In this paper we calculate $\mathcal{O}(μ^4)$ corrections from holonomies in the Loop Quantum Gravity, usually not taken into account. Allowance of the corrections of this kind is equivalent with the choice of the new quatization scheme. Quantization ambiguities in the Loop Quantum Cosmology allow for this additional freedom and presented corrections are consistent with the standard approach. We apply these corrections to the flat FRW cosmological model and calculate the modified Friedmann equation. We show that the bounce appears in the models with the standard $\mathcal{O}(μ^2)$ quantization scheme is shifted to the higher energies $ρ_{\text{bounce}} = 3 ρ_{\text{c}}$. Also a pole in the Hubble parameter appears for $ρ_{\text{pole}} = {3/2} ρ_{\text{c}}$ corresponding to \emph{hyper-inflation/deflation} phases. This pole represents a curvature singularity at which the scale factor is finite. In this scenario the singularity and bounce co-exist. Moreover we find that an ordinary bouncing solution appears only when quantum corrections in the lowest order are considered. Higher order corrections can lead to the nonperturbative effects.
Bouncing models are alternatives to inflationary cosmology that replace the initial Big-Bang singularity by a `bouncing' phase. A deeper understanding of the initial conditions of the universe, in these scenarios, requires knowledge of quantum aspects of bouncing models. In this work, we propose two classes of bouncing models that can be studied with great analytical ease and hence, provide test-bed for investigating more profound problems in quantum cosmology of bouncing universes. Our model's two key ingredients enable us to do straightforward analytical calculations: (i) a convenient parame…
We consider a 3-brane embedded in a warped 5-dimensional background with a dilaton and a Kalb-Ramond 2-form. We show that it is possible to find static solutions of the form of charged dS/AdS-like black hole with horizon which could have a negative mass parameter. The motion of the 3-brane in this bulk generates an effective 4-dimensional bouncing cosmology induced by the negative dark radiation term. This model avoids the instability that arises for bouncing brane in a Reissner-Nordstrøm-AdS bulk.
Bouncing geodesics, black hole singularities, and singularities of thermal correlators
Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；Higgs Centre for Theoretical Physics, University of Edinburgh（爱丁堡大学希格斯理论物理中心）
We derive the equations of motion for scalar metric perturbations in a particular nonsingular bouncing cosmology, where the big bang singularity is replaced by a spacetime defect with a degenerate metric. The adiabatic perturbation solution is obtained for nonrelativistic hydrodynamic matter. We get the same result by working with conformal coordinates. This last method is also valid for vector and tensor metric perturbations, and selected results are presented. We, finally, discuss several new effects from the linear perturbations of this nonsingular bouncing cosmology, such as across-bounce …
In this paper, we have presented a bouncing cosmological model of the Universe in an extended theory of gravity. The dynamical behaviour of the model obtained from the flat FLRW space-time along with the violation of null energy condition have been shown. The geometrical parameters show singularity behaviour at the bouncing epoch. The parameters involved in the scale factor play a major role in the bouncing behaviour. In addition, the coupling parameter that resulted in the minimal matter-geometry coupling in the extended gravity has significant role to avoid the singularity of equation of sta…
In this paper, we study $F(R)$ gravity by Hu-Sawicki model in Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) background. The Friedmann equations are calculated by modified gravity action, and then the obtained Friedmann equations are written in terms of standard Friedmann equations. Next behavior of bouncing cosmology is investigated in the modified gravity model, i.e., this behavior can solve problem of non-singular in standard Big Bang cosmology. We plot the cosmological parameters in terms of cosmic time and then bouncing condition is investigated. In what follows, we reconstruct the modified…
We investigate a particular type of classical nonsingular bouncing cosmology, which results from general relativity if we allow for degenerate metrics. The simplest model has a matter content with a constant equation-of-state parameter and we get the modified Hubble diagrams for both the luminosity distance and the angular diameter distance. Based on these results, we present a Gedankenexperiment to determine the length scale of the spacetime defect which has replaced the big bang singularity. A possibly more realistic model has an equation-of-state parameter which is different before and afte…
In this work, we analyzed the improved Deser-Woodard non-local gravity over the background of five different bouncing cosmologies, whose premise is avoid the initial singular state of the universe. We developed the numerical solution for the non-local distortion function, which encompass the modifications to the Einstein-Hilbert action, using the reconstruction procedure and we have found that they have a viable cosmological solution. Afterwards, we discussed the physical aspects and outcomes of the evolution of the distortion function throughout the bouncing point for these models, specifical…
