Abstract:
In a recently archived paper by Zhang\cite{Zhang}, it is claimed that before turnaround in a cyclic model two unexpected events happen: (1) black holes cease to contract and begin to expand; (2) separated causal patches start to reconnect. We show that both conclusions are erroneous and result from the author's choice of variables.

Abstract:
We investigate the effects of accretion of phantom energy onto primordial black holes. Since Hawking radiation and phantom energy accretion contribute to a {\it decrease} of the mass of the black hole, the primordial black hole that would be expected to decay now due to the Hawking process would decay {\it earlier} due to the inclusion of the phantom energy. Equivalently, to have the primordial black hole decay now it would have to be more massive initially. We find that the effect of the phantom energy is substantial and the black holes decaying now would be {\it much} more massive -- over 10 orders of magnitude! This effect will be relevant for determining the time of production and hence the number of evaporating black holes expected in a universe accelerating due to phantom energy.

Abstract:
In this article we review recent developments of cyclic cosmology. A typical non-singular cyclic model within General Relativity requires a non-conventional fluid with negative effective energy density, in order to cancel the matter component and lead to a non-singular bounce. However, the existence of such a non-conventional fluid usually leads to quantum instabilities and makes the theory ill-defined. In the present work we follow the alternative way, obtaining two scenarios of non-singular cyclic cosmological evolutions in the context of gravitational theories beyond General Relativity. The degrees-of-freedom examination reveals that these two models are free of the Phantom Menace. Our analysis illustrates that, if cyclic cosmology describes overall universe, a theory of gravity beyond Einstein may be expected.

Abstract:
The accretion of phantom fields by black holes within a thermodynamic context is addressed. For a fluid violating the dominant energy condition, case of a phantom fluid, the Euler and Gibbs relations permit two different possibilities for the entropy and temperature: a situation in which the entropy is negative and the temperature is positive or vice-versa. In the former case, if the generalized second law (GSL) is valid, then the accretion process is not allowed whereas in the latter, there is a critical black hole mass below which the accretion process occurs. In a universe dominated by a phantom field, the critical mass drops quite rapidly with the cosmic expansion and black holes are only slightly affected by accretion. All black holes disappear near the big rip, as suggested by previous investigations, if the GSL is violated.

Abstract:
A universe described by braneworlds is studied in a cyclic scenario. As expected such an oscillating universe will undergo turnarounds, whenever the phantom energy density reaches a critical value from either side. It is found that a universe described by RSII brane model will readily undergo oscillations if, either the brane tension, \lambda, or the bulk cosmological constant, \Lambda_{4}, is negative. The DGP brane model does not readily undergo cyclic turnarounds. Hence for this model a modified equation is proposed to incorporate the cyclic nature. It is found that there is always a remanent mass of a black hole at the verge of a turnaround. Hence contrary to known results in literature, it is found that the destruction of black holes at the turnaround is completely out of question. Finally to alleviate, if not solve, the problem posed by the black holes, it is argued that the remanent masses of the black holes do not act as a serious defect of the model because of Hawking evaporation.

Abstract:
We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative cosmological constant. In all these cases we calculate the classical trajectories in configuration space and give solutions to the Wheeler-DeWitt equation in quantum cosmology. In the cases of the toy model and the model with exponential potential we are able to solve the Wheeler-DeWitt equation exactly. For comparison, we also give the corresponding solutions for an ordinary scalar field. We discuss in particular the behaviour of wave packets in minisuperspace. For the phantom field these packets disperse in the region that corresponds to the Big Rip singularity. This thus constitutes a genuine quantum region at large scales, described by a regular solution of the Wheeler-DeWitt equation. For the ordinary scalar field, the Big-Bang singularity is avoided. Some remarks on the arrow of time in phantom models as well as on the relation of phantom models to loop quantum cosmology are given.

Abstract:
We show that in tilting perfect fluid cosmological models with an ultra-radiative equation of state, generically the tilt becomes extreme at late times and, as the tilt instability sets in, observers moving with the tilting fluid will experience singular behaviour in which infinite expansion is reached within a finite proper time, similar to that of phantom cosmology (but without the need for exotic forms of matter).

Abstract:
We explore a cyclic universe due to phantom and quintessence fields. We find that, in every cycle of the evolution of the universe, the phantom dominates the cosmic early history and quintessence dominates the cosmic far future. In this model of universe, there are infinite cycles of expansion and contraction. Different from the inflationary universe, the corresponding cosmic space-time is geodesically complete and quantum stable. But similar to the Cyclic Model, the flatness problem, the horizon problem and the large scale structure of the universe can be explained in this cyclic universe.

Abstract:
We consider quantum modifications to phantom cosmology in a Friedmann-Robertson-Walker spacetime. The cosmological evolution equations improved by the renormalization group are obtained. For exponential potential, we find two types of cosmological fixed point; the renormalization group scale either freezes in, or continues to evolve with scale factor. We discuss the implications of each of these points, and investigate especially whether the big rip can be avoided. If the fixed point of renormalization group flow coincides with the cosmological fixed point, the universe will be dominated by dark matter and will be free from the big rip.

Abstract:
We construct static multicenter solutions of phantom Einstein-Maxwell-dilaton theory from null geodesics of the target space, leading to regular black holes without spatial symmetry for certain discrete values of the dilaton coupling constant. We also discuss the three-dimensional gravitating sigma models obtained by reduction of phantom Einstein-Maxwell, phantom Kaluza-Klein and phantom Einstein-Maxwell-dilaton-axion theories. In each case, we generate by group transformations phantom charged black hole solutions from a neutral seed.