We consider the problem of matching two spacetimes, the previous and present aeons, in the Conformal Cyclic Cosmology model. The common boundary between them inherits two sets of constraints -- one for each solution of the Einstein field equations extended to the conformal boundaries. The previous aeon is assumed to be an asymptotically de Sitter spacetime, so the standard conformal formulation of the Einstein field equations suffice to derive the constraints on the future null infinity. For the future aeon, which is supposed to evolve from an initial singularity, they are obtained with the use of the Bach equation. This equation is regular at the past conformal infinity for conformally flat and conformally Einstein spacetimes, so we will mostly focus on them here. An example of the electrovacuum spacetime which does not fall into this class and has regular conformal Bach tensor will be discussed in the appendix.
In these lectures my aim is to review enough of conformal differential geometry in four dimensions to give an account of Penrose's conformal cyclic geometry.
This article is an extended version of a talk given in Oxford in June 2021 as part of an online meeting `Ninety minutes of CCC' to mark the 90th birthday of Sir Roger Penrose. I assemble some questions that I have been asked or have asked myself about CCC.
Considering the holographic dark energy (HDE) with two different Infrared (IR) cutoffs, we study the evolution of a cyclic universe which avoids the Big-Rip singularity. Our results show that, even in the absence of a mutual interaction between the cosmos sectors, the HDE model with the Hubble radius as IR cutoff can mimics a cosmological constant in the framework of a cyclic cosmology. In addition, we find that both the interacting and non-interacting universes may enter into a cycle of sequential contraction and expansion, if the Granda-Oliveros (GO) cutoff is chosen as the IR cutoff in the …
Conformal Cyclic Cosmology (CCC) is a cyclic model of the universe put forward by Sir Roger Penrose. A conformal invariance assumption in the neighbourhood of the crossover region between cycles (which Penrose calls aeons) allows successive space-times to be related by a conformal rescaling. A major open problem is how to choose the conformal factor in a unique way, and is a fundamental hurdle to further study. Proposals have been put forward by Newman, Tod and Nurowski, but they disagree in one way or another with Penrose's original assumptions as well as each other. In this paper we compare …
We consider two consecutive conformally flat eons in Penrose's Conformal Cyclic Cosmology and study how the perfect fluid matter content of the past eon determines the matter content of the present eon by means of Penrose's reciprocity hypothesis.
In this work we propose a new general model of eternal cyclic Universe. We start from the assumption that quantum gravity corrections can be effectively accounted by the addition of higher order curvature terms in the Lagrangian density for gravity. It is also taken into account that coefficients associated with these curvature corrections will in general be dependent on a curvature regime. We therewith assume no new ingredients, such as extra dimensions, new scalar fields, phantom energy or special space-time geometries. Evolution of the Universe in this framework is studied and general prope…
It is shown how quantum fluctuations of the radiation during the contraction era of a CBE (Comes Back Empty) cyclic cosmology can provide density fluctuations which re-enter the horizon during the subsequent expansion era and at lowest order are scale invariant, in a Harrison-Zel'dovich-Peebles sense, as necessary to be consistent with observations of large scale structure.
We consider an isotropic and homogeneous universe in loop quantum cosmology. We assume that the matter content of the universe is dominated by dust matter in early time and a phantom matter at late time which constitutes the dark energy component. The quantum gravity modifications to the Friedmann equation in this model indicate that the classical big bang singularity and the future big rip singularity are resolved and are replaced by quantum bounce. It turns out that the big bounce and recollapse in the herein model contribute to a cyclic scenario for the universe. We then study the quantum t…
We discuss a cyclic cosmology in which the visible universe, or introverse, is all that is accessible to an observer while the extroverse represents the total spacetime originating from the time when the dark energy began to dominate. It is argued that entanglement entropy of the introverse is the more appropriate quantity to render infinitely cyclic, rather than the entropy of the total universe. Since vanishing entanglement entropy implies disconnected spacetimes, at the turnaround when the introverse entropy is zero the disconnected extroverse can be jettisoned with impunity.
