Future Singularities Research Articles

Future singularity avoidance in phantom dark energy models

Different approaches to quantum cosmology are studied in order to deal with the future singularity avoidance problem. Our results show thatthese future singularities will persist but could take different forms. As an example we have studied the big rip which appear when one considers the state equation P = ωρwith ω < −1, showing that it does not disappear inmodified gravity. On the other hand, it is well-known that quantum geometric effects (holonomy corrections) in loop quantum cosmology introduce a quadratic modification, namely proportional to ρ2, in Friedmann's equationthat replace the big rip by a non-singular bounce. However this modified Friedmann equation could have been obtained in an inconsistent way, whatmeans that the obtained results from this equation, in particular singularity avoidance, would be incorrect. In fact, we will show that instead of a non-singular bounce, the big ripsingularity would be replaced, in loop quantum cosmology, by other kind of singularity.

Rip/singularity free cosmology models with bulk viscosity

In this paper we present two concrete models of non-perfect fluid with bulk viscosity to interpret the observed cosmic accelerating expansion phenomena, avoiding the introduction of exotic dark energy. The first model we inspect has a viscosity of the form ${\zeta} = {\zeta}_0 + ({\zeta}_1-{\zeta}_2q)H$ by taking into account of the decelerating parameter q, and the other model is of the form ${\zeta} = {\zeta}_0 + {\zeta}_1H + {\zeta}_2H^2$. We give out the exact solutions of such models and further constrain them with the latest Union2 data as well as the currently observed Hubble-parameter dataset (OHD), then we discuss the fate of universe evolution in these models, which confronts neither future singularity nor little/pseudo rip. From the resulting curves by best fittings we find a much more flexible evolution processing due to the presence of viscosity while being consistent with the observational data in the region of data fitting. With the bulk viscosity considered, a more realistic universe scenario is characterized comparable with the {\Lambda}CDM model but without introducing the mysterious dark energy.

Observational constraints on finite scale factor singularities

We discuss the combined constraints on a Finite Scale Factor Singularity (FSF) universe evolution scenario, which come from the shift parameter ℛ, baryon acoustic oscillations (BAO) \U0001d49c, and from the type Ia supernovae.We show that observations allow existence of such singularities in the 2 × 109 years in future (at 1σ CL) which is much farther than a Sudden Future Singularity (SFS), and that at the present moment of the cosmic evolution, one cannot differentiate between cosmological scenario which allow finite scale factor singularities and the standard ΛCDM dark energy models. We also show that there is an allowed value of m = 2/3 within 1σ CL, which corresponds to a dust-filled Einstein-de-Sitter universe limit of the early time evolution and so it is pasted into a standard early-time scenario.

Om diagnostic of dilaton dark energy with two-parameter ω in potential [1+(σ−A)2]e (−Bσ)

Based on a new geometric diagnostic method-Om, we consider a new independent-model parametrization $\omega=\omega_{0}+\omega_{1}(\frac{z}{1+z})^{n}$ . When we work in potential W σ [1+(σ−A)2]e (−Bσ), we investigate the evolutional behavior of Om with respect to red-shift z and the influence of coupling parameter α on the trajectory of Om with respect to z. We get that phantom model of Dilaton dark energy can avoid the future singularity “Big Rip”. The numerical results give current value of EOS $\omega_{\sigma_{0}}=-0.956$ which fits the latest observational data WMAP5+BAO+SNe very well.

Scalar dark energy models mimicking ΛCDM with arbitrary future evolution

Dark energy models with various scenarios of evolution are considered from the viewpoint of the formalism for the equation of state. It is shown that these models are compatible with current astronomical data. Some of the models presented here evolve arbitrarily close to ΛCDM up to the present, but diverge in the future into a number of different possible asymptotic states, including asymptotic de Sitter (pseudo-rip) evolution, little rips with disintegration of bound structures, and various forms of finite-time future singularities. Therefore it is impossible from observational data to determine whether the universe will end in a future singularity or not. We demonstrate that the models under consideration are stable for a long period of time (billions of years) before entering a Little Rip/Pseudo-Rip induced dissolution of bound structures or before entering a soft finite-time future singularity. Finally, the physical consequences of Little Rip, Types II, III and Big Crush singularities are briefly compared.

