Sudden singularities occur in FRW spacetimes when the scale factor remains finite and different from zero while some of its derivatives diverge. After proper rescaling, the scale factor close to such a singularity at $t=0$ takes the form $a(t)=1+ c |t|^η$ (where $c$ and $η$ are parameters and $η\geq 0$). We investigate analytically and numerically the geodesics of free and gravitationally bound particles through such sudden singularities. We find that even though free particle geodesics go through sudden singularities for all $η\geq 0$, bound systems get dissociated for a wide range of the parameter $c$. For $η<1$ bound particles receive a diverging impulse at the singularity and get dissociated for all positive values of the parameter $c$. For $η> 1$ (Sudden Future Singularities (SFS)) bound systems get a finite impulse that depends on the value of $c$ and get dissociated for values of $c$ larger than a critical value $c_{cr}(η,ω_0)>0$ that increases with the value of $η$ and the rescaled angular velocity $ω_0$ of the bound system. We obtain an approximate equation for the analytical estimate of $c_{cr}(η,ω_0)$. We also obtain its accurate form by numerical derivation of the bound system orbits through the singularities. Bound system orbits through Big Brake singularities ($c<0$, $1<η<2$) are also derived numerically and are found to get disrupted at the singularity. However, they remain bound for all values of the parameter $c$ considered.
Cosmological observations allow the possibility that dark energy is caused by phantom fields. These fields typically lead to the occurrence of singularities in the late Universe. We review here the status of phantom singularities and their possible avoidance in a quantum theory of gravity. We first introduce phantom energy and discuss its behavior in cosmology. We then list the various types of singularities that can occur from its presence. We also discuss the possibility that phantom behavior is mimicked by an alternative theory of gravity. We finally address the quantum cosmology of these m…
We show that cosmological sudden singularities that respect the energy conditions can occur at finite times in Brans-Dicke and more general scalar-tensor theories of gravity. We construct these explicitly in the Friedmann universes. Higher-order versions of these singularities are also possible, including those that arise with when scalar fields have a self-interaction potential of power-law form.7 pages, no figures
We demonstrate the existence of sudden, finite-time, singularities, with constant scale factor, expansion rate and density, in expanding Bianchi type IX universes with free anisotropic pressures. A new type of non-simultaneous anisotropic sudden singularity arises because of the divergences of the pressures, which may be of barrel or pancake type. The effect of one or more directions of expansion hitting a sudden singularity is tantamount to dimensional reductions as the non-singular directions continue expanding and can see the sudden singularity in their past.
We verify the existence of Generalized Sudden Future Singularities (GSFS) in quintessence models with scalar field potential of the form $V(ϕ)\sim \vert ϕ\vert^n$ where $0<n<1$ and in the presence of a perfect fluid, both numerically and analytically, using a proper generalized expansion ansatz for the scale factor and the scalar field close to the singularity. This generalized ansatz includes linear and quadratic terms, which dominate close to the singularity and cannot be ignored when estimating the Hubble parameter and the scalar field energy density; as a result, they are important for ana…
In this work, we explore cosmological sudden singularities arising in the dynamically equivalent scalar-tensor representation of generalized hybrid metric-Palatini gravity. Using a FLRW background, we show that the structure of the field equations prevents sudden singularities from arising at time derivatives of the scale factor of orders lower than four, but that they are allowed to appear for time derivatives of higher orders. Imposing an ansatz for the scale factor, we provide an explicit solution where these sudden singularities appear in the fourth-order time derivative of the scale facto…
The Belinski-Khalatnikov-Lifshitz scenario concerns the existence of generic singularity of general relativity. At the singularity, there is a breakdown of all known laws of physics. Quantization of this scenario leads, however, to regular quantum evolution. The singularity is avoided by a quantum bounce. It is fairly probable that quantum general relativity, to be constructed, would be free from singularities. Thus, it could be used to address issues such as the quantum fates of cosmological and black holes singularities.
"Expansion" around the vacuum equation of state - sudden future singularities and asymptotic behavior
研究了状态方程为p_d=-rho_d - A rho_d^alpha的暗能量模型.该模型包括并提供了几种类型的奇异性在不同的参数制度的实现：在有限时间和有限值的标度因子的暗能量密度和压力的发散，奇异性的“大裂缝”型和突然的未来的奇异性最近引入的巴罗。对于导致宇宙非奇异膨胀的参数选择，我们发现了各种类型的渐近演化，用解析和数值方法描述了宇宙的整个时间演化。讨论了这种暗能量状态方程作为暗能量参数化的优点。
We study the future cosmological singularities in the framework of massive gravity and minimal massive bigravity theory. In this regards, we consider the possible classes of finite-time future singularities such as sudden, big rip, big freeze and big brake singularities in the massive universe. In dRGT model with an open expanding universe we obtain the sudden singularity in the future at a finite-time which generally without taking account of any particular realistic equation of state, is not avoidable and except the fluid density, all dynamical physical quantities such as pressure approach t…
We demonstrate analytically and numerically the existence of geodesically complete singularities in quintessence and scalar tensor quintessence models with scalar field potential of the form $V(ϕ)\sim \vert ϕ\vert^n$ with $0<n<1$. In the case of quintessence, the singularity which occurs at $ϕ=0$, involves divergence of the third time derivative of the scale factor (Generalized Sudden Future Singularity (GSFS)), and of the second derivative of the scalar field. In the case of scalar-tensor quintessence with the same potential and with a linear minimal coupling ($F(ϕ)=1-λϕ$), the singularity is…
In this work, we study the possibility of finite-time future cosmological singularities appearing in $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the stress-energy tensor. We present the theory in both the geometrical and the dynamically equivalent scalar-tensor representation and obtain the respective equations of motion. In a background Friedmann-Lemaître-Robertson-Walker (FLRW) universe with an arbitrary curvature and for a generic $C^\infty$ function $f(R,T)$, we prove that the conservation of the stress-energy tensor prevents the appearance of sudden singulariti…
In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the appro…
Fate of "Space-like singularities" in $c=1$ Matrix Model
University of Kentucky（肯塔基大学）；Korea Institute for Advanced Study（韩国高等研究院）；Tsinghua University（清华大学）；International Center for Theoretical Physics（国际理论物理中心）
The discovery of accelerated expansion of the universe opened the possibility of new scenarios for the doom of our spacetime, besides aeternal expansion and a final contraction. In this paper we review the chances which may await our universe. In particular, there are new possible singular fates (sudden singularities, big rip...), but there also other evolutions which cannot be considered as singular. In addition to this, some of the singular fates are not strong enough in the sense that the spacetime can be extended beyond the singularity. For deriving our results we make use of generalised p…
We investigate further (cf. arXiv:1512.01199, JCAP01 (2016) 040) Starobinsky cosmological model $R+γR^2$ in the Palatini formalism with Chaplygin gas and baryonic matter as a source. For this aim we use dynamical system theory. The dynamics is reduced to the 2D sewn dynamical system of a Newtonian type (a piecewise-smooth dynamical system). We classify all evolutional paths in the model as well as trajectories in the phase space. We demonstrate the presence of a degenerate freeze singularity (glued freeze type singularities) for the positive $γ$. In this case it is a generic feature of early e…
