Abstract
A new form Time Crystal has been proposed and some of its consequences have been studied. The model is a generalization of the Friedmann-Robertson-Walker (FRW) cosmology endowed with noncommutative geometry corrections. In the mini-superspace approach the scale factor undergoes the time periodic behavior, or Sisyphus dynamics, which allows us to interpret this Cosmological Time Crystal as a physically motivated toy model to simulate cyclic universe. Analyzing our model purely from Time Crystal perspective reveals many novelties such as a complex singularity structure (more complicated than the previously encountered swallowtail catastrophe) and a richer form of Sisyphus dynamics. In the context of cosmology, the system can serve as a toy model in which, apart from inducing a form of cyclic universe feature, it is possible to generate an arbitrarily small positive effective Cosmological Constant. We stress that the model is purely geometrical without introduction of matter degrees of freedom.
Highlights
In this paper, we aim to apply the fascinating concept of classical time crystal (CTC), proposed by Shapere and Wilczek [1,2], in an extended model of Friedmann-Robertson-Walker (FRW) cosmology
The model is a generalization of the Friedmann-Robertson-Walker (FRW) cosmology endowed with noncommutative geometry corrections
The strict CTC inherently has singular behavior, whereas the physical realization is throughout well behaved. These will be discussed in more detail later, but essentially CTC has a noncanonical form of kinetic energy that minimizes at a nonzero velocity, much in analogy to spontaneous symmetry breaking (SSB) where a potential
Summary
We aim to apply the fascinating concept of classical time crystal (CTC), proposed by Shapere and Wilczek [1,2] (see [3] for a recent review), in an extended model of Friedmann-Robertson-Walker (FRW) cosmology. It is worthwhile to mention a remarkable coincidence concerning the present work with two earlier observations: from the time-symmetric nature of the NC metric, in [4] itself, the authors had suggested that the NC FRW metric might describe a bouncing universe from a restricted study of geodesics. This is not connected to the idea of TC because the latter appeared much later.
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