Reconstruction off(T)gravity: Rip cosmology, finite-time future singularities, and thermodynamics

We demonstrate that there appear finite-time future singularities in $f(T)$ gravity with $T$ being the torsion scalar. We reconstruct a model of $f(T)$ gravity with realizing the finite-time future singularities. In addition, it is explicitly shown that a power-law-type correction term ${T}^{\ensuremath{\beta}}$ ($\ensuremath{\beta}&gt;1$) such as a ${T}^{2}$ term can remove the finite-time future singularities in $f(T)$ gravity. Moreover, we study $f(T)$ models with realizing inflation in the early universe, the $\ensuremath{\Lambda}\mathrm{CDM}$ model, little rip cosmology and pseudo-rip cosmology. It is demonstrated that the disintegration of bound structures for little rip and pseudo-rip cosmologies occurs in the same way as in gravity with corresponding dark energy fluid. We also discuss that the time-dependent matter instability in the star collapse can occur in $f(T)$ gravity. Furthermore, we explore thermodynamics in $f(T)$ gravity and illustrate that the second law of thermodynamics can be satisfied around the finite-time future singularities for the universe with the temperature inside the horizon being the same as that of the apparent horizon.

Classical and quantum massive cosmology for the open FRW universe

In an open Friedmann-Robertson-Walker (FRW) space background, we study the classical and quantum cosmological models in the framework of the recently proposed nonlinear massive gravity theory. Although the constraints which are present in this theory prevent it from admitting the flat and closed FRW models as its cosmological solutions, for the open FRW universe it is not the case. We have shown that, either in the absence of matter or in the presence of a perfect fluid, the classical field equations of such a theory adopt physical solutions for the open FRW model, in which the mass term shows itself as a cosmological constant. These classical solutions consist of two distinguishable branches: One is a contacting universe which tends to a future singularity with zero size, while another is an expanding universe having a past singularity from which it begins its evolution. A classically forbidden region separates these two branches from each other. We then employ the familiar canonical quantization procedure in the given cosmological setting to find the cosmological wave functions. We use the resulting wave function to investigate the possibility of the avoidance of classical singularities due to quantum effects. It is shown that the quantum expectation values of the scale factor, although they have either contracting or expanding phases like their classical counterparts, are not disconnected from each other. Indeed, the classically forbidden region may be replaced by a bouncing period in which the scale factor bounces from the contraction to its expansion eras. Using the Bohmian approach of quantum mechanics, we also compute the Bohmian trajectory and the quantum potential related to the system, which their analysis shows are the direct effects of the mass term on the dynamics of the universe.

Cosmological tests of sudden future singularities

We discuss combined constraints, coming from the cosmic microwave background shift parameter $\mathcal{R}$, baryon acoustic oscillations (BAO) distance parameter $\mathcal{A}$, and from the latest type Ia supernovae data, imposed on cosmological models which allow sudden future singularities of pressure. We show that due to their weakness such sudden singularities may happen in the very near future and that at present they can mimic standard dark energy models.

Holographic induced gravity model with a Ricci dark energy: Smoothing the little rip and big rip through Gauss-Bonnet effects?

We present an holographic brane-world model of the Dvali-Gabadadze-Porrati (DGP) scenario with and without a Gauss-Bonnet term (GB) in the bulk. We show that an holographic dark energy component with the Ricci scale as the infrared cutoff can describe the late-time acceleration of the Universe. In addition, we show that the dimensionless holographic parameter is very important in characterizing the DGP branches, and in determining the behavior of the Ricci dark energy as well as the asymptotic behavior of the brane. On the one hand, in the DGP scenario the Ricci dark energy will exhibit a phantomlike behavior with no big rip if the holographic parameter is strictly larger than $1/2$. For smaller values, the brane hits a big rip or a little rip. On the other hand, we have shown that the introduction of the GB term avoids the big rip and little rip singularities on both branches but cannot avoid the appearance of a big freeze singularity for some values of the holographic parameter on the normal branch, however, these values are very unlikely because they lead to a very negative equation of state at the present and therefore we can speak in practice of singularity avoidance. At this regard, the equation of state parameter of the Ricci dark energy plays a crucial role, even more important than the GB parameter, in rejecting the parameter space where future singularities appear.

