Cosmological Singularity Research Articles

Analysis of big bounce in Einstein–Cartan cosmology

We analyze the dynamics of a homogeneous and isotropic universe in the Einstein–Cartan theory of gravity. The spin of fermions produces spacetime torsion that prevents gravitational singularities and replaces the big bang with a nonsingular big bounce. We show that a closed universe exists only when a particular function of its scale factor and temperature is higher than some threshold value, whereas an open and a flat universes do not have such a restriction. We also show that a bounce of the scale factor is double: as the temperature increases and then decreases, the scale factor decreases, increases, decreases, and then increases.

New loop quantum cosmology modifications from gauge-covariant fluxes

Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to phenomenology, its connection with loop quantum gravity has remained elusive. It is therefore important to integrate more and more features of the full theory into this framework and understand the reliability of physical predictions. In particular, if one wishes to connect the effective Hamiltonian in loop quantum cosmology to an expectation value of the scalar constraint operator in suitable coherent states for the full theory, one has to go beyond the standard setting of loop quantum cosmology. One possibility is to introduce gauge-covariant fluxes, which become necessary because the presence of a finite regularization parameter causes functions build out of the standard discretized variables to be in general not gauge invariant. Following the construction of gauge-covariant fluxes pioneered by Thiemann in [1], we show that the physics of loop quantum cosmology is affected in a non-trivial way. The bounce turns out to be generically asymmetric with a rescaling of the Newton's constant in the pre-bounce branch. Gauge-covariant fluxes result in a higher order quantum difference equation in comparison to loop quantum cosmology. Even the behavior of matter, which behaves innocuously in loop quantum cosmology, is enriched, resulting in an effective non-minimal coupling. These effects are shown to be common to different choices of regularization parameters.

Timelike geodesics in naked singularity and black hole spacetimes

In this paper, we derive the solutions of orbit equations for a class of naked singularity spacetimes, and compare these with timelike orbits, that is, particle trajectories in the Schwarzschild black hole spacetime. The Schwarzschild and naked singularity spacetimes considered here can be formed as end state of a spherically symmetric gravitational collapse of a matter cloud. We find and compare the perihelion precession of the particle orbits in the naked singularity spacetime with that of the Schwarzschild black hole. We then discuss different distinguishable physical properties of timelike orbits in the black hole and naked singularity spacetimes and implications are discussed. Several interesting differences follow from our results, including the conclusion that in naked singularity spacetimes, particle bound orbits can precess in the opposite direction of particle motion, which is not possible in Schwarzschild spacetime.

A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories

We derive transition rules for Kasner exponents in bouncing Bianchi I models with generic perfect fluid matter fields for a broad class of modified gravity theories where cosmological singularities are resolved and replaced by a non-singular bounce. This is a generalization of results obtained previously in limiting curvature mimetic gravity and loop quantum cosmology. A geometric interpretation is provided for the transition rule as a linear map in the Kasner plane. We show that the general evolution of anisotropies in a Bianchi I universe—including during the bounce phase—is equivalent to the motion of a point particle on a sphere, where the sphere is the one-point compactification of the Kasner plane. In addition, we study the evolution of anisotropies in a large family of bouncing Bianchi I space-times. We also present a novel explicit solution to the Einstein equations for a Bianchi I universe with ekpyrotic matter with a constant equation of state ω=3.

Polymer representation of the Bianchi IX cosmology in the Misner variables

We analyze the Bianchi IX Universe in the Polymer Quantum Mechanics framework by facing both semiclassical and purely quantum effects near the cosmological singularity. We adopt Misner variables to describe the model dynamics, applying the polymer paradigm simultaneously to the isotropic one (linked to the Universe volume) and to the two anisotropy ones (characterizing the physical gravitational degrees of freedom). Setting two different cut-off scales for the two different variable sets, i.e. the geometrical volume and the gravity tensor modes, we demonstrate how the semiclassical properties of the Bianchi IX dynamics are sensitive to the ratio of the cut-off parameters. In particular, the semiclassical evolution turns out to be chaotic only if the parameter associated to the volume discretization is greater or equal to that one of the anisotropies. Concerning the chaotic case we perform a purely quantum polymer analysis, demonstrating that the original Misner result about the existence of quasi-classical states near the singularity (in the sense of high occupation numbers) is still valid in the revised approach and able to account for cut-off physics effects. The possibility for a comparison with the original study by Misner is possible because the singularity is still present in the semiclassical evolution of the cosmological model for all the parameter space. We interpret this surprising feature as the consequence of a geometrical volume discretization which does not prevent the volume from vanishing, i.e. restoring in the Minisuperspace analysis its zero value.

