A Cosmological Theory without Singularities

Classical and Quantum Gravity, 2011

We show that the f (T ) gravitational paradigm, in which gravity is described by an arbitrary function of the torsion scalar, can provide a mechanism for realizing bouncing cosmologies, thereby avoiding the Big Bang singularity. After constructing the simplest version of an f (T ) matter bounce, we investigate the scalar and tensor modes of cosmological perturbations. Our results show that metric perturbations in the scalar sector lead to a background-dependent sound speed, which is a distinguishable feature from Einstein gravity. Additionally, we obtain a scale-invariant primordial power spectrum, which is consistent with cosmological observations, but suffers from the problem of a large tensor-to-scalar ratio. However, this can be avoided by introducing extra fields, such as a matter bounce curvaton.

International Journal of Theoretical Physics, 2014

We analyze the thermodynamical properties of the regular static and spherically symmetric black hole model presented by Mboyne and Kazanas. Equations for the thermodynamical quantities valid for an arbitrary density profile are deduced, and from them we show that the model is thermodynamically unstable. Evidence is also presented pointing to its dynamical instability. The gravitational entropy of this solution based on the Weyl curvature conjecture is calculated, following the recipe given by Rudjord, Gr∅n and Sigbj∅rn, and it is shown to have the expected behaviour for a good description of the gravitational entropy.

Physical Review D, 1995

We present a class of theories of two dimensional gravity which admits homogeneous and isotropic solutions that are nonsingular and asymptotically approach a FRW matter dominated universe at late times. These models are generalizations of two dimensional dilaton gravity and both vacuum solutions and those including conformally coupled matter are investigated. In each case our construction leads to an inflationary stage driven by the gravitational sector. Our work comprises a simple example of the 'Nonsingular Universe' constructions of ref.

Physical Review D, 1999

Under certain circumstances, the collision of magnetic monopoles, topologically locked-in regions of false vacuum, leads to topological inflation and the creation of baby universes. The future evolution of initial data represented by the two incoming monopoles may contain a timelike singularity but this need not be the case. We discuss the global structure of the spacetime associated with monopole collisions and also that of topological inflation. We suggest that topological inflation within magnetic monopoles leads to an eternally reproducing universe.

Journal of Cosmology and Astroparticle Physics, 2011

We present a wide class of models which realise a bounce in a spatially flat Friedmann universe in standard General Relativity. The key ingredient of the theories we consider is a noncanonical, minimally coupled scalar field belonging to the class of theories with Kinetic Gravity Braiding / Galileon-like self-couplings. In these models, the universe smoothly evolves from contraction to expansion, suffering neither from ghosts nor gradient instabilities around the turning point. The end-point of the evolution can be a standard radiation-domination era or an inflationary phase. We formulate necessary restrictions for Lagrangians needed to obtain a healthy bounce and illustrate our results with phase portraits for simple systems including the recently proposed Galilean Genesis scenario.

Classical and Quantum Gravity, 1995

The most general version of a renormalizable d = 4 theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains 12 independent functions, which are the generalized coupling constants of the theory. We calculate the one-loop beta functions and then consider the conditions for finiteness. The set of exact solutions of power type is proven to consist of precisely three conformal and three nonconformal solutions, given by remarkably simple (albeit nontrivial) functions that we obtain explicitly. The finiteness of the conformal theory indicates the absence of a conformal anomaly in the finite sector. The stability of the finite solutions is investigated and the possibility of renormalization group flows is discussed as well as several physical applications.

Physics Letters B, 1994

A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations corresponding to two different, multiplicatively renormalizable variants of the same are derived. The analysis of their asymptotic solutions shows that, depending on the sign of one of the coupling constants, we can construct an asymptotically free theory which is also asymptotically conformal invariant at strong (or small) curvature. The connection that can be established between one of the multiplicatively renormalizable variants of the theory and the effective theory of the conformal factor, aiming at the description of quantum gravity at large distances, is investigated.

Physical Review D, 1996

We study the cosmological implications of the one-loop terms in the string expansion. In particular, we find non-singular solutions which interpolate between a contracting universe and an expanding universe, and show that these solutions provide a mechanism for removing the initial conditions problem peculiar to spatially closed FRW cosmologies. In addition, we perform numerical calculations to show that the non-singular cosmologies do not require a careful choice of initial conditions, and estimate the likely magnitude of higher order terms in the string expansion.

Physical Review D, 2002

Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. We show that this singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory. A mathematical toy model is proposed for which the analytical nonsingular extension of FRW solutions is obtained.