Can quantum effects due to a massless conformally coupled field avoid gravitational singularities?

Using quantum corrections from massless fields conformally coupled to gravity, we study the possibility of avoiding singularities that appear in the flat Friedmann-Robertson-Walker model. We assume that the universe contains a barotropic perfect fluid with the state equation p = ωρ, where p is the pressure and ρ is the energy density. We study the dynamics of the model for all values of the parameter ω and also for all values of the conformal anomaly coefficients α and β. We show that singularities can be avoided only in the case where α > 0 and β −1 (only a one-parameter family of solutions, but no a general solution, has this behavior at late times), the initial conditions of the nonsingular solutions at early times must be chosen very exactly. These nonsingular solutions consist of a general solution (a two-parameter family) exiting the contracting de Sitter phase and a one-parameter family exiting the contracting Friedmann phase. On the other hand, for ω < −1 (a phantom field), the problem of avoiding singularities is more involved because if we consider an expanding Friedmann phase at early times, then in addition to fine-tuning the initial conditions, we must also fine-tune the parameters α and β to obtain a behavior without future singularities: only a oneparameter family of solutions follows a contracting Friedmann phase at late times, and only a particular solution behaves like a contracting de Sitter universe. The other solutions have future singularities.

Generalized second law of thermodynamics in f(T) gravity**K. Karami dedicated this paper to the 80 year Jubilee of Professor Yousef Sobouti.

We investigate the validity of the generalized second law (GSL) ofgravitational thermodynamics in the framework of f(T) modifiedteleparallel gravity. We consider a spatially flat FRW universecontaining only the pressureless matter. The boundary of theuniverse is assumed to be enclosed by the Hubble horizon. For twoviable f(T) models containing f(T) = T+μ1{(−T)}n andf(T) = T−μ2T(1−eβT0/T), we first calculate theeffective equation of state and deceleration parameters. Then,{we investigate the null and strong energy conditions andconclude that a sudden future singularity appears in both models.Furthermore, using a cosmographic analysis we check the viability oftwo models. Finally, we examine the validity of the GSL and findthat for both models it} is satisfied from the early times to thepresent epoch. But in the future, the GSL is violated for thespecial ranges of the torsion scalar T.

Screening of cosmological constant for de Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities

We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom-like phases. In particular, it is found that there is a case in which a crossing of the phantom divide from the non-phantom (quintessence) phase to the phantom one can be realized when a finite-time future singularity occurs. Moreover, it is demonstrated that the addition of an $R^2$ term can cure the finite-time future singularities in non-local gravity. It is also suggested that in the framework of non-local gravity, adding an $R^2$ term leads to possible unification of the early-time inflation with the late-time cosmic acceleration.

Phantom cosmology without Big Rip singularity

We construct phantom energy models with the equation of state parameter w which is less than −1, 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.

A thermodynamic characterization of future singularities?

In this Letter we consider three future singularities in different Friedmann–Lemaître–Robertson–Walker scenarios and show that the universe departs more and more from thermodynamic equilibrium as the corresponding singularity is approached. Though not proven in general, this feature may characterize future singularities of homogeneous and isotropic cosmologies.

Scalar-tensor theory with Lagrange multipliers: A way of understanding the cosmological constant problem, and future singularities

The use of Lagrange multipliers in the context of quintessence/phantom scalar fields allows us to constrain the behavior of the scalar field, which provides a powerful tool, not only for the reconstruction of cosmological solutions but also for the study of some problems in cosmology and gravitational physics. In the present paper, we focus on the reconstruction of cosmological solutions capable of controlling the cosmological constant value by imposing a constraint on the scalar field, providing a relaxation mechanism of the value of the cosmological constant. The formalism is also extended to the study of phantom scalar fields with a future singularity and their conformal transformation to the Jordan frame, where a type of modified gravity, constrained by the Lagrange multiplier, can be constructed.

