Jonas R. Mureika and Dejan Stojkovic, Detecting Vanishing Dimensions Via Primordial Gravitational Wave Astronomy, Physical Review Letters 106, 101101 (2011)
It has long been believed that there could be extra dimensions of space in the universe, beyond the usual 3. These dimensions are too small to be seen by the naked eye, but become relevant for the interactions of particles, as well as physics in the early universe. These extra dimensions help to explain a number of outstanding problems in modern physics. But the concept of more dimensions appearing at smaller scales or earlier in the history of the cosmos – which ideally started out as a point – can be seen as contrived.
In our paper, we discuss a new paradigm that posits less dimensions as one goes back in time or down in size – a model called “vanishing dimensions”. That is, the universe started as a point, expanded to a line (1-D), then a surface (2-D), and eventually became the 3-D world we see live in today. If true, we would be able to detect the transition between 2-D and 3-D by observing the gravitational effects. Gravitational waves – tiny ripples in the fabric of space – only propagate in the 3-D universe, but not in 2-D or 1-D. We have proposed that observing this “cut-off” frequency beyond which no waves exist is a unique and robust signature of these “vanishing dimensions.” The upcoming NASA mission “LISA” (Laser Interferometer Space Antenna) will be have unique access to this frequency range.