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

Phantom Cosmology without Big Rip Singularity

We construct phantom energy models with the equation-of-state parameter $w$ such that $w<-1$, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ("phantom energy" without "Big Rip" singularity) and (ii) energy density tends to constant value with time ("cosmological constant" with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of big trip via wormholes.Comment: LaTeX 13 pages, to appear in PL

Further stable neutron star models from f(R) gravity

Neutron star models in perturbative $f(R)$ gravity are considered with realistic equations of state. In particular, we consider the FPS, SLy and other equations of state and a case of piecewise equation of state for stars with quark cores. The mass-radius relations for $f(R)=R+R(e^{-R/R_{0}}-1)$ model and for $R^2$ models with logarithmic and cubic corrections are obtained. In the case of $R^2$ gravity with cubic corrections, we obtain that at high central densities ($\rho>10\rho_{ns}$, where $\rho_{ns}=2.7\times 10^{14}$ g/cm$^{3}$ is the nuclear saturation density), stable star configurations exist. The minimal radius of such stars is close to $9$ km with maximal mass $\sim 1.9 M_{\odot}$ (SLy equation). A similar situation takes place for AP4 and BSK20 EoS. Such an effect can give rise to more compact stars than in General Relativity. If observationally identified, such objects could constitute a formidable signature for modified gravity at astrophysical level. Another interesting result can be achieved in modified gravity with only a cubic correction. For some EoS, the upper limit of neutron star mass increases and therefore these EoS can describe realistic star configurations (although, in General Relativity, these EoS are excluded by observational constraints).Comment: 18 pages, 17 figures, revised version significally expanded, to appear in JCA

Maximal neutron star mass and the resolution of hyperon puzzle in modified gravity

The so-called hyperon puzzle in the theory of neutron stars is considered in the framework of modified $f(R)$ gravity. We show that for simple hyperon equations of state, it is possible to obtain the maximal neutron star mass which satisfies the recent observational data for PSR J1614-2230, in higher-derivative models with power-law terms as $f(R) = R+\alpha R^2+ \beta R^3$. The soft hyperon equation of state under consideration is usually treated as non-realistic in the standard General Relativity. The numerical analysis of Mass-Radius relation for massive neutron stars with hyperon equation of state in modified gravity turns out to be consistent with observations. Thus, we show that the same modified gravity can solve at once three problems: consistent description of the maximal mass of neutron star, realistic Mass-Radius relation and account for hyperons in equation of state.Comment: 10 pages, 6 figures, some misprints are fixe

Supermassive Neutron Stars in Axion F(R)F(R) Gravity

We investigated realistic neutron stars in axion $R^{2}$ gravity. The coupling between curvature and axion field $\phi$ is assumed in the simple form $\sim R^2\phi$. For the axion mass in the range $m_{a}\sim 10^{-11}-10^{-10}$ eV the solitonic core within neutron star and corresponding halo with size $\sim 100$ km can exist. Therefore the effective contribution of $R^2$ term grows inside the star and it leads to change of star parameters (namely, mass and radius). We obtained the increase of star mass independent from central density for wide range of masses. Therefore, maximal possible mass for given equation of state grows. At the same time, the star radius increases not so considerably in comparison with GR. {Hence, our model may predict possible existence of supermassive compact stars with masses $M\sim 2.2-2.3M_\odot$ and radii $R_{s}\sim 11$ km for realistic equation of state (we considered APR equation of state). In General Relativity one can obtain neutron stars with such characteristics only for unrealistic, extremely stiff equations of state.} Note that this increase of mass occurs due to change of solution for scalar curvature outside the star. In GR curvature drops to zero on star surface where $\rho=p=0$. In the model under consideration the scalar curvature dumps more slowly in comparison with vacuum $R^2$ gravity due to axion "galo" around the star.Comment: to appear in MNRAS, 9pp., 6 figure