Future Singularities Research Articles

“Expansion” around the vacuum: how far can we go fromΛ?

The cosmological constant ( Λ ), i.e., the energy density stored in the true vacuum state of all existing fields in the Universe, is the simplest and the most natural possibility for describing the current cosmic acceleration. However, despite its observational successes, such a possibility exacerbates the well known Λ problem, requiring a natural explanation for its small, but nonzero, value. In this paper we discuss how different our Universe may be from the Λ CDM model by studying observational aspects of a kind of “expansion” around the vacuum given by the equation of (EOS) $p_{\rm d}=-\rho_{\rm d} - A \rho_{\rm d}^{\alpha}$. In different parameter regimes, such a parametrization is capable of describing both quintessence-like and phantom-like dark energy, transient acceleration, and various (non)singular possibilities for the final destiny of the Universe, including singularities at finite values of the scale factor, the so-called “Big Rip”, as well as sudden future singularities. By using some of the most recent cosmological observations we show that, if the functional form of the dark energy EOS has additional parameters, very little can be said about their values from the current observational results, which postpones a definitive answer to the question posed above until the arrival of more precise observational data

DYNAMICS OF DARK ENERGY

We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Does the Big Rip survive quantization?

It is known that certain quantum cosmological models present quantum behavior for large scale factors. Since quantization can suppress past singularities, it is natural to inquire whether quantum effects can prevent future singularities. To this end, a Friedmann–Robertson–Walker quantum cosmological model dominated by a phantom energy fluid is investigated. The classical model displays accelerated expansion ending in a Big Rip. The quantization is performed in three different ways, which turn out to lead to the same result, namely there is a possibility that quantum gravitational effects could not remove the Big Rip.

Avoidance of future singularities in loop quantum cosmology

We consider the fate of future singularities in the effective dynamics of loop quantum cosmology. Nonperturbative quantum geometric effects which lead to ${\ensuremath{\rho}}^{2}$ modification of the Friedmann equation at high energies result in generic resolution of singularities whenever energy density $\ensuremath{\rho}$ diverges at future singularities of Friedmann dynamics. Such quantum effects lead to the avoidance of a big rip, which is followed by a recollapsing universe stable against perturbations. Resolution of sudden singularity, the case when pressure diverges but energy density approaches a finite value depends on the ratio of the latter to a critical energy density of the order of the Planck value. If the value of this ratio is greater than unity, the universe escapes the sudden future singularity and becomes oscillatory.

On the CMC foliation of future ends of a spacetime

We consider spacetimes with compact Cauchy hypersurfaces and with Ricci tensor bounded from below on the set of timelike unit vectors, and prove that the results known for spacetimes satisfying the timelike convergence condition, namely, foliation by CMC hypersurfaces, are also valid in the present situation, if corresponding further assumptions are satisfied. In addition we show that the volume of any sequence of spacelike hypersurfaces, which run into the future singularity, decays to zero provided there exists a time function covering a future end, such that the level hypersurfaces have nonnegative mean curvature and decaying volume.

Strings at future singularities

We discuss the behavior of strings propagating in spacetimes which allow future singularities of either a sudden future or a Big-Rip type. We show that in general the invariant string size remains finite at sudden future singularities while it grows to infinity at a Big-Rip. This claim is based on the discussion of both the tensile and null strings. In conclusion, strings may survive a sudden future singularity, but not a Big-Rip where they are infinitely stretched.

The oscillating dark energy: future singularity and coincidence problem

We consider the oscillating dark energy with periodic equation of state in two equivalent formulations: ideal fluid or scalar-tensor theory. It is shown that such dark energy suggests the natural way for the unification of early-time inflation with late-time acceleration. We demonstrate how it describes the transition from deceleration to acceleration or from non-phantom to phantom era and how it solves the coincidence problem. The occurence of finite-time future singularity for the oscillating (phantom) universe is also investigated.

Quantum cosmology: expectations and results

We study cosmologies based on low-energy effective string theory with higher-order string corrections to a tree-level action and with a modulus scalar field (dilaton or compactification modulus). In the presence of such corrections it is possible to construct nonsingular cosmological solutions in the context of Pre-Big-Bang and Ekpyrotic universes. We review the construction of nonsingular bouncing solutions and resulting density perturbations in Pre-Big-Bang and Ekpyrotic models. We also discuss the effect of higher-order string corrections on a dark energy universe and show several interesting possibilities of the avoidance of future singularities.