Physical Review D, 2006

We consider a simple toy model of a regular bouncing universe. The bounce is caused by an extra time-like dimension, which leads to a sign flip of the ρ 2 term in the effective four dimensional Randall Sundrum-like description. We find a wide class of possible bounces: big bang avoiding ones for regular matter content, and big rip avoiding ones for phantom matter. Focusing on radiation as the matter content, we discuss the evolution of scalar, vector and tensor perturbations. We compute a spectral index of ns = −1 for scalar perturbations and a deep blue index for tensor perturbations after invoking vacuum initial conditions, ruling out such a model as a realistic one. We also find that the spectrum (evaluated at Hubble crossing) is sensitive to the bounce. We conclude that it is challenging, but not impossible, for cyclic/ekpyrotic models to succeed, if one can find a regularized version.

Physical Review D

We apply the classical double copy procedure to a class of regular, non-singular black hole solutions. We give several examples, paying particular attention to a string-theory-corrected black hole solution emerging from T-duality. Non-perturbative stringy corrections introduce an ultraviolet (UV) zero-point length cutoff which results in non-singular black hole spacetimes. Apart from the UV regulator, the solution is equivalent to the Bardeen black hole spacetime. We extend this solution to include an asymptotic de Sitter background. All Yang-Mills field theory quantities associated with the double copy are well-behaved and finite for all values of parameters. We present a thorough analysis of the black hole horizon structure, additionally uncovering a simple yet new connection between horizons on the gravity side and electric fields on the gauge theory side of the double copy.

General Relativity and Gravitation, 2022

We present an exact five-dimensional (5D) rotating regular black hole metric, with a deviation parameter k ≥ 0, that interpolates between the 5D Kerr black hole (k = 0) and 5D Kerr-Newman (r ≫ k). This 5D rotating regular black hole is an exact solution of general relativity coupled to nonlinear electrodynamics. Interestingly, for a given value of parameter k there exits a critical angular momentum a = a E which corresponds to extremal rotating regular black hole with degenerate horizons, while for a < a E , one has non-extremal rotating regular black hole with outer and inner horizons. Owing to the correction factor (e -k/r 2 ), which is motivated by the quantum arguments, the ergoregion and black hole shadow are modified.

Physical Review D, 2000

We present a completely integrable deformation of the CGHS dilaton gravity model in two dimensions. The solution is a singularity free black hole that at large distances asymptotically joins to the CGHS solution.

Physical Review D, 1995

The running coupling constants (in particular, the gravitational one) are studied in asymptotically free GUTs and in finite GUTs in curved spacetime, with explicit examples. The running gravitational coupling is used to calculate the leading quantum GUT corrections to the Newtonian potential, which turn out to be of logarithmic form in asymptotically free GUTs. A comparison with the effective theory for the conformal factor-where leading quantum corrections to the Newtonian potential are again logarithmic-is made. A totally asymptotically free O(N) GUT with quantum higher derivative gravity is then constructed, using the technique of introducing renormalization group (RG) potentials in the space of couplings. RG equations for the cosmological and gravitational couplings in this theory are derived, and solved numerically, showing the influence of higher-derivative quantum gravity on the Newtonian potential. The RG-improved effective gravitational Lagrangian for asymptotically free massive GUTs is calculated in the strong (almost constant) curvature regime, and the non-singular De Sitter solution to the quantum corrected gravitational equations is subsequently discussed. Finally, possible extensions of the results here obtained are briefly outlined.

International Journal of Geometric Methods in Modern Physics, 2016

We investigate in this paper the possibilities that the observed cold dark matter density can be generated by decays of a heavy scalar field which dominate the universe at the quantum regime. Indeed, we present two approaches based on an extension of quantum field theory to the case when spacetime topology fluctuates (spacetime foam, at the quantum regime). In this extension the number of bosonic fields becomes a variable and the ground state is characterized by a finite particle number density. In the second approach it is the gauge-group parameters which became dynamical. This is tributary on the Centrally Extended Group and Cohomology.

Physical Review D, 2008

We propose a regular black hole whose inside generates a de Sitter space and then is finally frustrated into a singularity. It is a modified model which was suggested originally by Frolov, Markov, and Mukhanov. In our model, we could adjust a regular black hole so that its period before going into the extreme state is much longer than the information retention time. During this period an observer could exist who observes the information of the Hawking radiation, falls freely into the regular center of the black hole, and finally meets the free-falling information again. The existence of such an observer implies that the complementary view may not be consistent with a regular black hole, and therefore, is not appropriate as a generic principle of black hole physics.

