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Geodesically Complete Analytic Solutions for a Cyclic Universe · Around

2011

Geodesically Complete Analytic Solutions for a Cyclic Universe

Bars, Itzhak, Chen, Shih-Hung, Turok, Neil

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We present analytic solutions to a class of cosmological models described by a canonical scalar field minimally coupled to gravity and experiencing self interactions through a hyperbolic potential.

Using models and methods inspired by 2T-physics, we show how analytic solutions can be obtained in flat/open/closed Friedmann-Robertson-Walker universes.
Among the analytic solutions, there are many interesting geodesically complete cyclic solutions in which the universe bounces at either zero or finite sizes.
When geodesic completeness is imposed, it restricts models and their parameters to a certain parameter subspace, including some quantization conditions on initial conditions in the case of zero-size bounces, but no conditions on initial conditions for the case of finite-size bounces.

Built on

I. Bars, and G. Quelin, “Dualities among 1T-field theories with spin, emerging from a unifying 2T-field theory”, Phys. Rev. D77
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M. Abramowitz, I.A. Stegun, ” Handbook of Mathematical Functions
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A. Friedmann, Z. Phys. 10
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P. Hořava and E.Witten, Nucl. Phys. B460
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L. Randall and R. Sundrum, Phys. Rev. Lett. 83
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P. Steinhardt and N. Turok, Phys. Rev. D65
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Similar

P. McFadden and N. Turok, “Conformal Symmetry of Brane World Effective Actions”, Phys. Rev. D71
2005
Cited alongside, same era.
Z-K Guo, Y-S Piao, X-M Zhang, Y-Z Zhang, “Cosmological evolution of a quintom model of dark energy”, Phys. Lett. B608
2005
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I. Bars, “The standard model of particles and forces in the framework of 2T-physics”, Phys. Rev. D74
2006
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I. Bars, S-H. Chen and G. Quelin, “Dual field theories in (d-1)+1 emergent spacetimes from a unifying field theory in d+2 spacetime,” Phys. Rev. D76
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2007
Cited alongside, same era.
I. Bars and Y.C. Kuo, “Field theory in 2T-physics with N = 1 N=1 supersymmetry” Phys. Rev. Lett. 99
2007
Cited alongside, same era.

Then

I. Bars, S. H. Chen ”Geometry and Symmetry Structures in 2T Gravity”, Phys. Rev. D79
Original
2009
Later among the works it cites.
I. Bars and Y.C. Kuo, “N=2,4 Supersymmetric gauge field theory in 2T-physics” Phys. Rev. D79
Original
2009
Later among the works it cites.
For a recent summary and status of 2T-physics, see I. Bars, “Gauge Symmetry in Phase Space, Consequences for Physics and Spacetime”, Int. J. Mod. Phys. A25
Original
2010
Later among the works it cites.
I. Bars, “Constraints on interacting scalars in 2T field theory and no scale models in 1T field theory”, Phys. Rev. D82
Original
2010
Later among the works it cites.
I. Bars and S-H. Chen, “The Big Bang and Inflation United by an Analytic Solution”, Phys. Rev. D83

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