Dynamic properties of cyclic cosmologies

Abstract

Our first goal in this work is to study general and model-independent properties of cyclic cosmologies. The large number of studies of bouncing cosmologies and different cyclic scenarios published recently calls for a proper understanding of the universal properties of cyclic models. We thus first review and further elaborate the common physical and geometrical properties of various classes of cyclic models and then discuss how cyclic Universe can be treated as a dynamic system. We then discuss how two theorems from dynamic systems analysis can be used to ensure the existence of cyclic cosmological solutions under certain conditions on the field equations. After this we proceed towards our second goal which is the application of the obtained results to different frameworks of modified gravity theories: f (R) gravity, dynamic dark energy and f (T ) gravity. We discuss the general requirements for the existence of cyclic solutions in these theories and also obtain various examples of cyclic cosmologies, while discussing their basic properties.

Geodesically complete cyclic cosmologies and entropy

“…Cyclic cosmology avoids the problem of creation ex nihilo, describes the Universe as infinite in time, gives natural and continues evolution of the Universe without singularities, while also solving the additional problems of the standard cosmological model, such as the horizon problem. For more details regarding the cyclic cosmology in the context of the open problems of modern cosmology see Introduction in [1] and [2]. Starting from the early proposal of Tolman [3], there were many proposed models of cyclic universe, based on different specific assumptions and theoretical additions to general theory of relativity and standard cosmological model, specially in the last decades [4][5][6][7][8][9][10][11].…”

“…Starting from the early proposal of Tolman [3], there were many proposed models of cyclic universe, based on different specific assumptions and theoretical additions to general theory of relativity and standard cosmological model, specially in the last decades [4][5][6][7][8][9][10][11]. Recently, a general model-independent approach to study cyclic cosmologies was proposed in [2] and [1], and also applied to the problem of magnetogenea e-mail: petar.pavlovic@kozmologija.org b e-mail: marko.sossich@fer.hr (corresponding author) sis [12], cosmological constant problem [13] and creation of wormholes around the cosmological bounce [14].…”

“…The cosmologies of the form (22) and similar require the modification of the standard general relativity or can be supported by some appropriate forms of exotic fluids. Even the most simple modified gravity theories, such as f (R) and f (T ) gravity have the mathematical structure which is rich enough to support such type of solutions, although the appropriate modification function may not be expressible in analytical form (compare the discussion in [1]). Moreover, we can notice that the geodesically complete cosmologies can be constructed from some well known and already existing models avoiding the entropy problem, such as the one proposed in [4,5], if the extra condition, that a(t) → const as t → −∞ is imposed.…”

Creation of wormholes during the cosmological bounce

“…We first tried to contribute to this research program by studying the bouncing and cyclic solutions supported by a general type of higher order curvature corrections [36]. This research was then extended and generalized by studying the model independent dynamic properties of bouncing cosmologies and then applying the results to different types of modified gravity theories [37]. It was also demonstrated that the problem of magnetogenesis has a simple possible solution in the model-independent approach to bouncing cosmology [38].…”