Final Singularities Research Articles

Two-loop mixed QCD-EW corrections to neutral current Drell-Yan

We present the two-loop mixed strong-electroweak virtual corrections to the neutral current Drell-Yan process and we provide, as supplementary material, the explicit formulae of the infrared-subtracted finite remainder. The final state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two internal massive lines, has been worked out relying on analytical and semi-analytical techniques, in the case of complex-valued masses.

Effective LQC model for k=+1 isotropic cosmologies from spatial discretizations

The closed, spatially isotropic FLRW universe (k=+1) is endowed with modifications due to a discrete underlying space-structure. Motivated from Loop Quantum Gravity techniques, a full Thiemann regularisation is performed. The impact of these modifications of the single-graph-sector appearing in the scalar constraint are interpreted as physical quantum gravity effects. We investigate the form of the modified scalar constraint and its analytical approximations for k=+1 spacetimes and assume this effective constraint as the generator of dynamics on the reduced isotropic phase space. It transpires that the system still features a classical recollapse with only marginal discreteness corrections. Moreover, the initial and final singularities are resolved and we present an effective model mirroring the qualitative features of system.

Finite action principle revisited

We extend the cosmological predictions from assuming the total action of the universe is finite. When initial and final singularities in curvature invariants are avoided, it leads to singularities in the gravitational action of the universe. The following properties are required of a universe with finite action: Compact spatial sections (ie a closed universe) giving a finite total lifetime for the universe. Compactification of flat and open universes is excluded. The universe can contain perfect fluids with -1<p/\r{ho}<2 on approach to singularities. The universe cannot display a bounce' or indefinite cyclic behaviour to the past or the future. We find new consequences of imposing finite action: the universe cannot be dominated by massless scalar fields, the kinetic energy of scalar fields, or a p=\r{ho} perfect fluid on approach to the initial or final singularity The ekpyrotic scenario with an effective fluid obeying p/\r{ho}>2 in a closed, flat or open universe is excluded. Any bouncing model with indefinite past or future evolution is ruled out. Einstein static and steady-state universes are ruled out along with past or future eternal inflating universes. Anisotropies cannot dominate the dynamics at singularities. This excludes density inhomogeneity spectra versus mass, of the form {\delta}\r{ho}/\r{ho}proportional to M^{-q}, with q>2/3.Higher-order lagrangian theories of gravity are constrained. The Gauss-Bonnet combination causes an action singularity even though it does not contribute terms to the field equations. Scalar-tensor theories dominated by the scalar field on approach to singularities have action singularities. Dark energy cannot be a cosmological constant. The dark energy must evolve in a closed universe that collapses to a future singularity that cannot be dominated by the kinetic energy of the scalar field.

Local Brunella's Alternative II. Partial Separatrices

Here we state a conjecture concerning a local version of Brunella's alternative: any codimension one foliation in |$(\mathbb {C}^3,0)$| without germ of invariant surface has a neighborhood of the origin formed by leaves containing a germ of analytic curve at the origin. We prove the conjecture for the class of codimension one foliations whose reduction of singularities is obtained by blowing-up points and curves of equireduction and such that the final singularities are free of saddle-nodes. The concept of “partial separatrix” for a given reduction of singularities has a central role in our argumentations, as well as the quantitative control of the generic Camacho-Sad index in dimension three. The “nodal components” are the only possible obstructions to get such germs of analytic curves. We use the partial separatrices to push the leaves near a nodal component towards compact dicritical divisors, finding in this way the desired analytic curves.

A noncommutative Friedman cosmological model

AbstractThe closed Friedman cosmological model, based on noncommutative geometry, is presented. Two global effects exhibited by the model are discussed. The first effect is the “generation of matter out of geometry”. Gravitational field equation in this model has the form of the eigenvalue equation for the Einstein operator. It turns out that the eigenvalues of this operator reproduce components of the energy‐momentum tensor. The second effect concerns the existence of the initial and final singularities. Because of the strongly probabilistic character of the noncommutative dynamics on the fundamental level, although singularities do exist, they are probabilistically irrelevant.

