are approaching one another, yet this universe has no center or edge, nor is its space contracting. “Run the film backward” to visualize all of the galaxies receding from one another, with no existence of a cosmic center or edge, nor does the space of this universe expand.

The preceding thought experiment shows that an infinitely large universe can become sparser or denser without its space expanding or contracting, and without violating the cosmological principle. Then Occam’s razor strongly suggests that space doesn’t expand or contract in our own universe, which we have no reason to believe isn’t infinitely large.

When space itself doesn’t expand or contract:

  • Locally inertial frames can in principle be arbitrarily large. The Relativistic Rocket site, whose equations are those of special relativity (SR) and apply to locally inertial frames, warns “For distances bigger than about a thousand million light years, the formulas given here are inadequate because the universe is expanding.” This limitation goes away when space doesn’t expand or contract. Then:
    • Spacetime is globally (universe-wide) asymptotically flat at great distances from the galaxies and other centers of gravitational attraction. This solves the flatness problem, solving it far simpler than the inflation theory does.2, 3, 4 (Instead of adding a giant assumption to physics, like inflation theory does, we’ve removed an assumption.) And:
    • From any vantage point at an infinite distance from every center of gravitational attraction (which is to say, nowhere), every galaxy recedes slower than c, and galaxies at a limit of infinite distance recede at speeds up to c in the limit, and therefore can be infinitely redshifted in the limit and not aging in the limit.
  • Recession speeds of galaxies can in principle exceed c (without violating SR) as measured from a vantage point at a finite distance from a center of gravitational attraction (which is to say, anywhere) due to relative (depends on the observer) spatial expansion predicted by both special and general relativity, as explained at Dark Energy Obviated. This relative expansion is measurable, it adds (without limit in principle) to recession that is due to simple movement away, and it explains observations that purport to confirm the notion that space itself absolutely expands (i.e. in a way that can break sufficiently large objects).
  • No object need be out of causal contact with another object anywhere else in the universe.
  • The entire universe is observable from any vantage point, albeit objects may be redshifted out of practical observable range (e.g. perhaps a photon from a fast-receding object reaches the observer only once a year on average on the observer’s clock), providing a solution to Olbers’ paradox.
  • The terms “expanding universe” and “cosmic expansion” are still useful to refer to the recession of most galaxies from one another.
  • No explanations are required as to why galaxies and smaller objects don’t stretch or break apart in concert with cosmic expansion.

References and Notes

1. See Cosmic expansion is not to blame for expanding waistlines at http://www.newscientist.com/article/dn8082.

2. See The Flatness Problem at http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/FlatnessProblem.html.

3. See WMAP Cosmology 101: Inflationary Universe at http://map.gsfc.nasa.gov/m_uni/uni_101inflation.html. Note that the inflation theory creates a major additional problem for cosmology, namely as to the nature of the proposed inflaton field that inflated the universe. It’s easily the biggest assumption in all of the sciences.

4. Imagine a freely falling block of Swiss cheese, billions of light years wide / tall / deep, representing a section of the universe. The holes of the cheese are regions of significantly curved spacetime. At the centers of the holes are galaxies. Some of the holes may be merged into one another to form larger holes surrounding clusters and superclusters. The holes (the galaxies) are of course free to be moving relative to one another and relative to the block. The block of cheese except the holes is a free-floating region of negligibly curved spacetime, a locally inertial frame. The block can be arbitrarily large in principle; nothing prevents that possibility now that expanding space is obviated. When the block can be arbitrarily large it follows that the default curvature of the universe is zero, flat. Then no flatness problem arises when observations show that the universe might be flat.