We investigate the effects of quantum particle production on a classical sudden singularity occurring at fine time in a Friedmann universe. We use an exact solution to describe an initially radiation-dominated universe that evolves into a sudden singularity at finite time. We calculate the density of created particles exactly and find that it is generally much smaller than the classical background density and pressure which produce the sudden singularity. We conclude that, in the example studied, the quantum particle production does not lead to the avoidance or modification to the sudden future singularity. We argue that the effects of small residual anisotropies in the expansion will not change these results and show how they can be related to studies of classical particle production using a bulk viscosity. We conclude that we do not expect to see significant observable effects from local sudden singularities on our past light cone.
We discuss exotic singularities in the evolution of the universe motivated by the progress of observations in cosmology. Among them there are: Big-Rip (BR), Sudden Future Singularities (SFS), Generalized Sudden Future Singularities (GSFS), Finite Density Singularities (FD), type III, and type IV singularities. We relate some of these singularities with higher-order characteristics of expansion such as jerk and snap. We also discuss the behaviour of pointlike objects and classical strings on the approach to these 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.
We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-…
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.
We present a general form for the solution of an expanding general-relativistic Friedmann universe that encounters a singularity at finite future time. The singularity occurs in the material pressure and acceleration whilst the scale factor, expansion rate and material density remain finite and the strong energy condition holds. We also show that the same phenomenon occurs, but under different conditions, for Friedmann universes in gravity theories arising from the variation of an action that is an arbitrary analytic function of the scalar curvature.
We discuss the behaviour 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 standard energy conditions of classical general relativity are applied to FLRW cosmologies containing sudden future singularities. Here we show, in a model independent way, that although such cosmologies can satisfy the null, weak and strong energy conditions, they always fail to satisfy the dominant energy condition. They require a divergent spacelike energy flux in all but the comoving frame.
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.
We introduce a general characterization of sudden cosmological singularities and investigate the classical stability of homogeneous and isotropic cosmological solutions of all curvatures containing these singularities to small scalar, vector, and tensor perturbations using gauge invariant perturbation theory. We establish that sudden singularities at which the scale factor, expansion rate, and density are finite are stable except for a set of special parameter values. We also apply our analysis to the stability of Big Rip singularities and find the conditions for their stability against small …
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 show that a general solution of the Einstein equations that describes approach to an inhomogeneous and anisotropic sudden spacetime singularity does not experience geodesic incompleteness. This generalises the result established for isotropic and homogeneous universes. Further discussion of the weakness of the singularity is also included.
In this paper we analyze the effect of recently proposed classes of sudden future singularities on causal geodesics of FLRW spacetimes. Geodesics are shown to be extendible and just the equations for geodesic deviation are singular, although tidal forces are not strong enough to produce a Big Rip. For the sake of completeness, we compare with the typical sudden future singularities of phantom cosmologies.
We show that a singularity can occur at a finite future time in an expanding Friedmann universe even when the density is positive and the density plus the sum of the principal pressures is positive. Explicit examples are constructed and a simple condition is given which can be used to eliminate behaviour of this sort if it is judged to be unphysical.
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.
Solutions of the Friedmann-Lemaitre cosmological equations of general relativity have been found with finite-time singularities that are everywhere regular, have regular Hubble expansion rate, and obey the strong-energy conditions but possess pressure and acceleration singularities at finite time that are not associated with geodesic incompleteness. We show how these solutions with sudden singularities can be constructed using fractional series methods and find the limiting form of the equation of state on approach to the singularity.
The dark energy model with the equation of state p_d=-rho_d - A rho_d^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 …
The physically relevant singularities occurring in FRW cosmologies had traditionally been thought to be limited to the "big bang", and possibly a "big crunch". However, over the last few years, the zoo of cosmological singularities considered in the literature has become considerably more extensive, with "big rips" and "sudden singularities" added to the mix, as well as renewed interest in non-singular cosmological events such as "bounces" and "turnarounds". In this article we present a complete catalogue of such cosmological milestones, both at the kinematical and dynamical level. First, usin…
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…
It has been claimed in a recent paper \cite{bbfhd12} that sudden singularities will survive in semiclassical gravity. This issue is here carefully reviewed, pointing out that such conclusion, even if valid under some specific conditions, does not stand in other cases. An explicit example is studied in detail to support our statement, stemming from these other situations, that quantum effects may in fact drastically modify the behavior of sudden singularities.
