This study explores the feasibility of an effective Friedmann equation in removing the classical Big Bang initial singularity and replacing it with a non-singular bounce occurring at a critical energy density value. In a spatially flat, homogeneous, and isotropic universe, the effective theory is obtained by introducing a function that is parametrically dependent on the critical energy density. This function measures the deviation from the benchmark theory, which is recovered as the critical energy density approaches infinity. Focusing on the covariant single-field formulation in viable Horndeski gravity, our analysis shows that both the effective and the benchmark theories belong to the same scalar-tensor theory, without any additional propagating degrees of freedom: the cuscuton and extended cuscuton models.
In this paper we study the evolution of cosmological perturbations through a nonsingular bouncing universe using covariant perturbation theory and examine the validity of linear perturbation theory. The bounce is modeled by a two component perfect fluid. Gauge invariant perturbations are defined in terms of the comoving observers. The scalar and vector perturbations become singular at the turning point, which is the boundary of the spacetime region where the null energy condition is violated. Nonadiabatic modes of comoving curvature perturbation diverge at the turning point. The gravitational …
The nonsingular bounce models usually suffer from the ghost or gradient instabilities, as has been proved recently. In this paper, we propose a covariant effective theory for stable nonsingular bounce, which has the quadratic order of the second order derivative of the field $ϕ$ but the background set only by $P(ϕ,X)$. With it, we explicitly construct a fully stable nonsingular bounce model for the ekpyrotic scenario.
The similarity between Finsler and Riemann geometry is an intriguing starting point to extend general relativity. The lack of quadratic restriction over the line element (color) naturally generalize the Riemannian case and breaks the local symmetries of general relativity. In addition, the Finsler manifold is enriched with new geometric entities and all the classical identities are suitably extended. We investigate the covariant kinematics of a medium formed by a time-like congruence. After a brief view in the general case we impose particular geometric restrictions to get some analytic insigh…
We explore the relationship between the effective dynamics in standard loop quantum cosmology (LQC) based on holonomies and triads obtained from gauge-fixing fluxes, and a modification of LQC based on holonomies and gauge-covariant fluxes (referred to as gLQC). Both the models yield singularity resolution via a bounce because of non-perturbative quantum geometric effects resulting in a maximum for energy density. In LQC, the bounce is extremely well captured by a $ρ^2$ term in energy density with a negative sign which emerges as a non-perturbative modification to the classical Friedmann and Ra…
We provide an analytical solution to the quantum dynamics of a flat Friedmann-Lemaître- Robertson-Walker model with a massless scalar field in the presence of a small and positive cosmological constant, in the context of Loop Quantum Cosmology. We use a perturbative treatment with respect to the model without a cosmological constant, which is exactly solvable. Our solution is approximate, but it is precisely valid at the high curvature regime where quantum gravity corrections are important. We compute explicitly the evolution of the expectation value of the volume. For semiclassical states cha…
The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a massless scalar field was recently constructed. In this paper, its effective dynamics with the LQC discreteness corrections is studied and the equations of motion are analytically solved, showing that the big bang singularity is replaced by the big bounces, which take place up to three times, once in each diagonal direction, whenever each of the area scale factors approaches its critical value in the Planck regime measured by the reference of the scalar field momentum.