Quantum effects, soft singularities and the fate of the universe in a braneworld cosmology

We examine a class of braneworld models in which the expanding universe encounters a ‘quiescent’ future singularity. At a quiescent singularity, the energy density and pressure of the cosmic fluid as well as the Hubble parameter remain finite, while all derivatives of the Hubble parameter diverge (i.e., , etc →∞). Since the Kretschmann invariant diverges (RiklmRiklm → ∞) at the singularity, one expects quantum effects to play an important role as the quiescent singularity is approached. We explore the effects of vacuum polarization due to massless conformally coupled fields near the singularity and show that these can either cause the universe to recollapse or, else, lead to a softer singularity at which and remain finite, while and higher derivatives of the Hubble parameter diverge. An important aspect of the quiescent singularity is that it is encountered in regions of low density, which has obvious implications for a universe consisting of a cosmic web of high- and low-density regions—superclusters and voids. In addition to vacuum polarization, the effects of quantum particle production of non-conformal fields are also likely to be important. A preliminary examination shows that intense particle production can lead to an accelerating universe whose Hubble parameter shows oscillations about a constant value.

Duality gives rise to Chaplygin cosmologies with a big rip

We consider modifications to the Friedmann equation motivated by recent proposals along these lines pursuing an explanation to the observed late time acceleration. Here we show that these approaches can be framed within a theory with modified gravity, and we discuss the construction of the duals of the cosmologies generated within that framework. We then investigate the modifications required to generate extended, generalized and modified Chaplygin cosmologies, and then show that their duals belong to a larger family of cosmologies we call enlarged Chaplygin cosmologies. Finally, by letting the parameters of these models take values not earlier considered in the literature we show that some representatives of that family of cosmologies display sudden future singularities. This fact indicates that the behaviour of these spacetimes is rather different from that of generalized or modified Chaplygin gas cosmologies. This reinforces the idea that modifications of gravity can be responsible for unexpected evolutionary features in the universe.

Future state of the universe

AbstractFollowing the observational evidence for cosmic acceleration which may exclude a possibility for the universe to recollapse to a second singularity, we review alternative scenarios of its future evolution. Although the de Sitter asymptotic state is still an option, some other asymptotic states which allow new types of singularities such as Big‐Rip (due to a phantom matter) and sudden future singularities are also admissible and are reviewed in detail. The reality of these singularities which comes from the relation to observational characteristics of the universe expansion are also revealed and widely discussed.

Cosmologies from higher‐order string corrections

AbstractWe study cosmologies based on low‐energy effective string theory with higher‐order string corrections to a tree‐level action and with a modulus scalar field (dilaton or compactification modulus). In the presence of such corrections it is possible to construct nonsingular cosmological solutions in the context of Pre‐Big‐Bang and Ekpyrotic universes. We review the construction of nonsingular bouncing solutions and resulting density perturbations in Pre‐Big‐Bang and Ekpyrotic models. We also discuss the effect of higher‐order string corrections on a dark energy universe and show several interesting possibilities of the avoidance of future singularities.

VISCOUS FRW COSMOLOGY IN MODIFIED GRAVITY

We discuss a modified form of gravity implying that the action contains a power α of the scalar curvature. Coupling with the cosmic fluid is assumed. As equation of state for the fluid, we take the simplest version where the pressure is proportional to the density. Based upon a natural ansatz for the time variation of the scale factor, we show that the equations of motion are satisfied for a general α. Also the condition of conservation of energy and momentum is satisfied. Moreover, we investigate the case where the fluid is allowed to possess a bulk viscosity, and find the noteworthy fact that consistency of the formalism requires the bulk viscosity to be proportional to the power (2α-1) of the scalar expansion. In Einstein's gravity, where α = 1, this means that the bulk viscosity is proportional to the scalar expansion. This mathematical result is of physical interest; as discussed recently by the authors, there exists in principle a viscosity-driven transition of the fluid from the quintessence region into the phantom region, implying a future Big Rip singularity.