We construct solutions of the Friedmann equations near a sudden singularity using generalized series expansions for the scale factor, the density, and the pressure of the fluid content. In this way, we are able to arrive at a solution with a sudden singularity containing two free constants, as required for a general solution of the cosmological equations.
In this talk we analyze the effect of recently proposed classes of sudden future singularities on causal geodesics of FLRW spacetimes. Geodesics are shown to be extendible and just the equations for geodesic deviation are singular, although tidal forces are not strong enough to produce a Big Rip.
We solve the Klein-Gordon equation for a massive, non-minimally coupled scalar field, with a conformal coupling, undergoing cosmological evolution from a radiation-dominated phase to a future sudden singularity. We show that, after regularisation, the energy of the created particles is zero and the back-reaction from quantum effects does not change the evolution of the universe near the future singularity and cannot prevent the finite-time sudden singularity.
We discuss the constraints coming from current observations of type Ia supernovae on cosmological models which allow sudden future singularities of pressure (with the scale factor and the energy density regular). We show that such a sudden singularity may happen in the very near future (e.g. within ten million years) and its prediction at the present moment of cosmic evolution cannot be distinguished, with current observational data, from the prediction given by the standard quintessence scenario of future evolution. Fortunately, sudden future singularities are characterized by a momentary pea…
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 par…
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…
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…
This paper is committed to calculations near a type of future singularity driven by phantom energy. At the singularities considered, the scale factor remains finite but its derivative diverges. The general behavior of barotropic phantom energy producing this singularity is calculated under the assumption that near the singularity such fluid is the dominant contributor. We use the semiclassical formula for renormalized stress tensors of conformally invariant fields in conformally flat spacetimes and analyze the softening/enhancing of the singularity due to quantum vacuum contributions. This dyn…
We consider the fate of future singularities in the effective dynamics of loop quantum cosmology. Non-perturbative quantum geometric effects which lead to $ρ^2$ modification of the Friedmann equation at high energies result in generic resolution of singularities whenever energy density $ρ$ 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…
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…
We consider finite-time, future (sudden or Big Rip type) singularities which may occur even when strong energy condition is not violated but equation of state parameter is time-dependent. Recently, example of such singularity has been presented by Barrow, we found another example of it. Taking into account back reaction of conformal quantum fields near singularity, it is shown explicitly that quantum effects may delay (or make milder) the singularity. It is argued that if the evolution to singularity is realistic, due to quantum effects the universe may end up in deSitter phase before scale fa…
We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of Loop Quantum Cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficien…
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…
The familiar Bang/Crunch singularities of classical cosmology have recently been augmented by new varieties: rips, sudden singularities, and so on. These tend to be associated with final states. Here we consider an alternative possibility for the initial state: a singularity which has the novel property of being inaccessible to physically well-defined probes. These singularities arise naturally in cosmologies with toral spatial sections.
Although it has been believed that the models with generalised Chaplygin gas do not contain singularities, in a previous work we have studied how a big freeze could take place in some kinds of phantom generalised Chaplygin gas. In the present work, we study some types of generalised Chaplygin gas in order to show how different sorts of singularities could appears in such models, in the future or in the past. We point out that: (i) singularities may not be originated from the phantom nature of the fluid, and (ii) if initially the tension of the brane in a brane-world Chaplygin model is large en…
In this talk we review the appearance of new types of singularities (big rip, sudden singularities...) in FLRW cosmological models that have arisen on considering explanations for accelerated expansion of our universe.