We consider the process of magnetogenesis in the context of nonsingular bounce cosmology. We show that large primordial magnetic fields can be generated during contraction without encountering strong coupling and backreaction issues. The fields may seed large-scale magnetic fields with observationally interesting strengths. This result leads to a theoretical constraint on the relation of the energy scale of the bounce cosmology to the number of effective e-folding of the contracting phase in the case of scale invariance for the power spectrum of primordial magnetic fields. We show that this co…
Bouncing Geodesics, Singularities, and the Cavity Thermal Product Formula in Asymptotically Flat and de Sitter Black Holes
Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学物理学院）；Higgs Centre for Theoretical Physics, University of Edinburgh（爱丁堡大学希格斯理论物理中心）
We discuss the effects of a (possibly) negative $(1+z)^6$ type contribution to the Friedmann equation. No definite answer can be given as to the presence and magnitude of a particular mechanism, because any test using the general relation $H(z)$ is able to estimate only the total of all sources of such a term. That is why we describe four possibilities: 1) geometric effects of loop quantum cosmology, 2) braneworld cosmology, 3) metric-affine gravity, and 4) cosmology with spinning fluid. We find the exact solutions for the models with $ρ^2$ correction in terms of elementary functions, and show…
We study how a cosmological bounce with a Type IV singularity at the bouncing point, can be generated by a classical vacuum $F(G)$ gravity. We focus our investigation on the behavior of the vacuum $F(G)$ theory near the Type IV singular bouncing point and also we address the stability of the resulting solution, by treating the equations of motion as a dynamical system. In addition, we investigate how the scalar perturbations of the background metric evolve, emphasizing to cosmological times near the Type IV singular bouncing point. Finally, we also investigate which mimetic vacuum $F(G)$ gravi…
We consider the introduction of anisotropy in a class of bouncing models of cosmology. The presence of anisotropy often spells doom on bouncing models, since the energy density due to the anisotropic stress outweighs that of other matter components, as the universe contracts. Different suggestions have been made in the literature to resolve this pathology, classically. Here, we introduce a family of bouncing models, in which the shear density can be tuned to either allow or forbid classical bouncing scenarios. Following this, we show that quantum cosmological considerations can drastically cha…
A bouncing universe is a viable candidate to solve the initial singularity problem. Here we consider bouncing solutions in the context of $f(R,\mathcal{G})$ gravity by using an order reduction technique which allows one to find solutions that are perturbatively close to General Relativity. This procedure also acts as a model selection approach. Indeed, several covariant gravitational actions leading to a bounce are directly selected by demanding that the Friedmann equation derived within such gravity theories coincides with the one emerging from Loop Quantum Cosmology.
In this paper, we have studied the bouncing behavior of the cosmological models formulated at the background of the Hubble function in the F(R, G) theory of gravity, where R and G denote the Ricci scalar and Gauss-Bonnet invariant. The actions of bouncing cosmology are studied under consideration of different viable models and can resolve the difficulty of singularity in standard Big-Bang cosmology. Both models show bouncing behavior and satisfy the bouncing cosmological properties. Models based on dynamical, deceleration, and energy conditions indicate the accelerating behavior at the late ev…
We in this paper investigate the formation and evolution of primordial black holes (PBHs) in nonsingular bouncing cosmologies. We discuss the formation of PBH in the contracting phase and calculate the PBH abundance as a function of the sound speed and Hubble parameter. Afterwards, by taking into account the subsequent PBH evolution during the bouncing phase, we derive the density of PBHs and their Hawking radiation. Our analysis shows that nonsingular bounce models can be constrained from the backreaction of PBHs.
We consider f(Q) extended symmetric teleparallel cosmologies, where Q is the non-metricity scalar, and constrain its functional form through the order reduction method. By using this technique, we are able to reduce and integrate the field equations and thus to select the corresponding models giving rise to bouncing cosmology. The selected Lagrangian is then used to develop the Hamiltonian formalism and to obtain the Wave Function of the Universe which suggests that classical observable universes can be recovered according to the Hartle Criterion.
In this note, we revisit the thermal fluctuations generated during bouncing cosmology, taking Unruh effect into account. We find that due to the additional effect on temperature, the dependence of power spectrum on $k$ will get corrected with an indication of blue tilt at large $k$ region, which is in consistent with the case of vacuum initial conditions.