Holographic signatures of resolved cosmological singularities II: numerical investigations

A common strategy to investigate the fate of gravitational singularities in asymptotically AdS spacetimes is to translate the question from the gravitational side to a dual field theory using the gauge/gravity correspondence and to do a field theory computation. Given recent progress in singularity resolution via non-perturbative quantum gravity, it is natural to now turn the question around and to ask about field theory signatures of resolved singularities. An investigation along this line has been initiated in a companion paper, where a finite-distance pole exhibited by the two-point correlator in the dual field theory, which has previously been linked directly to the gravitational bulk singularity, has been resolved in this way. In order to perform analytic computations, some simplifications were necessary. In this paper, we lift these restrictions by tackling the problem numerically. Our analysis shows that the pole in the two-point correlator gets resolved in the same manner as before.

Asymptotically Weyl-invariant gravity

We propose a novel theory of gravity that by construction is renormalizable, evades Ostrogradsky’s no-go theorem, is locally scale-invariant in the high-energy limit, and equivalent to general relativity in the low-energy limit. The theory is defined by a pure [Formula: see text] action in the Palatini formalism, where the dimensionless exponent [Formula: see text] runs from a value of two in the high-energy limit to one in the low-energy limit. We show that the proposed model contains no obvious cosmological curvature singularities. The viability of the proposed model is qualitatively assessed using several key criteria.

Cosmological singularities in conformal Weyl gravity

In this work, we study the issue of the past and future cosmological singularities in the context of the fourth-order conformal Weyl gravity. In particular, we investigate the emergent universe scenario proposed by Ellis et al., and find the stability conditions of the corresponding Einstein static state using the fixed point approach. We show that depending on the values of the parameters of the conformal Weyl gravity theory, there are possibilities for having initially stable emergent states for an FRW universe with both the positive and negative spatial curvatures. This represents that the conformal Weyl gravity can be free of the initial singularity problem. Then, following Barrow et al., we address the possible types of the finite-time future cosmological singularities. We discuss how these singularities also can be avoided in the context of this theory.

On resolutions of cosmological singularities in higher-spin gravity

We study the resolution of certain cosmological singularity in the context of higher-spin three-dimensional gravity. We consider gravity coupled to a spin-3 field realized as Chern–Simons theory with gauge group [Formula: see text]. In this context, we elaborate and extend a singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big bang singularity in the case of gravity coupled to a spin-4 field realized as Chern–Simons theory with gauge group [Formula: see text]. In all these cases, we show the existence of gauge transformations that do not change the holonomy of the Chern–Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-[Formula: see text] field when described by Chern–Simons with gauge group [Formula: see text].

Effects of electromagnetic field on gravitational collapse in f(R, T) gravity

In this paper, we examine spherically symmetric collapse with perfect fluid matter under the effect of electromagnetic field in f(R, T) gravity. We used the Darmois as well as Senovilla matching conditions by considering static exterior and non-static interior spherically symmetric spacetimes. The analytical solutions of field equations are obtained. We investigate the apparent horizon and their physical importance. It is pointed out that electromagnetic field diminishes the bound of f(R, T) term by diminishing the pressure and hence the whole collapsing process accelerates. The time interval between the cosmological horizon and singularities are also effected by electromagnetic field.

Form factors in asymptotic safety: conceptual ideas and computational toolbox

Over the last years the asymptotic safety program has matured into a serious candidate for a quantum theory of gravity compatible with observations. The rapid technical progress in computing renormalisation group flows for gravity and gravity-matter systems in the non-perturbative regime has put many interesting physical questions within reach. In particular, the construction of the non-perturbative quantum corrections to the propagation of fields on a fluctuating spacetime allows addressing the effective propagation of matter on a quantum spacetime or the possible resolution of spacetime singularities based on first principle computations. In this article, we assemble a technical toolbox for carrying out investigations on this promising research frontier. As a specific example we present results for the momentum-dependent two-point function for a scalar field induced by the quantum fluctuations of the underlying geometry in a self-consistent way.

Anisotropic cosmological dynamics in f(T) gravity in the presence of a perfect fluid

We consider the cosmological evolution of a flat anisotropic Universe in f(T) gravity in the presence of a perfect fluid. It is shown that the matter content of the Universe has a significant impact of the nature of a cosmological singularity in the model studied. Depending on the parameters of the f(T) function and the equation of state of the perfect fluid in question the well-known Kasner regime of general relativity can be replaced by a new anisotropic solution, or by an isotropic regime, or the cosmological singularity changes its nature to a non-standard one with a finite values of Hubble parameters. Six possible scenarios of the cosmological evolution for the model studied have been found numerically.

Noncommutativity and the weak cosmic censorship

We show that a noncommutative massless scalar probe can dress a naked singularity in AdS3 spacetime, consistent with the weak cosmic censorship. The dressing occurs at high energies, which is typical at the Planck scale. Using a noncommutative duality, we show that the dressed singularity has the geometry of a rotating BTZ black hole which satisfies all the laws of black hole thermodynamics. We calculate the entropy and the quasi-normal modes of the dressed singularity and show that the corresponding spacetime can be quantum mechanically complete. The noncommutative duality also gives rise to a light scalar, which can be relevant for early universe cosmology.