Different regularizations of the Hamiltonian constraint in loop quantum cosmology yield modified loop quantum cosmologies, namely mLQC-I and mLQC-II, which lead to qualitatively different Planck scale physics. We perform a comprehensive analysis of resolution of various singularities in these modified loop cosmologies using effective spacetime description and compare with earlier results in standard loop quantum cosmology. We show that the volume remains non-zero and finite in finite time evolution for all considered loop cosmological models. Interestingly, even though expansion scalar and ene…
We discuss various types of exotic (non-standard) singularities in the Universe: a Big-Rip (BR or type I), a Sudden Future Singularity (SFS or type II), a Generalized Sudden Future Singularity, a Finite Scale Factor singularity (FSF or type III), a Big-Separation (BS or type IV) and a $w$-singularity. They are characterized by violation of all or some of the energy conditions which results in a blow-up of all or some of the physical quantities: the scale factor, the energy density, the pressure, and the barotropic index. We relate the emergence of these singularities with physical theories (su…
We present a review of selected topics concerning the creation and evolution of child universes, together with a concise account of some recent progress in the field.
Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and $w-$singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.
It is argued that the Universe reheating in bouncing cosmologies could be explained via gravitational particle production, as due to a sudden phase transition in the contracting regime. To this end, it is shown that gravitational production of massive particles conformally coupled with gravity in a matter-ekpyrotic bouncing Universe, where the sudden phase transition occurs in the contracting regime, yields a reheating temperature which is in good agreement with cosmological observations.
General relativity allows a variety of future singularities to occur in the evolution of the universe. At these future singularities, the universe will end in a singular state after a finite proper time and geometrical invariants of the space time will diverge. One question that naturally arises with respect to these cosmological scenarios is the following: can quantum effects lead to the avoidance of these future singularities? We analyze this problem considering massless and conformally coupled scalar fields in an isotropic and homogeneous background leading to future singularities. It is sh…
The Eddington-inspired-Born-Infeld scenario (EiBI) can prevent the Big Bang singularity for a matter content whose equation of state is constant and positive. In a recent paper we showed that, on the contrary, it is impossible to smooth a big rip in the EiBI setup. In fact the situations are still different for other singularities. In this paper we show that a big freeze singularity in general relativity (GR) can in some cases be smoothed to a sudden or a type IV singularity under the EiBI scenario. Similarly, a sudden or a type IV singularity in GR can be replaced in some regions of the param…
Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven toward a drastic end known as the `Big Rip' singularity where all the matter in the universe will be destroyed. Motivated by this possibility, other evolutionary scenarios have been explored by Barrow, including the phenomena which he called Sudden Future Singularities (SFS). In such a model it is possible to have a blow up of the pressure occurring at sometime in the future evolution of the universe while the…
The Born-Infeld determinantal gravity has been recently proposed as a way to smooth the Big Bang singularity. This theory is formulated on the Weitzenbock space-time and the teleparallel representation is used instead of the standard Riemannian representation. We find that although this theory is shown to be singularity-free for certain region of the parameter space in which the divergence of the Hubble rate at the high energy regime is substituted by a de-Sitter stage or a bounce in a Friedmann-Lemaitre-Robertson-Walker universe, cosmological singularities such as Big Rip, Big Bang, Big Freez…
We investigate various dark energy models by taking into account the thermal effects induced from Hawking radiation on the apparent horizon of the Universe, for example near a finite-time future singularity. If the dark energy density increases as the Universe expands, the Universe's evolution reaches a singularity of II type (or sudden future singularity). The second derivative of scale factor diverges but the first remains finite. Quasi-de Sitter evolution can change on sudden future singularity in the case of having an effective cosmological constant larger than the maximum possible value o…
The evolution of a closed Friedmann universe filled by a tachyon scalar field with a trigonometric potential and cold dark matter (CDM) is investigated. A subset of the evolutions consistent to 1$σ$ confidence level with the Union 2.1 supernova data set is identified. The evolutions of the tachyon field are classified. Some of them evolve into a de Sitter attractor, while others proceed through a pseudo-tachyonic regime into a sudden future singularity. Critical evolutions leading to Big Brake singularities in the presence of CDM are found and a new type of cosmological evolution characterized…