The usual Einstein's equations is modified as a one parameter family of equations in the framework of rainbow gravity. In this paper we derive the modified Friedmann-Robertson-Walker (FRW) equations when the cosmological evolution of radiation particles is taken into account. In particular, given some specific dispersion relations, the big bounce solutions to the modified FRW equations can be derived. Notably, to obtain a well defined rainbow metric at the moment of the big bounce, we find it seems necessary to introduce a cosmological constant which depends on the energy of probes as well, im…
In this work, we investigate the notion of time and unitarity in the vicinity of a bounce in quantum cosmology, that is, a turning point for the scale factor. Because WKB methods drastically fail near a turning point, the scale factor cannot play the role of time in such scenarios. We overcome this difficulty by studying the dynamics of matter transitions when using its conjugate momentum as a time. We find precise conditions so as to recover unitarity, and hence, a consistent notion of probability. We then compute transitions in a concrete example, extract the specific feature of a bounce and…
We discuss whether black holes could persist in a universe which recollapses and then bounces into a new expansion phase. Whether the bounce is of classical or quantum gravitational origin, such cosmological models are of great current interest. In particular, we investigate the mass range in which black holes might survive a bounce and ways of differentiating observationally between black holes formed just after and just before the last bounce. We also discuss the consequences of the universe going through a sequence of dimensional changes as it passes through a bounce.
In this paper we examine the validity of the linear perturbation theory near a bounce in the covariant analysis. Some linearity parameters are defined to set up conditions for a linear theory. Linear evolution of density perturbation and gravitational waves have been computed previously. We have calculated the vector and scalar induced parts of the shear tensor. For radiationlike and dustlike single fluid dominated collapsing Friedmann-Lemaitre-Robertson-Walker background it is shown that the linearity conditions are not satisfied near a bounce.
Quasiclassical methods are used to define dynamical tunneling times in models of quantum cosmological bounces. These methods provide relevant new information compared with the traditional treatment of quantum tunneling by means of tunneling probabilities. As shown here, the quantum dynamics in bounce models is not secure from reaching zero scale factor, re-opening the question of how the classical singularity may be avoided. Moreover, in the examples studied here, tunneling times remain small even for large barriers, highlighting the quantum instability of underlying bounce models.
We analyse the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant characterizing its evolution in term of the dust-time dualism. We demonstrate that in a canonical metric approach, the cosmological singularity is removed in correspondence to a positive defined value of the dust energy density. Furthermore, the quantum Big-Bounce is connected to the Universe turning point via a well-defined semiclassical limit. Then we can reliably infer that the proposed scenario is compatible with a cyclical Universe picture. We also show how, when th…
We remind the way to obtain integrable models with non-minimally coupled scalar fields. We are interesting to models with bounce solutions and compare bounce solutions in two known integrable models. We show that only one model has a bounce solution that tends to a stable de Sitter solution.
In quantum cosmology, one has to select a specific wave function solution of the quantum state equations under consideration in order to obtain concrete results. The simplest choices have been already explored, in different frameworks, yielding, in many cases, quantum bounces. As there is no consensually established boundary condition proposal in quantum cosmology, we investigate the consequences of enlarging known sets of initial wave functions of the universe, in the specific framework of the Wheeler-DeWitt equation interpreted along the lines of the de Broglie-Bohm quantum theory, on the po…
We study a novel class of nonsingular time-symmetric cosmological bounces. In this class of four dimensional models the bounce is induced by a perfect fluid with a negative energy density. Metric perturbations are solved in an analytic way all through the bounce. The conditions for generating a scale invariant spectrum of tensor and scalar metric perturbations are discussed.
The big bounce singularity of a simple 5D cosmological model is studied. Contrary to the standard big bang space-time singularity, this big bounce singularity is found to be an event horizon at which the scale factor and the mass density of the universe are finite, while the pressure undergoes a sudden transition from negative infinity to positive infinity. By using coordinate transformation it is also shown that before the bounce the universe contracts deflationary, and the universe has been existed, according to the proper-time, for an infinitely long time.