Contracting asymptotics of the linearized lapse-scalar field sub-system of the Einstein-scalar field equations

We prove an asymptotic stability result for a linear coupled hyperbolic-elliptic system on a large class of singular background spacetimes in CMC gauge on the n-torus. At each spatial point these background spacetimes are perturbations of Kasner-like solutions of the Einstein-scalar field equations which are not required to be close to the homogeneous and isotropic case. We establish the existence of a homeomorphism between Cauchy data for this system and a set of functions naturally associated with the asymptotics in the contracting direction, which we refer to as asymptotic data. This yields a complete characterization of the degrees of freedom of all solutions of this system in terms of their asymptotics. Spatial derivative terms can in general not be fully neglected which yields a clarification of the notion of asymptotic velocity term dominance (AVTD).

Can we distinguish black holes from naked singularities by the images of their accretion disks?

We study here images of thin accretion disks around black holes and two classes of naked singularity spacetimes and compare these scenarios. The naked singularity models which have photon spheres have single accretion disk with its inner edge lying outside the photon sphere. The images and shadows created by these models mimic those of black holes. It follows, therefore, that further and more detailed analysis of the images and shadows structure in such case is needed to confirm or otherwise the existence of an event horizon for the compact objects such as the galactic centers. However, naked singularity models which do not have any photon spheres can have either double disks or a single disk extending up to the singularity. The images obtained from such models significantly differ from those of black holes. Moreover, the images of the two classes of naked singularities in this latter case, differ also from one another, thereby allowing them to be distinguish from one another through the observation of the images.

New classes of spherically symmetric, inhomogeneous cosmological models

We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to the known inhomogeneous charged perfect fluid solutions of the Einstein field equations and under some other limits we obtain new charged and uncharged solutions with cosmological constant. Uncharged solutions in particular represent cosmological models where the universe may undergo a topology change and in between is a mixture of two different Friedmann-Robertson-Walker universes with different spatial curvatures. We show that there exist some spacelike surfaces where the Ricci scalar and pressure of the fluid diverge but the mass density of the fluid distribution remains finite. Such spacelike surfaces are known as (sudden) cosmological singularities. We study the behavior of our new solutions in their general form as the radial distance goes to zero and infinity. Finally, we briefly address the null geodesics and apparent horizons associated to the obtained solutions.

Effective quantum extended spacetime of polymer Schwarzschild black hole

The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches. In the context of loop quantum gravity (LQG), one of the major candidates for a non-perturbative background-independent quantisation of general relativity, considerable effort has been devoted to construct effective models in which these questions can be studied. In these models, classical singularities are replaced by a ‘bounce’ induced by quantum geometry corrections. Undesirable features may arise however depending on the details of the model. In this paper, we focus on Schwarzschild black holes and propose a new effective quantum theory based on polymerisation of new canonical phase space variables inspired by those successful in loop quantum cosmology. The quantum corrected spacetime resulting from the solutions of the effective dynamics is characterised by infinitely many pairs of trapped and anti-trapped regions connected via a space-like transition surface replacing the central singularity. Quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon. The effective quantum metric describes also the exterior regions and asymptotically classical Schwarzschild geometry is recovered. We however find that physically acceptable solutions require us to select a certain subset of initial conditions, corresponding to a specific mass (de-)amplification after the bounce. We also sketch the corresponding quantum theory and explicitly compute the kernel of the Hamiltonian constraint operator.

Scale factor — Cosmic time relation and occurrences of future cosmic singularities with different redshift parametrizations of dark energy EoS-s

While modeling our late time cosmically accelerated universe, it is popular to involve different dark energy (DE) models, the equation of state (EoS) of which can be taken as a function of the redshift and some unknown parameters. Barboza and Alcaniz have proposed one such kind of DE EoS model. We use some new parametrizations like Feng, Shen, Li, Li I and II and Polynomial parametrizations to get more accurate concepts about the fate of our expanding universe. We try to find how the hypothesis of the fate of our universe behaves in the above background of DE models. Possibilities of occurrences of future cosmic singularities are studied.

Resolving Spacetime Singularities within Asymptotic Safety.

A key incentive of quantum gravity is the removal of spacetime singularities plaguing the classical theory. We compute the nonperturbative momentum dependence of a specific structure function within the gravitational asymptotic safety program which encodes the quantum corrections to the graviton propagator for momenta above the Planck scale. The resulting quantum-corrected Newtonian potential approaches a constant negative value as the distance between the two point masses goes to zero, thereby removing the classical singularity. The generic nature of the underlying mechanism suggests that it will remain operative in the context of black hole and cosmic singularities.

Holographic bulk reconstruction and cosmological singularities

We study the structure of entanglement wedges in the Kasner-AdS geometry, which provides an example of AdS/CFT engineered cosmological singularity. We investigate the specific limitations of causal reconstruction methods, imposed by the presence of the cosmological singularities, and we show the supremacy of modular reconstruction. This model provides an example where modular reconstruction based on a proper operator subalgebra is more powerful than the strongest possible causal reconstruction, based on the complete operator algebra.