In this paper we constructed a semi-realistic cosmological model in a dynamic domain wall framework. Our universe is considered to be a (3+1) dimensional dynamic domain wall in a higher dimensional Einstein-Maxwell-Born-Infeld background. One of our interesting outcomes from the effective Hubble equation for the domain wall dynamics is that it contains an additional component of "dark matter" which is induced from the charge of the bulk Born-Infeld gauge field. In this background spacetime we have studied the cosmological dynamics of the domain wall. In addition to the Born-Infield gauge field…
In this paper, we describe physical effects occurring in the regularized Robertson-Walker spacetime which can reveal the presence of the defect. Our analysis is based on two main physical quantities: the compressive forces acting on (human) observers and the energy possessed by massive particles and photons during their dynamical evolution. In Sec. 3, we claim that with a characteristic length scale of the order of the Planck length compressive forces become so intense near the defect that no (human) observer is able to cross it. In Sec. 4, we show that the energy exhibits an unusual character…
The Big Bang initial singularity problem can be solved by means of bouncing solutions. In the context of extended theories of gravity, we will look for covariant effective actions whose field equations contain up to fourth-order derivatives of the metric tensor. In finding such bouncing solutions, we will make use of an order reduction technique based on a perturbative approach. Reducing the order of the field equations to second-order, we are able to find solutions which are perturbatively close to General Relativity. We will build the covariant effective actions of the resulting order reduce…
In this article, we present a bouncing cosmology inspired by a family of regular black holes. This scale-dependent cosmology deviates from the cosmological principle by means of a scale factor which depends on the time and the radial coordinate as well. The model is isotropic but not perfectly homogeneous. That is, this cosmology describes a universe almost homogeneous only for large scales, such as our observable universe.
In the recent past there have been many attempts to associate the generation of primordial magnetic seed fields with the inflationary era, but with limited success. We thus take a different approach by using a model for nonsingular bouncing cosmology. A coupling of the electromagnetic Lagrangian $F_{μν}F^{μν}$ with a non background scalar field has been considered for the breaking of conformal invariance. We have shown that non singular bouncing cosmology supports magnetogenesis evading the long standing back reaction and strong coupling problems which have plagued inflationary magnetogenesis.…
The Deser-Woodard (DW) nonlocal gravity model has been proposed in order to describe the late-time acceleration of the universe without introducing dark energy. In this paper we focus, however, on the early stage of the universe and demonstrate how a primordial bounce in the vacuum spacetime can be realized in the framework of the DW nonlocal model. We reconstruct the nonlocal distortion function, which encodes all the modifications to the Einstein-Hilbert action, in order to generate bouncing solutions to solve the initial singularity problem. We show that the initial conditions can be chosen…
We have investigated some bouncing models in the framework of an extended gravity theory where the usual Ricci scalar in the gravitational action is replaced by a sum of the Ricci scalar and a term proportional to the trace of the energy momentum tensor. The dynamical parameters of the model are derived in most general manner. We considered two bouncing scenarios through an exponential and a power law scale factor. The non singular bouncing models also favour a late time cosmic speed up phenomenon. The dynamical behaviour of the equation of state parameter is studied for the models. It is obse…
According to the Belinskii-Khalatnikov-Lifshitz scenario, a collapsing universe approaching a spacelike singularity can be approximated by homogeneous cosmological dynamics, but only if asymptotically small spatial regions are considered. It is shown here that the relevant small-volume behavior in solvable models of loop quantum cosmology is crucially different from the large-volume behavior exclusively studied so far. While bouncing solutions exist and may even be generic within a given quantum representation, they are not generic if quantization ambiguities such as choices of representations…
This note emphasizes the role of multi-scale wave structures and junction conditions in many fields of physics, from the dynamics of fluids with non-convex equations of state to the study of gravitational singularities and bouncing cosmologies in general relativity. Concerning the definition and construction of bouncing spacetimes, we review the recent proposal in collaboration with B. Le Floch and G. Veneziano based on the notion of singularity scattering maps. We also present recent numerical investigations of small-scale phenomena arising in compressible fluid flows on FRLW or Kasner geomet…
