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Cyclic Model: Image from Astronomy Magazine, April 2009
  (click image to see movie version)
The Cyclic Universe: 
Popular Intro: Endless Universe: The Big Bang and Beyond  (Broadway Books, 2008).
(Somewhat dated -- emphasizes M-theory and colliding brane picture whereas this is not required. 
Simpler versions, including next few examples, use ordinary quantum fields in ordinary spacetime.)  



The simplest cyclic/ekpyrotic model: gaussian fluctuations, stable, and minimal tuning 
Scale-invariant perturbations in ekpyrotic cosmologies without fine-tuning
of initial conditions
PRD
(A. Levy, A. Ijjas and PJS)

The Higgs, the cyclic universe, and geodesic completeness 
Cyclic Cosmology, Conformal Symmetry and the Metastability of the Higgs
Physics Letters
(I. Bars, S-H. Chen, PJS, N. Turok)

Cosmological predictions if fundamental physics is scale-free: 
Large scale and small-scale properties of the universe appear to be scale-free,
so it is useful to compare predictions of scale-free inflation models with 
scale-free cyclic models to see which is simpler and more predictve
Physical Review D
(A. Ijjas, PJS, A. Loeb)

Can cyclic Cosmology be made geodesically complete?
Sailing through the big crunch-big bang transition
Physical Review D
(I. Bars,  PJS, N. Turok)

New approach for generating density fluctuations with small non-gaussianity in ekpyrotic/cyclic models
in a cyclic universe
General mechanism for producing scale-invariant perturbations and small
non-Gaussianity in ekpyrotic models Physical Review D (A. Ijjas, J-L. Lehners, PJS)
A new non-ekpyrotic cyclic approach to smoothing and flattening the universe The anamorphic universe JCAP (A. Ijjas and PJS) Planck2013 implications for the cyclic universe Planck2013 results support the simplest cyclic models Preprint (J.-L. Lehners and PJS) Introduction to conformal symmetry for cosmologists Local Conformal Symmetry in Physics and Cosmology Preprint (I. Bars, S-H. Chen, PJS, N. Turok) A new approach for tracking the universe through a big crunch/big bang transition Antigravity and the big crunch/big Bang Transition Physics Letters (I. Bars, S-H. Chen, PJS, N. Turok) Naturally explaining the amplitude of density perturbations in cyclic models PRL 106, 081301 (2011) (J.-L. Lehners & PJS) Can the bounce be non-singular? PRL 105, 261301 (2010) (see also PRD84, 083520) (B.-K. Xue & PJS) Dark Energy & the Return of the Phoenix Universe PRD 79, 063503 (2009) (J.-L. Lehners & PJS) Generation of Gravitational Waves in the Cyclic Universe (Subdominant) Primordial perturbations (Dominant) 2nd Order Scalar-induced g-waves Non-gaussianity: A Key Prediction of the Cyclic Model How to compute non-gaussianity in cyclic models An Intuitive Approach, 2nd Order An Intuitive Approach, 3rd Order Predictions of Spectral tilt Inflationary vs. Cyclic Model Predictions Generation of Density Perturbations in the Cyclic Universe (Linear Order) PRD76, 103501 (2007) (J.-L. Lehners, P. McFadden, PJS & N. Turok) Why the cosmological constant is small and positive (a cyclic solution) SCIENCE 312, 1180 (2006) (PJS & N. Turok) The Cyclic Model of the Universe Original Paper (SCIENCE) More detailed description (PJS & N. Turok) For Fun: Cyclocosmos: Poetic Rendition of the Cyclic Model by Bill Robinson George Carlin on the cyclic universe Jim Carrey, Stephen Hawking and the Ekpyrotic Universe Cosmocard: Summary of Basic Cosmological Parameters