We study a model for a non-singular cosmic bounce in N=1 supergravity, based on supergravity versions of the ghost condensate and cubic Galileon scalar field theories. The bounce is preceded by an ekpyrotic contracting phase which prevents the growth of anisotropies in the approach to the bounce, and allows for the generation of scale-invariant density perturbations that carry over into the expanding phase of the universe. We present the conditions required for the bounce to be free of ghost excitations, as well as the tunings that are necessary in order for the model to be in agreement with c…
The baryon-antibaryon asymmetry (excess of matter over antimatter in our Universe), indicated by observational data from the Cosmic Microwave Background anisotropies, predictions of primordial Nucleosynthesis, and the absence of intense radiation from matter-antimatter annihilation, constitutes an unsolved puzzle in cosmology. Two mechanisms for baryon asymmetry have been proposed as extensions of the Standard Model of Particle Physics at high energies. They rely on new couplings involving the baryon number current, one with a scalar field, called Spontaneous Baryogenesis, and the other with s…
The big bounce transition of the quantum FRW model in the setting of loop quantum cosmology is presented. We determine the physical self-adjoint Hamiltonian generating the dynamics. It is used to define, via the Stone theorem, an evolution operator. We examine properties of expectation values of physical observables in the process of the quantum big bounce transition. The dispersion of observables are studied in the context of the Heisenberg uncertainty principle. We suggest that the real nature of the bounce may become known only after we quantize the Belinskii-Khalatnikov-Lifshitz scenario, …
We investigate cosmological scenarios containing one canonical scalar field with an exponential potential in the context of bouncing models, where the bounce happens due to quantum cosmological effects. The only possible bouncing solutions in this scenario (discarding an infinitely fine tuned exception) must have one and only one dark energy phase, either occurring in the contracting era or in the expanding era. Hence,these bounce solutions are necessarily asymmetric. We calculate the spectral indexes and amplitudes of scalar and tensor perturbations numerically, considering the whole history …
We investigate if theories yielding bouncing cosmological models also generate wormhole solutions. We show that two of them present sensible traversable static wormhole solutions, while for the third possibility such solutions are absent.
We study a "classical" bouncing scenario in beyond Horndeski theory. We give an example of spatially flat bouncing solution that is non-singular and stable throughout the whole evolution. The model is arranged in such a way that the scalar field driving the cosmological evolution initially behaves like full-fledged beyond Horndeski, whereas at late times it becomes a massless scalar field minimally coupled to gravity.
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…
The cosmological solution with a long-term bouncing off time is presented. The solution has a preceding contracting and a subsequent expanding phases and between them there exists a bouncing off phase with arbitrary time duration.
We determine the causal structure of the McVittie spacetime for a cosmological model with an asymmetric bounce. The analysis includes the computation of trapping horizons, regular, trapped, and anti-trapped regions, and the integration of the trajectories of radial null geodesics before, during, and after the bounce. We find a trapped region since the beginning of the contracting phase up to shortly before the bounce, thus showing the existence of a black hole. When the universe reaches a certain minimum scale in the contracting phase, the trapping horizons disappear and the central singularit…
The implications of a deformed Heisenberg algebra on the Friedmann-Robertson-Walker cosmological models are investigated. We consider the Snyder non-commutative space in which the translation group is undeformed and the rotational invariance preserved. When this framework is implemented to one-dimensional systems (which is this case) the modifications are uniquely fixed up to a sign. A cosmological quantum bounce à la loop quantum cosmology is then obtained. We also get the Randall-Sundrum braneworld scenario and this way a Snyder-deformed quantum cosmology can be considered as a common phenom…
We study quantum cosmology with conformal matter comprising a perfect radiation fluid and a number of conformally coupled scalar fields. Focusing initially on the collective coordinates (minisuperspace) associated with homogeneous, isotropic backgrounds, we are able to perform the quantum gravity path integral exactly. The evolution describes a "perfect bounce", in which the Universe passes smoothly through the singularity. We extend the analysis to spatially flat, anisotropic universes, treated exactly, and to generic inhomogeneous, anisotropic perturbations treated at linear and nonlinear or…
Bouncing Cosmological Models and Energy Conditions in $f(Q, L_m)$ gravity
Centre for Interdisciplinary Studies and Research, D Y Patil International University（D Y Patil国际大学跨学科研究与中心）；JSPM’s Bhivarabai Sawant Institute of Technology and Research（JSPM Bhivarabai Sawant技术与研究所）；Department of Mathematics, SR University（SR大学数学系）
