Title: Bouncing models with a cosmological constant Authors: Rodrigo Maier, Stella Pereira, Nelson Pinto-Neto, Beatriz B. Siffert

Bouncing models have been proposed by many authors as a completion, or even as an alternative to inflation for the description of the very early and dense Universe. However, most bouncing models contain a contracting phase from a very large and rarefied state, where dark energy might have had an important role as it has today in accelerating our large Universe. In that case, its presence can modify the initial conditions and evolution of cosmological perturbations, changing the known results already obtained in the literature concerning their amplitude and spectrum. In this paper, we assume the simplest and most appealing candidate for dark energy, the cosmological constant, and evaluate its influence on the evolution of cosmological perturbations during the contracting phase of a bouncing model, which also contains a scalar field with a potential allowing background solutions with pressure and energy density satisfying p = w*rho, w being a constant. An initial adiabatic vacuum state can be set at the end of domination by the cosmological constant, and an almost scale invariant spectrum of perturbations is obtained for w~0, which is the usual result for bouncing models. However, the presence of the cosmological constant induces oscillations and a running towards a tiny red-tilted spectrum for long wavelength perturbations.

We investigate the Weyl space-time extension of general relativity (GR) for studying the FLRW cosmology through focusing and defocusing of the geodesic congruences. We have derived the equations of evolution for expansion, shear and rotation in the Weyl space-time. In particular we consider the Starobinsky modification, f(R)=R+\beta R^2-2\Lambda, of gravity in the Einstein-Palatini formalism, which turns out to reduce to the Weyl integrable space-time (WIST) with the Weyl vector being a gradient. The modified Raychaudhuri equation takes the form of the Hill-type equation which is then analysed for studying formation of the caustics. In this model, it is possible to have a Big Bang singularity free cyclic Universe but unfortunately the periodicity turns out to be extremely short.

Title: A Simple Harmonic Universe Authors: Peter W. Graham, Bart Horn, Shamit Kachru, Surjeet Rajendran, Gonzalo Torroba

We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k=+1, and are supported by a negative cosmological term and matter with -1 < w < -1/3. In the case of moderate bounces (where the ratio of the maximal scale factor a_+ to the minimal scale factor a_- is {\cal O}(1)), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large a_+/a_-, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.

Title: G-Bounce Authors: Damien A. Easson (Arizona State U.), Ignacy Sawicki (Heidelberg U.), Alexander Vikman (CERN)

We present a wide class of models which realise a bounce in a spatially flat Friedmann universe in standard General Relativity. The key ingredient of the theories we consider is a noncanonical, minimally coupled scalar field belonging to the class of theories with Kinetic Gravity Braiding / Galileon-like self-couplings. In these models, the universe smoothly evolves from contraction to expansion, suffering neither from ghosts nor gradient instabilities around the turning point. The end-point of the evolution can be a standard radiation-domination era or an inflationary phase. We formulate necessary restrictions for Lagrangians needed to obtain a healthy bounce and illustrate our results with phase portraits for simple systems including the recently proposed Galilean Genesis scenario.

Title: Cyclic, ekpyrotic and little rip universe in modified gravity Authors: Shin'ichi Nojiri, Sergei D. Odintsov, Diego Saez-Gomez

We propose the reconstruction of F(R) gravity in such a way that corresponding theory admits cyclic and ekpyrotic universe solutions. The number of explicit examples of such F(R) model is found. The comparison with the reconstructed scalar-tensor theory is made. We also present F(R) gravity which provides the little rip evolution and gives the realistic gravitational alternative for \Lambda CDM cosmology. The time for little rip dissolution of bound structures in such theory is estimated. We demonstrate that transformed little rip F(R) solution becomes qualitatively different cosmological solution with Big Bang type singularity in Einstein frame.

Title: Diversity in the Phoenix Universe Authors: Jean-Luc Lehners

It has recently been argued by Copeland et al. that in eleven dimensions two orbifold planes can collide and bounce in a regular way, even when the bulk metric is perturbed away from Milne spacetime to a Kasner solution. In this paper, we point out that as a consequence the global "phoenix" structure of the cyclic universe is significantly enriched. Spatially separated regions, with different density fluctuation amplitudes as well as different non-gaussian characteristics, are all physically realized. Those regions containing by far the most structure are specified by a fluctuation amplitude of Q ~ 10^{-4.5} and local non-gaussianity parameters f_{NL} ~ O(± 10) and g_{NL} ~ O(-10^3), in agreement with current observations.

Title: Do we live in the universe successively dominated by matter and antimatter? Authors: Dragan Slavkov Hajdukovic

We wonder if a cyclic universe may be dominated alternatively by matter and antimatter. Such a scenario demands a mechanism for transformation of matter to antimatter (or antimatter to matter) during the final stage of a big crunch. By giving an example, we have shown that in principle such a mechanism is possible. Our mechanism is based on a hypothetical repulsion between matter and antimatter, existing at least deep inside the horizon of a black hole. When universe is reduced to a supermassive black hole of a small size, a very strong field of the conjectured force might create (through a Schwinger type mechanism) particle-antiparticle pairs from the quantum vacuum. The amount of antimatter created from the vacuum is equal to the decrease of mass of the black hole and violently repelled from it. When the size of the black hole is sufficiently small, the creation of antimatter may become so fast, that matter of our Universe might be transformed to antimatter in a fraction of second. Such a fast conversion of matter into antimatter may look as a Big Bang. Our mechanism prevents a singularity; a new cycle might start with an initial size more than 30 orders of magnitude greater than the Planck length, suggesting that there is no need for inflationary scenario in Cosmology. In addition, there is no need to invoke CP violation for explanation of matter-antimatter asymmetry. Simply, our present day Universe is dominated by matter, because the previous universe was dominated by antimatter.

Title: Cosmic Bounces and Cyclic Universes Authors: Jean-Luc Lehners

Cosmological models involving a bounce from a contracting to an expanding universe can address the standard cosmological puzzles and generate "primordial" density perturbations without the need for inflation. Some such models, in particular the ekpyrotic and cyclic models that we focus on, fit rather naturally into string theory. We discuss a number of topics related to these models: the reasoning that leads to the ekpyrotic phase, the predictions for upcoming observations, the differences between singular and non-singular models of the bounce as well as the predictive and explanatory power offered by these models.

Title: Persistence of black holes through a cosmological bounce Authors: B. J. Carr, A.A. Coley

We discuss whether black holes could persist in a universe which recollapses and then bounces into a new expansion phase. Whether the bounce is of classical or quantum gravitational origin, such cosmological models are of great current interest. In particular, we investigate the mass range in which black holes might survive a bounce and ways of differentiating observationally between black holes formed just after and just before the last bounce. We also discuss the consequences of the universe going through a sequence of dimensional changes as it passes through a bounce.

Title: No evidence for anomalously low variance circles on the sky Authors: Adam Moss, Douglas Scott, James P. Zibin (Version v3)

In a recent paper, Gurzadyan & Penrose claim to have found directions on the sky centred on which are circles of anomalously low variance in the cosmic microwave background (CMB). These features are presented as evidence for a particular picture of the very early Universe. We attempted to repeat the analysis of these authors, and we can indeed confirm that such variations do exist in the temperature variance for annuli around points in the data. However, we find that this variation is entirely expected in a sky which contains the usual CMB anisotropies. In other words, properly simulated Gaussian CMB data contain just the sorts of variations claimed. Gurzadyan & Penrose have not found evidence for pre-Big Bang phenomena, but have simply re-discovered that the CMB contains structure.