Quantum effects due to particle creation on a classical sudden singularity have been investigated in a previous work. The conclusion was that quantum effects do not lead to the avoidance nor the modification of the sudden future singularity. In this paper, we investigate quantum corrections coming from conformal anomaly near the sudden future singularity. We conclude that when the equation of state is chosen to be $p=-ρ-Aρ^α$, the conformal anomaly can transform the sudden singularity in the singularity of type III for any $α> 1/2$ and in the singularity of the type I (the big rip) or the big crunch for $1/2<α<3/2$.
We construct a formal asymptotic series expansion for a general solution of the Brans-Dicke equations with a fluid source near a sudden singularity. This solution contains eleven independent arbitrary functions of the spatial coordinates as required by the Cauchy problem of the theory. We show that the solution is geodesically complete and has the character of a shock wave in the sudden asymptotic region. This solution is weak in the senses of Tipler and Krolak as in the corresponding case of general relativity.
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 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…
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 futur…
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.
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 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…
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…
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 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…
We consider the role of quantum effects, mainly, Weyl anomaly in modifying FLRW model singular behavior at early times. Weyl anomaly corrections to FLRW models have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly corrections changes the nature of the initial singularity from a big bang singularity to a sudden singularity. The two branches of solutions consistent with the semiclassical treatment form a disconnected manif…
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…
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 …
We study global Calabi-Yau realizations of multiple singularity enhancement relevant for family-unification model building in F-theory. We examine the conditions under which the generation of extra chiral matter at multiple singularities on 7-branes in six-dimensional F-theory can be consistent with anomaly cancellation. It is shown that the generation of extra matter is consistent only if it is accompanied by simultaneous degenerations of loci of the leading polynomial of the discriminant so that the total number of chiral matter does not change. We also show that the number of singlets expec…
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…
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…
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 consider the back reaction of the energy due to quantum fluctuation of the background fields considering the trace anomaly for Schwarzschild black hole. It is shown that it will result in modification of the horizon and also formation of an inner horizon. We show that the process of collapse of a thin shell stops before formation of the singularity at a radius slightly smaller than the inner horizon at the order of $(c_{A}\frac{M}{M_p})^{1/3}l_p$. After the collapse stops the reverse process takes place. Thus we demonstrate that without turning on quantum gravity and just through the effect…
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 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.
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.
We consider quantum theoretical effects of the sudden change of the boundary conditions which mimics the occurrence of naked singularities. For a simple demonstration, we study a massless scalar field in $(1 + 1)$-dimensional Minkowski spacetime with finite spatial interval. We calculate the vacuum expectation value of the energy-momentum tensor and explicitly show that singular wave or {\em thunderbolt} appears along the Cauchy horizon. The thunderbolt possibly destroys the Cauchy horizon if its backreaction on the geometry is taken into account, leading to quantum restoration of the global h…
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…
The number of asymptotically de Sitter (non-singular) solutions of 5d dilatonic gravity with positive cosmological constant is found. These solutions are similar to the previously known asymptotically AdS spaces where dilaton may generate the singularity. Using these solutions the consistent $c$-function is proposed in the same way as in AdS/CFT. The consistency of RG flow gives further support for dS/CFT correspondence. From holographic RG flow equations we calculate the holographic 4d conformal anomaly with dilatonic contributions. This conformal anomaly turns out to be the same as in AdS/CF…
In this study, we have analytically considered a dislocation in three-dimensional Weyl semimetal and its holographic model. A quantum singularity that originated in the dislocation creates a defect in momentum space. This defect causes topologically protected zero-energy mode bound to the quantum singularity. The defect has two aspects: First, it prevents the formation of a topological winding number. Second, it provides another topological number around itself. The gauge field adjusts these effects of the defect, and it is possible to control the phase transition. Further, from holographic du…
We consider the cosmological evolution in a recently suggested new model of quantum initial conditions for the Universe. The effective Friedmann equation incorporates the effect of the conformal anomaly of quantum fields and, interestingly, shows that their vacuum Casimir energy is completely screened and does not gravitate. The cosmological evolution also features a new mechanism for a cosmological acceleration stage. This stage is followed by a big boost singularity -- a rapid growth up to infinity of the scale factor acceleration parameter. We also briefly discuss the relation between our m…
We investigate the effect of vacuum corrections, due to the trace anomaly and Casimir effect, on the stability of an oscillating universe with respect to decay by tunneling to the singularity. We find that these corrections do not generally stabilize an oscillating universe. However, stability may be achieved for some specially fine-tuned non-vacuum states.
Boundary condition changing operators in conformal field theory describe various types of "sudden switching" problems in condensed matter physics such as the X-ray edge singularity. We review this subject and give two extensions of previous work. A general derivation of a connection between the X-ray edge singularity, the Anderson orthogonality catastrophe and finite-size scaling of energies is given. The formalism is also extended to include boundstates.
By dropping particles into black hole, we have employed the recently new assumption [1] that the change of the black hole mass(enthalpy) should be the same amount as the energy of an infalling particle($ω= dM$), to carefully test the laws of thermodynamics and the weak cosmic censorship conjecture of a conformal anomaly corrected AdS black hole in different phase spaces. Using the energy-momentum relation, the result shows that the first law, second law and weak cosmic censorship conjecture of black hole are all valid in the normal phase space, no violations occur. In the extended phase space,…
The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory…
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…
Two predictions about finite-N non-supersymmetric "orientifold field theories" are made by using the dual type 0' string theory on C^3 / Z_2 x Z_2 orbifold singularity. First, the mass ratio between the lowest pseudoscalar and scalar color-singlets is estimated to be equal to the ratio between the axial anomaly and the scale anomaly at strong coupling, M_- / M_+ ~ C_- / C_+. Second, the ratio between the domain wall tension and the value of the quark condensate is computed.
We propose general relations between the conformal anomaly and the chiral (R-symmetry and gravitational) anomaly coefficients in 6d (1,0) superconformal theories. The suggested expressions for the three type B conformal anomaly c-coefficients complement the expression for the type A anomaly a-coefficient found in arXiv:1506.03807. We check them on several examples -- the standard (1,0) hyper and tensor multiplets as well as some higher derivative short multiplets containing vector fields that generalize the superconformal 6d vector multiplet discussed in arXiv:1506.08727. We also consider a fa…
We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are…
We explicitly prove that a class of finite quantum gravitational theories (in odd as well as in even dimension) is actually a range of anomaly-free conformally invariant theories in the spontaneously broken phase of the conformal Weyl symmetry. At classical level we show how the Weyl conformal invariance is likely able to tame the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. This latter statement is rigorously proved by a singularity theorem that applies to a large class of weakly non-local theories. Following th…
The theory of free Majorana-Weyl spinors is the prototype of conformal field theory in two dimensions in which the gravitational anomaly and the Weyl anomaly obstruct extending the flat spacetime results to curved backgrounds. In this paper, we investigate a quantization scheme in which the short distance singularity in the two-point function of chiral fermions on a two dimensional curved spacetime is given by the Green's function corresponding to the classical field equation. We compute the singular term in the Green's function explicitly and observe that the short distance limit is not well-…