Instituto Argentino de Radioastronomía (IAR, CONICET/CIC/UNLP)（阿根廷射电天文研究所）；Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata（拉普拉塔国立大学天文与地球物理学院）；Departamento de Física Teórica, Instituto de Física, Universidade do Estado de Rio de Janeiro（里约热内卢州立大学物理研究所理论物理系）
It has been known for some time that the cosmological Friedmann equation deduced from General Relativity can be also obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior of the solutions of these modified cosmological equations paying special attention to the sign of the quantum corrections. We find different quantum effects crucially depending on this sign. One such a solution displays a qualitative resemblance to ot…
The present work analyzes the various conditions in which there can be a bouncing universe solution in f(R) gravity. In the article an interesting method, to analyze the bouncing FRW solutions in a spatially flat universe using f(R) gravity models using an effective Einstein frame description of the process, is presented. The analysis shows that a cosmological bounce in the f(R) theory need not be described by an equivalent bounce in the Einstein frame description of the process where actually there may be no bounce at all. Nevertheless the Einstein frame description of the bouncing phenomena …
Dynamical solutions for an evolving multiple network of black holes near a cosmological bounce dominated by a scalar field are investigated. In particular, we consider the class of black hole lattice models in a hyperspherical cosmology, and we focus on the special case of eight regularly-spaced black holes with equal masses when the model parameter $κ> 1$. We first derive exact time evolving solutions of instantaneously-static models, by utilizing perturbative solutions of the constraint equations that can then be used to develop exact 4D dynamical solutions of the Einstein field equations. W…
We present a rich class of exact solutions which contains radiation-dominated and matter-dominated models for the early and late universe. They include a variable cosmological ``constant'' which is derived from a higher dimension and manifests itself in spacetime as an energy density for the vacuum. This is in agreement with observational data and is compatible with extensions of general relativity to string and membrane theory. Our solutions are also typified by a non-singular ``big bounce'' (as opposed to a singular big bang), where matter is created as in inflationary cosmology.
In this paper, we study a big bounce universe typified by a non-singular big bounce, as opposed to a singular big bang. This cosmological model can describe radiation dominated early universe and matter dominated late universe in FRW model. The connections between thermodynamics and gravity are observed here. In the early stage of both cold and hot universes, we find there is only one geometry containing a 4D de Sitter universe with a general state parameter. We also find the form of the apparent horizon in the early universe strongly depends on the extra dimension, which suggests that the inf…
We study the classical dynamics of black holes during a nonsingular cosmological bounce. Taking a simple model of a nonsingular bouncing cosmology driven by the combination of a ghost and ordinary scalar field, we use nonlinear evolutions of the Einstein equations to follow rotating and non-rotating black holes of different sizes through the bounce. The violation of the null energy condition allows for a shrinking black hole event horizon and we find that for sufficiently large black holes (relative to the minimum Hubble radius) the black hole apparent horizon can disappear during the contract…
In this paper we study the flat (k=0) cosmological FRW model with holonomy corrections of Loop Quantum Gravity. The considered universe contains a massless scalar field and the cosmological constant Lambda. We find analytical solutions for this model in different configurations and investigate its dynamical behaviour in the whole phase space. We show the explicit influence of Lambda on the qualitative and quantitative character of solutions. Even in the case of positive Lambda the oscillating solutions without the initial and final singularity appear as a generic case for some quantisation sch…
The purpose of this short review is to describe cosmological models with a linear inhomogeneous time-dependent equation of state (EoS) for the dark energy, when the dark fluid is coupled with dark matter. This may lead to a bounce cosmology. We consider equivalent descriptions in terms of the EoS parameters for an exponential, a power-law, or a double-exponential law for the scale factor $a$. Stability issues are discussed by considering small perturbations around the critical points for the bounce, in the early as well as in the late, universe. The latter part of the paper is concerned with d…
String-inspired cosmologies, whereby a non-singular curvature bounce is induced by a general-covariant, $T$-duality-invariant, non-local dilaton potential, are used to study numerically how inhomogeneities evolve and to compare the outcome with analytic expressions obtained through different matching conditions across the bounce. Good agreement is found if continuity across the bounce is assumed to hold for $\cal{R}$, the curvature perturbation on comoving hypersurfaces, rather than for the Bardeen potential.