The holographic principle provides a deep insight into quantum gravity and resolves the fine-tuning crisis concerning the cosmological constant. Holographic dark energy introduces new ultra-violet (UV) and infra-red (IR) cutoffs into quantum gravity which are necessarily strongly related. The equation of state for dark energy $ω= p/ρ$ is discussed from the holographic point of view. The phantom option of $ω< -1$ is resurrected, as in an earlier cyclic cosmology. Such a cyclic model can, however, equally use the cosmological constant with $ω= -1$.
As quotient spaces, Minkowski and de Sitter are fundamental, non-gravitational spacetimes for the construction of physical theories. When general relativity is constructed on a de Sitter spacetime, the usual Riemannian structure is replaced by a more general structure called de Sitter-Cartan geometry. In the contraction limit of an infinite cosmological term, the de Sitter-Cartan spacetime reduces to a singular, flat, conformal invariant four-dimensional cone spacetime, in which our ordinary notions of time interval and space distance are absent. It is shown that such spacetime satisfies all p…
We address how to construct an infinitely cyclic universe model. A major consideration is to make the entropy cyclic which requires the entropy to be reset to zero in each cycle expansion to turnaround, to contraction, to bounce, etc. Here we reset entropy at the turnaround by selecting the introverse (visible universe) from the extroverse which is generated by the accelerated expansion. In the model, the observed homogeneity is explained by the low entropy at the bounce, The observed flatness arises from the contraction together with the reduction in size between the expanding and contracting…
From the Wheeler-Dewitt solutions, the scale factor of the initial universe is discussed. In this study, scale factors from Wheeler-Dewitt solutions, loop quantum gravity, and phantom energy dominated stages are compared. Certain modifications have been attempted in scale factor and quantum potentials driven by canonical quantum gravity approaches. Their results are discussed in this work. Despite an increment of phantom energy density, avoidance of Big Rip is reported. Scale factors predicted from various models are discussed in this work. The relationship between scale factors and the smooth…
We study the bounce and cyclicity realization in the framework of new gravitational scalar-tensor theories. In these theories the Lagrangian contains the Ricci scalar and its first and second derivatives, in a specific combination that makes them free of ghosts, and transformed into the Einstein frame they are proved to be a subclass of bi-scalar extensions of general relativity. We present analytical expressions for the bounce requirements, and we examine the necessary qualitative behavior of the involved functions that can give rise to a given scale factor. Having in mind these qualitative f…
Complete cosmic evolution is a popular model in cosmology. But the possibility of other different cosmic evolution model can not be negated. The nonsingular bouncing scenario models are now found in literature. This work is a representation of such a model.
We investigate the bounce and cyclicity realization in the framework of weakly broken galileon theories. We study bouncing and cyclic solutions at the background level, reconstructing the potential and the galileon functions that can give rise to a given scale factor, and presenting analytical expressions for the bounce requirements. We proceed to a detailed investigation of the perturbations, which after crossing the bouncing point give rise to various observables, such as the scalar and tensor spectral indices and the tensor-to-scalar ratio. Although the scenario at hand shares the disadvant…
In the Big Rip cosmological scenario, a FRW universe containing dark energy with $w < -1$ in its equation of state (phantom energy) expands in such way that, in a finite time span, the scale factor diverges to infinity and the size of the cosmic horizon goes to zero. Here we revisit this scenario in light of the fact that Hawking radiation is expected to be generated at the apparent horizon of a FRW universe, and show that the energy density and temperature of that radiation both diverge at the Big Rip. We then use this fact to propose a new variant of Penrose's conformal cyclic cosmology mode…
We use the phase plane analysis technique of Madsen and Ellis to consider a universe with a true cosmological constant as well as a cosmological "constant" that is decaying. Time symmetric dynamics for the inflationary era allows eternally bouncing models to occur. Allowing for scalar field dynamic evolution, we find that if dark energy decays in the future, chaotic cyclic universes exist provided the spatial curvature is positive. This is particularly interesting in light of current observations which do not yet rule out either closed universes or possible evolution of the cosmological consta…
It has recently been reported by Cresswell et al. [1] that correlations in the noise surrounding the observed gravitational wave signals, GW150194, GW151226, and GW170194 were found by the two LIGO detectors in Hanford and Livingston with the same time delay as the signals themselves. This raised some issues about the statistical reliability of the signals themselves, which led to much discussion, the current view appearing to support the contention that there is something unexplained that may be of genuine astrophysical interest [2]. In this note, it is pointed out that a resolution of this p…
In the framework of $f(T)$-gravity theory, classical and quantum cosmology has been studied in the present work for FLRW space-time model. The Noether symmetry, a point-like symmetry of the Lagrangian is used to the physical system and a specific functional form of $f(T)$ is determined. A point transformation in the 2D augmented space restricts one of the variable to be cyclic so that the Lagrangian as well as the field equations are simplified so that they are solvable. Lastly for quantum cosmology, the WD equation is constructed and possible solution has been evaluated.