We construct a piecewise model that gives a physical viable realization of finite-time future singularity for a spatially flat Friedmann-Robertson-Walker universe within the interacting dark matter--dark energy framework, with the latter one in the form of a variable vacuum energy. The scale factor solutions provided by the model are accommodated in several branches defined in four regions delimited by the scale factor and the effective energy density. A branch starts from a big bang singularity and describes an expanding matter-dominated universe until the sudden future singularity occurs. Th…
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…
We investigate $f(R,T)$ gravity models ($R$ is the curvature scalar and $T$ is the trace of the stress-energy tensor of ordinary matter) that are able to reproduce the four known types of future finite-time singularities. We choose a suitable expression for the Hubble parameter in order to realise the cosmic acceleration and we introduce two parameters, $α$ and $H_s$, which characterise each type of singularity. We address conformal anomaly and we observe that it cannot remove the sudden singularity or the type IV one, but, for some values of $α$, the big rip and the type III singularity may b…
We show that some types of sudden singularities admit a natural explanation in terms of regular changes of signature on brane-worlds in AdS$_{5}$. The present accelerated expansion of the Universe and its possible ending at a sudden singularity may therefore simply be an indication that our braneworld is about to change its Lorentzian signature to an Euclidean one, while remaining fully regular. An explicit example of this behaviour satisfying the weak and strong energy conditions is presented.
We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of $k = \pm 1$ Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for the equation of state. We highlight the non-trivial role played by the intrinsic curvature for these singularities and the new physics which emerges at the Planck scale. We show that quantum gravity effects generically resolve all strong curvature singularities including big rip and big freeze singularities. The weak singularities, which include sudden and b…
A unified treatment of all known types of singularities for flat, isotropic and homogeneous spacetimes in the framework of loop quantum cosmology (LQC) is presented. These include bangs, crunches and all future singularities. Using effective spacetime description we perform a model independent general analysis of the properties of curvature, behavior of geodesics and strength of singularities. For illustration purposes a phenomenological model based analysis is also performed. We show that all values of the scale factor at which a strong singularity may occur are excluded from the effective lo…
We investigate the effects of the underlying quantum geometry in loop quantum cosmology on spacetime curvature invariants and the extendibility of geodesics in the Bianchi-I model for matter with a vanishing anisotropic stress. Using the effective Hamiltonian approach, we find that even though quantum geometric effects bound the energy density and expansion and shear scalars, divergences of curvature invariants are potentially possible under special conditions. However, as in the isotropic models in LQC, these do not necessarily imply a physical singularity. Analysis of geodesics and strength …
An analysis is first given of the situation where a scalar field is contained between two fixed, spatially flat, branes. The usual fine-tuning (RS) condition is relaxed, and the branes are allowed to possess a positive effective cosmological constant λ. We first analyze the eigenvalue problem for the Kaluza-Klein masses when the metric is time dependent, and consider in detail the case when λis small. Thereafter we consider, in the case of one single brane, the opposite limit in which λis large, acting in a brief period of time T, and present a "sudden approximation" calculation of the energy …
We consider a generalized Einstein-Cartan theory, in which we add the unique covariant dimension four operators to general relativity that couples fermionic spin current to the torsion tensor (with an arbitrary strength). Since torsion is local and non-dynamical, when integrated out it yields an effective four-fermion interaction of the gravitational strength. We show how to renormalize the theory, in the one-loop perturbative expansion in generally curved space-times, obtaining the first order correction to the 2PI effective action in Schwinger-Keldysh (${\it in-in}$) formalism. We then apply…
Recently it was shown that Dirac's method of quantizing constrained dynamical systems can be used to impose the Lorenz gauge condition in a four-dimensional cosmological spacetime. In this paper we use Dirac's method to impose the Lorenz gauge condition in a general four-dimensional conformally flat spacetime and find that there is no particle production. We show that in cosmological spacetimes with dimension $D\neq 4$ there will be particle production when the scale factor changes, and we calculate the particle production due to a sudden change.
