The Cosmological Models with Jump Discontinuities

The article is dedicated to one of the most undeservedly overlooked properties of the cosmological models: the behaviour at, near and due to a jump discontinuity. It is most interesting that while the usual considerations of the cosmological dynamics deals heavily in the singularities produced by the discontinuities of the second kind (a.k.a. the essential discontinuities) of one (or more) of the physical parameters, almost no research exists to date that would turn to their natural extension/counterpart: the singularities induced by the discontinuities of the first kind (a.k.a. the jump discontinuities). It is this oversight that this article aims to amend. In fact, it demonstrates that the inclusion of such singularities allows one to produce a number of very interesting scenarios of cosmological evolution. For example, it produces the cosmological models with a finite value of the equation of state parameter $w=p/\rho$ even when both the energy density and the pressure diverge, while at the same time keeping the scale factor finite. Such a dynamics is shown to be possible only when the scale factor experiences a finite jump at some moment of time. Furthermore, if it is the first derivative of the scale factor that experiences a jump, then a whole new and different type of a sudden future singularity appears. Finally, jump discontinuities suffered by either a second or third derivatives of a scale factor lead to cosmological models experiencing a sudden dephantomization -- or avoiding the phantomization altogether. This implies that theoretically there should not be any obstacles for extending the cosmological evolution beyond the corresponding singularities; therefore, such singularities can be considered a sort of a cosmological phase transition.Comment: 27 pages, 5 figures. Inserted additional references; provided in Introduction a specific example of a well-known physical field leading to a cosmological jump discontinuity; seriously expanded the discussion of possible physical reasons leading to the jump discontinuities in view of recent theoretical and experimental discoverie

Brane cosmology from observational surveys and its comparison with standard FRW cosmology

Several dark energy models on the brane are investigated. They are compared with corresponding theories in the frame of 4d Friedmann-Robertson-Walker cosmology. To constrain the parameters of the models considered, recent observational data, including SNIa apparent magnitude measurements, baryon acoustic oscillation results, Hubble parameter evolution data and matter density perturbations are used. Explicit formulas of the so-called {\it state-finder} parameters in teleparallel theories are obtained that could be useful to test these models and to establish a link between Loop Quantum Cosmology and Brane Cosmology. It is concluded that a joint analysis as the one developed here allows to estimate, in a very convenient way, possible deviation of the real universe cosmology from the standard Friedmann-Robertson-Walker one.Comment: 19 pages, 6 figures. arXiv admin note: text overlap with arXiv:1206.219

The linearization method and new classes of exact solutions in cosmology

We develop a method for constructing exact cosmological solutions of the Einstein equations based on representing them as a second-order linear differential equation. In particular, the method allows using an arbitrary known solution to construct a more general solution parameterized by a set of 3\textit{N} constants, where \textit{N} is an arbitrary natural number. The large number of free parameters may prove useful for constructing a theoretical model that agrees satisfactorily with the results of astronomical observations. Cosmological solutions on the Randall-Sundrum brane have similar properties. We show that three-parameter solutions in the general case already exhibit inflationary regimes. In contrast to previously studied two-parameter solutions, these three-parameter solutions can describe an exit from inflation without a fine tuning of the parameters and also several consecutive inflationary regimes.Comment: 7 page

Astronomical bounds on future big freeze singularity

Recently it was found that dark energy in the form of phantom generalized Chaplygin gas may lead to a new form of the cosmic doomsday, the big freeze singularity. Like the big rip singularity, the big freeze singularity would also take place at a finite future cosmic time, but unlike the big rip singularity it happens for a finite scale factor.Our goal is to test if a universe filled with phantom generalized Chaplygin gas can conform to the data of astronomical observations. We shall see that if the universe is only filled with generalized phantom Chaplygin gas with equation of state $p=-c^2s^2/\rho^{\alpha}$ with $\alpha<-1$, then such a model cannot be matched to the data of astronomical observations. To construct matched models one actually need to add dark matter. This procedure results in cosmological scenarios which do not contradict the data of astronomical observations and allows one to estimate how long we are now from the future big freeze doomsday.Comment: 8 page

The Big Trip and Wheeler-DeWitt equation

Of all the possible ways to describe the behavior of the universe that has undergone a big trip the Wheeler-DeWitt equation should be the most accurate -- provided, of course, that we employ the correct formulation. In this article we start by discussing the standard formulation introduced by Gonz\'alez-D\'iaz and Jimenez-Madrid, and show that it allows for a simple yet efficient method of the solution's generation, which is based on the Moutard transformation. Next, by shedding the unnecessary restrictions, imposed on aforementioned standard formulation we introduce a more general form of the Wheeler-DeWitt equation. One immediate prediction of this new formula is that for the universe the probability to emerge right after the big trip in a state with $w=w_0$ will be maximal if and only if $w_0=-1/3$.Comment: accepted in Astrophysics and Space Scienc

An Infrared Divergence Problem in the cosmological measure theory and the anthropic reasoning

An anthropic principle has made it possible to answer the difficult question of why the observable value of cosmological constant ($\Lambda\sim 10^{-47}$ GeV${}^4$) is so disconcertingly tiny compared to predicted value of vacuum energy density $\rho_{SUSY}\sim 10^{12}$ GeV${}^4$. Unfortunately, there is a darker side to this argument, as it consequently leads to another absurd prediction: that the probability to observe the value $\Lambda=0$ for randomly selected observer exactly equals to 1. We'll call this controversy an infrared divergence problem. It is shown that the IRD prediction can be avoided with the help of a Linde-Vanchurin {\em singular runaway measure} coupled with the calculation of relative Bayesian probabilities by the means of the {\em doomsday argument}. Moreover, it is shown that while the IRD problem occurs for the {\em prediction stage} of value of $\Lambda$, it disappears at the {\em explanatory stage} when $\Lambda$ has already been measured by the observer.Comment: 9 pages, RevTe

Slow-roll, acceleration, the Big Rip and WKB approximation in NLS-type formulation of scalar field cosmology

Aspects of non-linear Schr\"{o}dinger-type (NLS) formulation of scalar (phantom) field cosmology on slow-roll, acceleration, WKB approximation and Big Rip singularity are presented. Slow-roll parameters for the curvature and barotropic density terms are introduced. We reexpress all slow-roll parameters, slow-roll conditions and acceleration condition in NLS form. WKB approximation in the NLS formulation is also discussed when simplifying to linear case. Most of the Schr\"{o}dinger potentials in NLS formulation are very slowly-varying, hence WKB approximation is valid in the ranges. In the NLS form of Big Rip singularity, two quantities are infinity in stead of three. We also found that approaching the Big Rip, $w_{\rm eff}\to -1 + {2}/{3q}$, $(q<0)$ which is the same as effective phantom equation of state in the flat case.Comment: [7 pages, no figure, more reference added, accepted by JCAP