Generalizing the generalized Chaplygin gas

The generalized Chaplygin gas is characterized by the equation of state p = - A/rho^alpha, with alpha > -1 and w > -1. We generalize this model to allow for the cases where alpha < -1 or w < -1. This generalization leads to three new versions of the generalized Chaplygin gas: an early phantom model in which w << -1 at early times and asymptotically approaches w = -1 at late times, a late phantom model with w \approx -1 at early times and w -> - \infty at late times, and a transient model with w \approx -1 at early times and w -> 0 at late times. We consider these three cases as models for dark energy alone and examine constraints from type Ia supernovae and from the subhorizon growth of density perturbations. The transient Chaplygin gas model provides a possible mechanism to allow for a currently accelerating universe without a future horizon, while some of the early phantom models produce w < -1 without either past or future singularities.

Two-Flux Colliding Plane Waves in String Theory**The project supportedby National Natural Science Foundation of China under Grant No. 10405028

We construct the two-flux colliding plane wave solutions inhigher-dimensional gravity theory with dilaton, and two complementaryfluxes. Two kinds of solutions have been obtained: Bell-Szekeres (BS) type andhomogeneous type. After imposing the junction condition, we find thatonly the BS type solution is physically well-defined. Furthermore,we show that the future curvature singularity is always developedfor our solutions.

Statefinders, higher-order energy conditions, and sudden future singularities

We link observational parameters such as the deceleration parameter, the jerk, the kerk (snap) and higher-order derivatives of the scale factor, called statefinders, to the conditions which allow to develop sudden future singularities of pressure with finite energy density. In this context, and within the framework of Friedmann cosmology, we also propose higher-order energy conditions which relate time derivatives of the energy density and pressure which may be useful in general relativity.

Inhomogeneous equation of state of the universe: Phantom era, future singularity, and crossing the phantom barrier

The dark energy universe equation of state (EOS) with inhomogeneous, Hubble parameter dependent term is considered. The motivation to introduce such a term comes from time-dependent viscosity considerations and modifications of general relativity. For several explicit examples of such EOS it is demonstrated how the type of future singularity changes, how the phantom epoch emerges and how the crossing of a phantom barrier occurs. Similar cosmological regimes are considered for the universe with two interacting fluids and for the universe with implicit EOS. For instance, the crossing of the phantom barrier is realized in an easier way, thanks to the presence of inhomogeneous term. The thermodynamical dark energy model is presented where the universe entropy may be positive even at the phantom era as a result of the crossing of the $w=\ensuremath{-}1$ barrier.

LATE-TIME PHANTOM UNIVERSE IN SO(1, 1) DARK ENERGY MODEL WITH EXPONENTIAL POTENTIAL

We discuss the late-time property of universe and phantom field in the SO(1, 1) dark energy model for the potential V = V0e-βΦα with α and β two positive constants. We assume in advance some conditions satisfied by the late-time field to simplify equations, which are confirmed to be correct from the eventual results. For α &lt; 2, the field falls exponentially off and the phantom equation of state rapidly approaches -1. When α = 2, the kinetic energy ρk and the coupling energy ρc become comparable but there is always ρk &lt; -ρc so that the phantom property of field proceeds to hold. The analysis on the perturbation to the late-time field Φ illustrates the square effective mass of the perturbation field is always positive and thus the phantom is stable. The universe considered currently may evade the future sudden singularity and will evolve to de Sitter expansion phase.

Inhomogenized sudden future singularities

We find that sudden future singularities may also appear in spatially inhomogeneous Stephani models of the universe. They are temporal pressure singularities and may appear independently of the spatial finite density singularities already known to exist in these models. It is shown that the main advantage of the homogeneous sudden future singularities which is the fulfillment of the strong and weak energy conditions may not be the case for inhomogeneous models.

Expansion around the vacuum equation of state: Sudden future singularities and asymptotic behavior

The dark energy model with the equation of state ${p}_{d}=\ensuremath{-}{\ensuremath{\rho}}_{d}\ensuremath{-}A{\ensuremath{\rho}}_{d}^{\ensuremath{\alpha}}$ is studied. The model comprises and provides realization of several types of singularities in different parameter regimes: the divergence of the dark energy density and pressure at finite time and finite value of the scale factor, the singularity of the ``big rip'' type and the sudden future singularity recently introduced by Barrow. For parameter choices which lead to a nonsingular expansion of the universe, various types of the asymptotic evolution are found. The entire time evolution of the universe is described both analytically and numerically. The advantages of this dark energy EOS as a parametrization of dark energy are discussed.