Cosmology sometimes seems mysterious: you often hear about dark matter, dark energy, big bang, multiverse, extra dimensions… I think we can undoubtedly say that our Universe is weird… And fascinating. A problem with some of these yet to be explained mysteries is that the models created to describe them are mainly purely theoretical, without being testable. This is particularly true with theories involving extra dimensions (who said string theory?..). Other theories even explore the possibility of lower dimensionality, in which the Universe had a smaller number of spatial dimensions in the past.

Recently, physicists Jonas Mureika from Loyola Marymount University in Los Angeles, California, and Dejan Stojkovic from SUNY at Buffalo in Buffalo, New York, have proposed an interesting way to investigate lower dimensions of the Universe. They’ve published their study in a recent issue of Physical Review Letters.

According to them, our four-dimensional spacetime may not have been the same in the past: it may have existed in a lower dimensional state. In the beginning, spacetime would have only two dimensions, one dimension of space and one dimension of time. In other words, shortly after the Big Bang, the Universe was a straight line. With the expansion, this straight line “wrapped up” so that it appears as the four-dimensional spacetime we see today, after going through a three-dimensional state, with two dimensions of space.

Although they don’t know exactly at which energy levels (or when) the transitions between higher dimensional states occurred, they gave some estimates assuming that the Universe’s energy level and size determine its number of dimensions. The first transition from one dimension of space to two dimensions of space happened when the Universe’s energy level was about 100 Tev (Tera-electron volt – a unit of energy used in particle physics). Later, when the Universe cooled down to an energy level of about 1 TeV (about the kinetic energy of a flying mosquito), it reached its third dimension of space: it is the Universe we live in today. The current energy level of the Universe is about 0.001 eV.

Is there any evidence of a lower-dimensional structure for the Universe? Maybe. Indeed, when observing cosmic ray particles in space, scientists found that at energies higher than 1 TeV they appear to align in a two-dimensional plane.

Mureika and Stojkovic even propose another test: in a Universe with two dimensions of space, there are no gravitational degrees of freedom, hence there are no gravitational waves. If the Universe was ever in a three-dimensional state, then no primordial gravitational waves of this epoch can exist today: the cut-off in gravitational wave frequency would represent the transition between a two-dimensional space and a three-dimensional space. It would be like observing one of our dimensions “vanishing” in the past.

Pushing the idea further, we can imagine that a fourth dimension of space will appear in the future, as the Universe keeps cooling down: this could provide a solution to the cosmological constant problem, where energy would be hidden in our four-dimensional spacetime before the Universe is promoted to a five-dimensional state.