Cosmological time versus CMC time in spacetimes of constant curvature

In this paper, we investigate the existence of foliations by constant mean curvature (CMC) hypersurfaces in maximal, globally hyperbolic, spatially compact, spacetimes of constant curvature. In the non-positive curvature case (i.e. for flat and locally anti-de Sitter spacetimes), we prove the existence of a global foliation of the spacetime by CMC Cauchy hypersurfaces. The positive curvature case (i.e. locally de Sitter spacetimes) is more delicate: in general, we are only able to prove the existence of a foliation by CMC Cauchy hypersurfaces in a neighbourhood of the past (or future) singularity. Except in some exceptional and elementary cases, the leaves of the foliation we construct are the level sets of a time function, and the mean curvature of the leaves increases with time. In this case, we say that the spacetime admits a CMC time function. Our proof is based on using the level sets of the cosmological time function as barriers. A major part of the work consists of proving the required curvature estimates for these level sets. One of the difficulties is the fact that the local behaviour of the cosmological time function near one point depends on the global geometry of the spacetime.

Sudden singularities survive massive quantum particle production

We solve the Klein-Gordon equation for a massive, nonminimally coupled scalar field, with a conformal coupling, undergoing cosmological evolution from a radiation-dominated phase to a future sudden singularity. We show that, after regularization, the energy of the created particles is zero and the backreaction from quantum effects does not change the evolution of the Universe near the future singularity and cannot prevent the finite-time sudden singularity.

Universal procedure to cure future singularities of dark energy models

A systematic search for different viable models of the dark energy universe, all of which give rise to finite-time, future singularities, is undertaken, with the purpose to try to find a solution to this common problem. After some work, a universal procedure to cure all future singularities is developed and carefully tested with the help of explicit examples corresponding to each one of the four different types of possible singularities, as classified in the literature. The cases of a fluid with an equation of state which depends on some parameter, of modified gravity non-minimally coupled to a matter Lagrangian, of non-local gravity, and of isotropic turbulence in a dark fluid universe theory are investigated in detail.

Alternative mechanism of avoiding the big rip or little rip for a scalar phantom field

Depending on the choice of its potential, the scalar phantom field ϕ (the equation of state parameter w<−1) leads to various catastrophic fates of the universe including big rip, little rip and other future singularity. For example, big rip results from the evolution of the phantom field with an exponential potential and little rip stems from a quadratic potential in general relativity (GR). By choosing the same potential as in GR, we suggest a new mechanism to avoid these unexpected fates (big and little rip) in the inverse-R gravity. As a pedagogical illustration, we give an exact solution where phantom field leads to a power-law evolution of the scale factor in an exponential type potential. We also find the sufficient condition for a universe in which the equation of state parameter crosses w=−1 divide. The phantom field with different potentials, including quadratic, cubic, quantic, exponential and logarithmic potentials are studied via numerical calculation in the inverse-R gravity with R2 correction. The singularity is avoidable under all these potentials. Hence, we conclude that the avoidance of big or little rip is hardly dependent on special potential.

Viscous little rip cosmology

Dark energy of phantom or quintessence nature with an equation of state parameter $w$ almost equal to $\ensuremath{-}1$ often leads the universe evolution to a finite-time future singularity. An elegant solution to this problem has been recently proposed [P. H. Frampton, K. J. Ludwick, and R. J. Scherrer, Phys. Rev. D 84, 063003 (2011).] under the form of the so-called little rip cosmology, which appears to be a realistic alternative to the $\ensuremath{\Lambda}\mathrm{CDM}$ model. A viscous little rip cosmology is here proposed. Whereas generically bulk viscosity tends to promote the big rip, we find that there are a number of situations where this is not the case and where the formalism nicely adjusts itself to the little rip scenario. We prove, in particular, that a viscous fluid (or, equivalently, one with an inhomogeneous [imperfect] equation of state) is perfectly able to produce a little rip cosmology as a purely viscosity effect. The possibility of its induction as a combined result of viscosity and a general (powerlike) equation of state is also investigated in detail. To finish, a physical, inertial force interpretation of the dissolution of bound structures in the little rip cosmology is presented.