Effects of the quantization ambiguities on the Big Bounce dynamics

In this paper we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator $\hat{F}$ and result in different forms of the effective Hamiltonian. Such an ambiguity of the choice of this expression from some class of functions is allowed in the framework of loop quantisation. Our main goal is to show how such modifications can influence the bouncing universe scenario in the loop quantum cosmology. In effective models considered we classify all evolutional paths for all admissible initial conditions. The dynamics is reduced to the form of a dynamical system of the Newtonian type on a 2-dimensional phase plane. These models are equivalent dynamically to the FRW models with the decaying effective cosmological term parametrised by the canonical variable $p$ (or by the scale factor $a$). We find that for the positive cosmological constant there is a class of oscillating models without the initial and final singularities. The new phenomenon is the appearance of curvature singularities for the finite values of the scale factor, but we find that for the positive cosmological constant these singularities can be avoided. For the positive cosmological constant the evolution begins at the asymptotic state in the past represented by the deSitter contracting (deS$_{-}$) spacetime or the static Einstein universe H=0 or $H=-\infty$ state and reaches the deSitter expanding state (deS$_{+}$), the state H=0 or $H=+\infty$ state. In the case of the negative cosmological constant we obtain the past and future asymptotic states as the Einstein static universes.

Hamiltonian dynamics of linearly polarized Gowdy models coupled to massless scalar fields

The purpose of this paper is to analyze in detail the Hamiltonian formulation for the compact Gowdy models coupled to massless scalar fields as a necessary first step toward their quantization. We will pay special attention to the coupling of matter and those features that arise for the and topologies that are not present in the well-studied case—in particular the polar constraints that come from the regularity conditions on the metric. As a byproduct of our analysis we will get an alternative understanding, within the Hamiltonian framework, of the appearance of initial and final singularities for these models.

String theory and cosmological singularities

In general relativity space-like or null singularities are common: they imply that ‘time’ can have a beginning or end. Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics. In this article, we describe some of these approaches.

The Bianchi IX model in loop quantum cosmology

The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behaviour. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities.

Next-to-leading order QCD calculations with parton showers. II. Soft singularities

Programs that calculate observables in quantum chromodynamics at next-to-leading order typically generate events that consist of partons rather than hadrons -- and just a few partons at that. These programs would be much more useful if the few partons were turned into parton showers, which could be given to one of the Monte Carlo event generators to produce hadron showers. In a previous paper, we have seen how to generate parton showers related to the final state collinear singularities of the perturbative calculation for the example of e+ + e- --> 3 jets. This paper discusses the treatment of the soft singularities.

Next-to-leading order QCD calculations with parton showers. I. Collinear singularities

Programs that calculate observables in quantum chromodynamics at next-to-leading order typically suffer from the problem that, when considered as event generators, the events generated consist of partons rather than hadrons and just a few partons at that. Thus the events generated are completely unrealistic. These programs would be much more useful if the few partons were turned into parton showers, in the style of standard Monte Carlo event generators. Then the parton showers could be given to one of the Monte Carlo event generators to produce hadron showers. We show how to generate parton showers related to the final state collinear singularities of the next-to-leading order perturbative calculation for the example of e+ + e- --> 3 jets . The soft singularities are left for a separate publication.

Non-equilibrium model of steady detonations in aluminum particles - oxygen suspensions

Steady-state detonation regimes are studied on the basis of the mathematical model of detonation of aluminum particles in oxygen taking into account differences in velocities and temperatures of the mixture components. The final steady state is analyzed by determining the types of final singularities in the plane of relaxation parameters (the ratios of characteristic times of thermal and velocity relaxations and combustion). The regions of existence of steady-state regimes are found numerically, depending on the detonation wave velocity and relaxation parameters. Numerical illustrations of various flow types are presented, and the properties of the detonation wave structure caused by velocity nonequilibrium are examined. Qualitative agreement of data obtained with frozen relaxation parameters and their dependence on the flow parameters is shown.

Open and closed cosmological solutions of Hořava-Witten theory

The cosmological solutions of Horava-Witten theory discovered by Lukas, Ovrut and Waldram are generalized to allow non vanishing spatial curvature. The solution with closed spatial sections has initial and final curvature singularities. We find two solutions with open spatial sections, both of which evolve from an initial curvature singularity to the supersymmetric domain wall solution at late times. We also present a solution with open spatial sections and a non-zero Ramond-Ramond scalar. The behaviour of the solutions in eleven dimensions is discussed.