The modified field equations are written in logarithmic and power law versions of entropy corrected models in Einstein's gravity in the background of FRW universe. In one section, a brief review of the Ho$\check{\text r}$ava-Lifshitz gravity is discussed and the modified field equations in logarithmic and power law versions of entropy corrected models in Ho$\check{\text r}$ava-Lifshitz gravity are formulated. The stability analysis for these models are performed by describing the dynamical system. In another section, a brief review of the fractal universe is presented and the modified field eq…
We present a bouncing cosmology which evolves from the contracting to the expanding phase in a smooth way, without developing instabilities or pathologies and remaining in the regime of validity of 4d effective field theory. A nearly scale invariant spectrum of perturbations is generated during the contracting phase by an isocurvature scalar with a negative exponential potential and then converted to adiabatic. The model predicts a slightly blue spectrum, n_S >~ 1, no observable gravitational waves and a high (but model dependent) level of non-Gaussianities with local shape. The model represen…
We present exact non-singular bounce solutions of general relativity in the presence of a positive cosmological constant and an electromagnetic field, without any exotic matter. The solutions are distinguished by being spatially inhomogeneous in one direction, while they can also contain non-trivial electromagnetic field lines. The inhomogeneity may be substantial, for instance, there can be one bounce in one region of the universe and two bounces elsewhere. Since the bounces are followed by a phase of accelerated expansion, the metrics described here also permit the study of (geodesically com…
We investigate which Jordan frame $F(R)$ gravity can describe a Type IV singular bouncing cosmological evolution, with special emphasis given near the point at which the Type IV singularity occurs. The cosmological bounce is chosen in such a way so that the bouncing point coincides exactly with Type IV singularity point. The stability of the resulting $F(R)$ gravity is examined and in addition, we study the Einstein frame scalar-tensor theory counterpart of the resulting Jordan frame $F(R)$ gravity. Also, by assuming that the Jordan frame metric is chosen in such a way so that, when conformall…
We develop a Gauss-Bonnet extension of Loop Quantum Cosmology, by introducing holonomy corrections in modified $F(\mathcal{G})$ theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of Loop Quantum Gravity theories, and we result in having leading order corrections to the classical $F(\mathcal{G})$ theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes possible to find the Loop Quantum Cosmology corrected $F(\mathcal{G})$ theory that can realize va…
We study cosmological perturbations arising from thermal fluctuations in the big-bounce cosmology in the Einstein-Cartan-Sciama-Kibble theory of gravity. We show that such perturbations cannot have a scale-invariant spectrum if fermionic matter minimally coupled to the torsion tensor is macroscopically averaged as a spin fluid, but have a scale-invariant spectrum if the Dirac form of the spin tensor of the fermionic matter is used.
We investigate bouncing scenario in the modified $f(T)$ gravity, $T$ being the torsion scalar. Attention is attached to the reconstruction of $f(T)$ able to describe type IV singular bouncing evolution, where we adopt as assumption that the bouncing and type IV singularity points coincide. In the context of the reconstructed $f(T)$ model we calculate the Hubble slow-roll parameters in order to determine the dynamical evolution of the cosmological system under study. The results show that the Hubble slow-roll parameters become singular at the type IV singularity indicating a dynamical instabili…
We study a cosmological scenario in which inflation is preceded by a bounce. In this scenario, the primordial singularity, one of the major shortcomings of inflation, is replaced by a non-singular bounce, prior to which the universe undergoes a phase of contraction. Our starting point is the bouncing cosmology investigated in Falciano et al. (2008), which we complete by a detailed study of the transfer of cosmological perturbations through the bounce and a discussion of possible observational effects of bouncing cosmologies. We focus on a symmetric bounce and compute the evolution of cosmologi…
We introduce the "wedge diagram," an intuitive way to illustrate how cosmological models with a classical (non-singular) bounce generically resolve fundamental problems in cosmology. These include the well-known horizon, flatness, and inhomogeneity problems; the small tensor-to-scalar ratio observed in the cosmic microwave background; the low entropy at the beginning of a hot, expanding phase; and the avoidance of quantum runaway. The same diagrammatic approach can be used to compare with other cosmological scenarios.