Among many models which can describe the bouncing cosmology, A matter bounce scenario that is deformed by a running vacuum model of dark energy (RVM-DE) has been interested. In this research, I show that a class of RVM-CDM (cold dark matter) model can also describe a cyclical cosmology in which the universe undergoes cycles of expansion to the contraction phase and vice versa. To this end, following our previous work, I consider one of the most successful class of RVM-CDM model in bouncing cosmology, $ρ_x=n_0+n_2 H^2 +n_4 H^4$, in which the power spectral index gets a red tilt and the running …
Combining intervals of ekpyrotic (ultra-slow) contraction with a (non-singular) classical bounce naturally leads to a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically, but the scale factor grows by an exponential factor from one cycle to the next. The resulting cosmology not only resolves the homogeneity, isotropy, flatness and monopole problems and generates a nearly scale invariant spectrum of density perturbations, but it also addresses a number of age-old cosmological issues that big bang inflationary cosmology does no…
It is generally believed that a cosmological arrow of time must be associated with entropy production. Indeed, in his seminal work on cyclic cosmology, Tolman introduced a viscous fluid in order to make successive expansion/contraction cycles larger than previous ones, thereby generating an arrow of time. However, as we demonstrate in this letter, the production of entropy is not the only means by which a cosmological arrow of time may emerge. Remarkably, systems which are dissipationless may nevertheless demonstrate a preferred direction of time provided they possess attractors. An example of…
In the present paper we study the evolution of the modes of a scalar field in a cyclic cosmology. In order to keep the discussion clear, we study the features of a scalar field in a toy model, a Friedman-Robertson-Walker universe with a periodic scale factor, in which the universe expands, contracts and bounces infinite times, in the approximation in which the dynamic features of this universe are driven by some external factor, without the backreaction of the scalar field under study. In particular, we show that particle production exhibits features of the cyclic cosmology. Also, by studying …
We study the cosmological implications of interactions between spacetime quanta in the Group Field Theory (GFT) approach to Quantum Gravity from a phenomenological perspective. Our work represents a first step towards understanding Early Universe Cosmology by studying the dynamics of the emergent continuum spacetime, as obtained from a fundamentally discrete microscopic theory. In particular, we show how GFT interactions lead to a recollapse of the Universe while preserving the bounce replacing the initial singularity, which has already been shown to occur in the free case. It is remarkable th…
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…
Using the idea of regularisation of singularities due to the variability of the fundamental constants in cosmology we study the cyclic universe models. We find two models of oscillating and non-singular mass density and pressure ("non-singular" bounce) regularised by varying gravitational constant $G$ despite the scale factor evolution is oscillating and having sharp turning points ("singular" bounce). Both violating (big-bang) and non-violating (phantom) null energy condition models appear. Then, we extend this idea onto the multiverse containing cyclic individual universes with either growin…
