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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).
(NB Popular/historical treatment that emphasizes original colliding brane picture and extra dimensions; 
this is not required in the simplest models, as shown in papers below).   

The simplest cyclic/ekpyrotic model: gaussian fluctuations, stable evolution, and minimal tuning 
Scale-invariant perturbations in ekpyrotic cosmologies without fine-tuning of initial conditions
PRD (2015)
(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 (2013)
(I. Bars, S-H. Chen, PJS, N. Turok)

Cosmological predictions if fundamental physics is scale-free: 
Scale-free inflation models vs. scale-free cyclic models 
Physical Review D (2014)
(A. Ijjas, PJS, A. Loeb)

Can cyclic Cosmology be made geodesically complete?
Sailing through the big crunch-big bang transition
Physical Review D (2014)
(I. Bars,  PJS, N. Turok)

A new non-ekpyrotic cyclic approach to smoothing and flattening the universe  
The anamorphic universe
JCAP (2015)
(A. Ijjas and PJS)

Planck2013 implications for the cyclic universe
Planck2013 results support the simplest cyclic models
PRD (2013)
(J.-L. Lehners and PJS)

Introduction to conformal symmetry for cosmologists 
Local Conformal Symmetry in Physics and Cosmology
PRD (2014)
(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 
(Negligibly small) Primordial perturbations
(Dominant) 2nd Order Scalar-induced g-waves

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