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 non-orientable 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;
- Einstein-Maxwell spacetimes spacetimes with fluids radiation or classical fields;
- Vacuum gauges;
- Singularity theory;
- Physics - General Physics;
- 83F05;
- 83C75;
- 81T20
- E-Print:
- To appear in Proceedings of "Quantum Retrocausation: Theory and Experiment