An Exploration of Symmetries in the Friedmann Equation
Abstract
The Friedmann Equation for a conformal scale factor a(t) is observed to be invariant under a Mobius transformation. Using that freedom, a synthetic scale factor z(t) is defined that obeys a modified Friedman equation invariant under the replacement z(t)→±1/z(t). If this is taken this to be the more fundamental form then the traditional Friedmann equation can be shown to be missing a term due to a species with equation of state w = 2/3. We investigate in detail one particular cosmology in which it is possible to specify the contribution from this new species.
We suggest a means of avoiding a potentially redundant copy of the development of the universe the above implies through a novel cosmological spacetime manifold that is a Mobius band closed in time and nonorientable in space. Though it is closed, a Dirac field in such a spacetime may still possess a global arrow of time by virtue of the twist of the Mobius band.
 Publication:

Quantum Retrocausation: Theory and Experiment
 Pub Date:
 November 2011
 DOI:
 10.1063/1.3663718
 arXiv:
 arXiv:1106.3783
 Bibcode:
 2011AIPC.1408...75I
 Keywords:

 Dirac equation;
 cosmology;
 radiation;
 vacuum gauges;
 singular value decomposition;
 03.65.Pm;
 98.80.Bp;
 04.40.Nr;
 07.30.Dz;
 02.40.Xx;
 Relativistic wave equations;
 Origin and formation of the Universe;
 EinsteinMaxwell spacetimes spacetimes with fluids radiation or classical fields;
 Vacuum gauges;
 Singularity theory;
 Physics  General Physics;
 83F05;
 83C75;
 81T20
 EPrint:
 To appear in Proceedings of "Quantum Retrocausation: Theory and Experiment