We explore bounce cosmology in $F(\mathcal{G})$ gravity with the Gauss-Bonnet invariant $\mathcal{G}$. We reconstruct $F(\mathcal{G})$ gravity theory to realize the bouncing behavior in the early universe and examine the stability conditions for its cosmological solutions. It is demonstrated that the bouncing behavior with an exponential as well as a power-law scale factor naturally occurs in modified Gauss-Bonnet gravity. We also derive the $F(\mathcal{G})$ gravity model to produce the ekpyrotic scenario. Furthermore, we construct the bounce with the scale factor composed of a sum of two expo…
Although inflation is a natural candidate to generate the lengths of coherence of magnetic fields needed to explain current observations, it needs to break conformal invariance of electromagnetism to obtain significant magnetic amplitudes. Of the simplest realizations are the kinetically-coupled theories $f^2(ϕ)F_{μν}F^{μν}$ (or $IFF$ theories). However, these are known to suffer from electric fields backreaction or the strong coupling problem. In this work we shall confirm that such class of theories are problematic to support magnetogenesis during inflationary cosmology. On the contrary, we …
We examine the dynamics of a closed cosmology whose matter source is that of a conformally coupled scalar field with a broken ${\rm SO}(1,1)$ symmetry, which correspond to the $α$-attractors proposed by Linde and Kallosh. Following a field redefinition, such models give rise to "T-model" inflationary potentials, whose dynamics provide both an inflationary phase and a classical bounce. We show that the universe can undergo bounces far from the regime of quantum gravity. We analyse perturbations on this background with particular attention given to the effects of a double-bouncing scenario (with…
A gravitational mirror is a non-singular finite redshift surface which bounces all incident null geodesics. While a white mirror (outward bouncing) resembles 't Hooft's brick wall, a black mirror (inward bouncing) offers a novel mechanism for sealing off curvature singularities. The geometry underlying a two-sided mirror is characterized by a single signature change, to be contrasted with the signature flip which governs the black hole geometry. To demonstrate the phenomenon analytically, we derive an exact, static, radially symmetric, two-sided mirror solution, which asymptotes the massless B…
We present the graviton propagator for an infinite derivative, $D$-dimensional, non-local action, up to quadratic order in curvature around a Minkowski background, and discuss the conditions required for this class of gravity theory to be ghost-free. We then study the gravitational entropy for de-Sitter and Anti-de Sitter backgrounds, before comparing with a recently derived result for a Schwarzschild blackhole, generalised to arbitrary $D$-dimensions, whereby the entropy is given simply by the area law. A novel approach of decomposing the entropy into its $(r, t)$ and spherical components is …
An old question surrounding bouncing models concerns their stability under vector perturbations. Considering perfect fluids or scalar fields, vector perturbations evolve kinematically as $a^{-2}$, where $a$ is the scale factor. Consequently, a definite answer concerning the bounce stability depends on an arbitrary constant, therefore, there is no definitive answer. In this paper, we consider a more general situation where the primeval material medium is a non-ideal fluid, and its shear viscosity is capable of producing torque oscillations, which can create and dynamically sustain vector pertur…
We present the method of describing an evolution in quantum cosmology in the framework of the reduced phase space quantization of loop cosmology. We apply our method to the flat Friedman-Robertson-Walker model coupled to a massless scalar field. We identify the physical quantum Hamiltonian that is positive-definite and generates globally an unitary evolution of considered quantum system. We examine properties of expectation values of physical observables in the process of the quantum big bounce transition. The dispersion of evolved observables are studied for the Gaussian state. Calculated rel…
According to classical GR, Anti-de Sitter (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by nonsingular bounces. This may have important implications for the beginning of the multiverse. Geodesics in cosmological spacetimes are known to be past-incomplete, as long as the average expansion rate along the geodesic is positive, but it is not clear that the latter condition is satisfied if the geodesic repeatedly passes through crunching AdS bubbles. We investigate…
A cosmological model with a specific form of the Hubble parameter is constructed in a flat homogeneous, and isotropic background in the framework of $f(R, T)$ gravity, where $R$ is the scalar curvature and $T$ is the trace of the stress-energy-momentum tensor. The proposed functional form of the Hubble parameter is taken in such a way that it fulfills the successful bouncing criteria to find the solution of the gravitational field equations provided the Universe is free from initial singularity. The various constraints on the parameters are involved in the functional form of the Hubble paramet…
We consider the ADM formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond General Relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the universe following the spirit of Weyl's postulate, has been fixed, $f$ theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation, i.e., the constraint and dynamical equations have the same form for all these observers. Moreov…
A companion paper provides a proposal for cosmic singularity resolution based upon general features of a bouncing unitary cosmological model in the mini-superspace approximation. This paper analyses novel phenomenology that can be identified within particular solutions of that model. First, we justify our choice of particular solutions based upon a clearly articulated and observationally-motivated principle. Second, we demonstrate that the chosen solutions follow a classical mini-superspace cosmology before smoothly bouncing off the classically singular region. Third, and most significantly, w…