A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in…
We investigate bounce cosmological models in the presence of a viscous fluid, making use of generalized holographic cutoffs introduced by Nojiri and Odintsov (2017). We consider both an exponential, a power-law, and a double exponential form for the scale factor. By use of these models we calculate expressions for infrared cutoffs analytically, such that they correspond to the particle horizon at the bounce. Finally we derive the energy conservation equation, from the holographic point of view. In that way the relationship between the viscous fluid bounce and the holographic bounce is demonstr…
Cosmological Bounce Relics: Black Holes, Gravitational Waves, and Dark Matter
Institute of Cosmology & Gravitation, University of Portsmouth（宇宙学与引力研究所，朴茨茅斯大学）；Institute of Space Sciences (ICE, CSIC)（空间科学研究所（ICE，CSIC））；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚太空研究学院（IEEC））
The cosmological model with two phantom scalar fields with the special choice of field's potential is considered. The obtained regular solution describes a bounce with a subsequent transition to the de Sitter stage of the expansion of the Universe. This solution also could be interpreted as a S-brane solution.
We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler-De Witt equation) in the FLRW minisuper- space without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice con- sisting of modified Gaussian wave functions, aiming at obtaining a non singular bounce…
The evolution of the luminosity distance in a contracting universe is studied. It is shown that for quite a lot of natural dynamical evolutions, its behavior is far from trivial and its value can even decrease with an increasing time interval between events. The consequences are investigated and it is underlined that this could both put stringent consistency conditions on bouncing models and open a new observational window on "pre Big Bang" physics using standard gravitational waves.
Einstein-Cartan theory is an extension of the standard formulation of General Relativity characterized by a non-vanishing torsion. The latter is sourced by the matter fields via the spin tensor, and its effects are expected to be important at very high spin densities. In this work we analyze in detail the physics of Einstein-Cartan theory with Dirac and Maxwell fields minimally coupled to the spacetime torsion. This breaks the $U(1)$ gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe. The resulting Dirac-like and Maxwell-like equat…
In bouncing cosmology, the primordial fluctuations are generated in a cosmic contraction phase before the bounce into the current expansion phase. For a nonsingular bounce, curvature and anisotropy grow rapidly during the bouncing phase, raising questions about the reliability of perturbative analysis. In this paper, we study the evolution of adiabatic perturbations in a nonsingular bounce by nonperturbative methods including numerical simulations of the nonsingular bounce and the covariant formalism for calculating nonlinear perturbations. We show that the bounce is disrupted in regions of th…
One of the fundamental questions of theoretical cosmology is whether the universe can undergo a non-singular bounce, i.e., smoothly transit from a period of contraction to a period of expansion through violation of the null energy condition (NEC) at energies well below the Planck scale and at finite values of the scale factor such that the entire evolution remains classical. A common claim has been that a non-singular bounce either leads to ghost or gradient instabilities or a cosmological singularity. In this letter, we examine cubic Galileon theories and present a procedure for explicitly co…
An exactly solvable bounce model in loop quantum cosmology is identified which serves as a perturbative basis for realistic bounce scenarios. Its bouncing solutions are derived analytically, demonstrating why recent numerical simulations robustly led to smooth bounces under the assumption of semiclassicality. Several effects, easily included in a perturbative analysis, can however change this smoothness. The effective theory is not only applicable to such situations where numerical techniques become highly involved but also allows one to discuss conceptual issues. For instance, consequences of…
