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

Nonperturbative models of quark stars in f(R)f(R) gravity

Quark star models with realistic equation of state in nonperturbative $f(R)$ gravity are considered. The mass-radius relation for $f(R)=R+\alpha R^2$ model is obtained. Considering scalar curvature $R$ as an independent function, one can find out, for each value of central density, the unique value of central curvature for which one has solutions with the required asymptotic $R\rightarrow 0$ for $r\rightarrow\infty$. In another words, one needs a fine-tuning for $R$ to achieve quark stars in $f(R)$ gravity. We consider also the analogue description in corresponding scalar-tensor gravity. The fine-tuning on $R$ is equivalent to the fine-tuning on the scalar field $\phi$ in this description. For distant observers, the gravitational mass of the star increases with increasing $\alpha$ ($\alpha>0$) but the interpretation of this fact depends on frame where we work. Considering directly $f(R)$ gravity, one can say that increasing of mass occurs by the "gravitational sphere" outside the star with some "effective mass". On the other hand, in scalar-tensor theory, we also have a dilaton sphere (or "disphere") outside the star but its contribution to gravitational mass for distant observer is negligible. We show that it is possible to discriminate modified theories of gravity from General Relativity due to the gravitational redshift of the thermal spectrum emerging from the surface of the star.Comment: 9 pages, 5 figures, accepted for publication in Phys. Lett.

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

Dynamical analysis of the Tsallis holographic dark energy models with event horizon as cut-off and interaction with matter

The model of generalized Tsallis holographic dark energy (which is known to be particular representative of Nojiri-Odintsov HDE) with event horizon as cut-off is investigated using methods of dynamical analysis. We take into consideration possible interaction with dark energy and matter in various forms. Critical points are determined. Cosmological evolution of the Universe depends from interaction parameters. If we use event horizon scale as cutoff quasi-de Sitter expansion is possible only for interaction of type $\sim H(\alpha\rho_{de}+\beta\rho_{m})$ (where $H$ is the Hubble parameter). For interactions $\sim \rho_m \rho_{de} /H$ and $\sim H \rho_{m}^{\alpha}\rho_{de}^{1-\alpha}$ Universe eventually stops ($H\rightarrow 0$) or ends its existence in final singularity ($H\rightarrow\infty$). In first case fraction of dark energy tends to $1$ or constant value lesser than 1 because dynamical equilibrium between matter and dark energy is established on late times.Comment: 23 pp., 9 figs., to appear in Int. J. Mod. Phys.

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

Causal Limit of Neutron Star Maximum Mass in f(R)f(R) Gravity in View of GW190814

We investigate the causal limit of maximum mass for stars in the framework of$f(R)$ gravity. We choose a causal equation of state, with variable speed of sound, and with the transition density and pressure corresponding to the SLy equation of state. The transition density is chosen to be equal to twice the saturation density $\rho_t\sim 2\rho_0$, and also the analysis is performed for the transition density, chosen to be equal to the saturation density $\rho_t\sim \rho_0$. We examine numerically the combined effect of the stiff causal equation of state and of the sound speed on the maximum mass of static neutron stars, in the context of Jordan frame of $f(R)$ gravity. This yields the most extreme upper bound for neutron star masses in the context of extended gravity. As we will evince for the case of $R^2$ model, the upper causal mass limit lies within, but not deeply in, the mass-gap region, and is marginally the same with the general relativistic causal maximum mass, indicating that the $\sim 3M_{\odot}$ general relativistic limit is respected. In view of the modified gravity perspective for the secondary component of the GW190814 event, we also discuss the strange star possibility. Using several well established facts for neutron star physics and the Occam's razor approach, although the strange star is exciting, for the moment, it remains a possibility for describing the secondary component of GW190814. We underpin the fact that the secondary component of the compact binary GW190814 is probably a neutron star, a black hole or even a rapidly rotating neutron star, but not a strange star. We also discuss, in general, the potential role of the extended gravity description for the binary merging.Comment: PLB Accepte

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

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

Multiple Λ\LambdaCDM cosmology with string landscape features and future singularities

Multiple $\Lambda$CDM cosmology is studied in a way that is formally a classical analog of the Casimir effect. Such cosmology corresponds to a time-dependent dark fluid model or, alternatively, to its scalar field presentation, and it motivated by the string landscape picture. The future evolution of the several dark energy models constructed within the scheme is carefully investigated. It turns out to be almost always possible to choose the parameters in the models so that they match the most recent and accurate astronomical values. To this end, several universes are presented which mimick (multiple) $\Lambda$CDM cosmology but exhibit Little Rip, asymptotically de Sitter, or Type I, II, III, and IV finite-time singularity behavior in the far future, with disintegration of all bound objects in the cases of Big Rip, Little Rip and Pseudo-Rip cosmologies.Comment: LaTeX 11 pages, 10 figure