Kinematic Cosmology in Conformally Flat Spacetime

In a recent series of papers Endean examines the properties of spatially homogeneous and isotropic (FLRW) cosmological models filled with dust in the ``conformally flat spacetime presentation of cosmology'' (CFS cosmology). This author claims it is possible to resolve a certain number of the difficulties the standard model exhibits when confronted to observations, if the theoretical predictions are obtained in the special framework of CFS cosmology. As a by-product of his analysis Endean claims that no initial (big-bang) nor final (big-crunch) singularities occur in the closed FLRW model. In this paper we show up the fallacious arguments leading to Endean's conclusions and we consistently reject his CFS cosmology.

Quantum potential and cosmological singularities

We apply the de Broglie-Bohm interpretation to the Wheeler-DeWitt equation for the quantum FRW cosmological model with a minimal massless scalar field. We find that the quantum FRW cosmological model has quantum potential dominated solutions that avoid the initial and the final cosmological singularities. It is suggested that the quantum potential and the back-reaction of geometry and matter fields may change the property of the cosmological singularities of the universe.

Parametric amplification of perturbations in closed universe and an arrow of time

We consider a toy model of a vacuum closed Friedman-Robertson-Walker universe. The parametric amplification of vacuum metric fluctuations dynamically induced close to the initial singularity results in production of squeezed gravitons. Then we recall that the longest wavelength gravitons propagating in the closed Friedman-Robertson-Walker background are maintaining the symmetry of Bianchi IX type. As the scale factor goes to zero (and gravitons gain their importance) the complex behavior of the Bianchi IX model (mixmaster dynamics) close to the singularity may be interpreted as a result of interaction between gravity waves. A similar scenario may be expected in a more general inhomogeneous case. Therefore we put foreward an idea that the initial and the final singularities may be fundamentally different. This point of view is analogous to that of Penrose who claims that such a fundamental distinction is an inevitable feature of gravity expressed in overwhelming tendency to produce clumpiness in the universe.

The closed Friedman world model with the initial and final singularities as a non-commutative space

The most elegant definition of singularities in general relativity as b-boundary points, when applied to the closed Friedman world model, leads to the disastrous situation: both the initial and final singularities form the single point of the b-boundary w

Exact Bianchi type I models for an exponential-potential scalar field

A non-local transformation is used to linearize the evolution equation for Bianchi type I universes filled with an exponential-potential scalar field. Among the many new explicit solutions there is a family which shows, for different parameter ranges, the two generic asymptotic behaviours that were previously found in numerical and qualitative analyses. A simpler expression for the general solution allows a better insight into the problem and reveals a damped oscillatory behaviour which corresponds to an effective negative cosmological constant. We are also now able to discuss the existence of initial and final singularities. We found families of explicit singular solutions which represent universes which after evolving from a singularity reach a final anisotropic or isotropic Friedmann - Robertson - Walker stage. There are also solutions which avoid the initial singularity and others with a finite time span.

Noncommutative structure of singularities in general relativity

Initial and final singularities in the closed Friedman world model are typical examples of malicious singularities. They form the single point of Schmidt’s b-boundary of this model and are not Hausdorff separated from the rest of space–time. The method of noncommutative geometry, developed by A. Connes and his co-workers, is applied to this case. We rephrase Schmidt’s construction in terms of the groupoid Ḡ of orthonormal frames over space–time and carry out the ‘‘desingularization’’ process. We define the line bundle τ:Ω1/2→Ḡ over Ḡ and change the space of its cross sections into an involutive algebra. This algebra is represented in the space of operators on a Hilbert space and, with the norm inherited from these operators, it becomes a C*-algebra. The initial and final singularities of the closed Friedman model are given by two distinct representations of this C*-algebra in the space of operators acting on the Hilbert space L2(O(3,1)).

The interaction of outgoing and ingoing spherically symmetric null fluids

Using similarity methods, the Einstein field equations coupled to two oppositely directed null fluids for a spherically symmetric space–time are reduced to an autonomous system of three ordinary differential equations. The space of solutions is studied in some detail and solutions are found that represent: (i) the backscattering of an initially outgoing thick null fluid shell in a background gravitational field with a central naked singularity, (ii) the formation of strong space–time singularities by the interaction of thick null fluid shells, (iii) the interaction of a core of null radiation with an incoming shell of null fluid, and (iv) cosmological models of Kantowski–Sachs type with initial and final singularities clothed by apparent horizons.