Journal of Cosmology and Astroparticle Physics

With the recent release of the black hole image of Sgr A* alongside the earlier image of M87*, one can now really hope to acquire a better understanding of the gravitational physics at the horizon scale. In this paper, we investigate the prospect of the regular black hole scenario with a Minkowski core in explaining the observed shadow of M87* and Sgr A*. Regular black holes generally appear in Einstein gravity coupled to non-linear electrodynamics and are interesting as they can evade the r = 0 curvature singularity arising in general relativity. Using the previously determined mass and distance we compute the observables associated with the black hole shadow. These when compared with the observed angular diameter reveals that the shadow of M87* and Sgr A* favor the regular black hole scenario with a small but non-zero charge. The implications are discussed.

The European Physical Journal C, 2015

We derive a radiating regular rotating black hole solution, radiating Kerr-like regular black hole solution. We achieve this by starting from the Hayward regular black hole solution via a complex transformation suggested by Newman-Janis. The radiating Kerr metric, the Kerr-like regular black hole and the standard Kerr metric are regained in the appropriate limits. The structure of the horizon-like surfaces are also determined.

Physical Review D, 1995

Physical Review D

The phenomenology of primordial black holes (PBHs) physics and the associated PBH abundance constraints, can be used in order to probe the physics of the early Universe. In this work, we investigate the PBH formation during the standard radiation-dominated era by studying the effect of an early F (R) modified gravity phase with a bouncing behavior which is introduced to avoid the initial spacetime singularity problem. In particular, we calculate the energy density power spectrum at horizon crossing time and then we extract the PBH abundance in the context of peak theory as a function of the parameter α of our F (R) gravity bouncing model at hand. Interestingly, we find that in order to avoid PBH overproduction at formation time, namely Ω PBH,f < 1, α should lie within the range α ≤ 10 −17 M 2 Pl. This constraint can be translated to a constraint on the energy scale at the onset of the Hot Big Bang (HBB) phase, H RD ∼ √ α /2 which can be recast as H RD ≤ 2 × 10 −8 M Pl .

Physical Review D, 2012

In the theories of generalized modified gravity, the acceleration equation is generally fourth order. So it is hard to analyze the evolution of the Universe. In this paper, we present a class of generalized modified gravity theories which have the acceleration equation of second order derivative. Then both the cosmic evolution and the weak-field limit of the theories are easily investigated. We find that not only the Big-bang singularity problem but also the current cosmic acceleration problem could be easily dealt with.

The European Physical Journal C

We investigate the inflation driven by a nonlinear electromagnetic field based on an NLED lagrangian density $${\mathscr {L}}_{\text {nled}} = - {F} f \left( {F} \right) $$ L nled = - F f F , where $$f \left( {F}\right) $$ f F is a general function depending on F. We first formulate an f-NLED cosmological model with a more general function $$f \left( {F}\right) $$ f F and show that all NLED models can be expressed in this framework; then, we investigate in detail two interesting examples of the function $$f \left( {F}\right) $$ f F . We present our phenomenological model based on a new Lagrangian for NLED. Solutions to the field equations with the physical properties of the cosmological parameters are obtained. We show that the early Universe had no Big-Bang singularity, which accelerated in the past. We also investigate the qualitative implications of NLED by studying the inflationary parameters, like the slow-roll parameters, spectral index $$n_s$$ n s , and tensor-to-scalar ratio...

Brazilian Journal of Physics, 2014

A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge independent quantities. We shall see that in the QM-scheme we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz et al that deals with perturbation in the standard Einstein framework. For completeness, we compare the QMscheme to the gauge-independent method of Bardeen, a procedure consisting on particular choices of the perturbed variables as a combination of gauge dependent quantities.

Astrophysics and Space Science, 2013

In this work, we consider the framework of nonlinear electrodynamics in Bianchi type I universe model composed of matter and electromagnetic field. We deal with electric and magnetic universe separately. In this scenario, we calculate the electric and magnetic fields and their corresponding matter densities using two particular types of interaction terms. We also check the validity of generalized second law of thermodynamics in both universe models enclosed by apparent horizon. It turns out that this law holds on the apparent horizon for a particular range depending upon the parameters. Finally, we discuss the deceleration and statefinder parameters to check the viability of these models.

European Physical Journal C, 2015

Physical Review D, 2004

The possibility to avoid the cosmic initial singularity as a consequence of nonlinear effects on the Maxwell eletromagnetic theory is discussed. For a flat FRW geometry we derive the general nonsingular solution supported by a magnetic field plus a cosmic fluid and a nonvanishing vacuum energy density. The nonsingular behavior of solutions with a time-dependent Λ(t)-term are also examined. As a general result, it is found that the functional dependence of Λ(t) can uniquely be determined only if the magnetic field remains constant. All these models are examples of bouncing universes which may exhibit an inflationary dynamics driven by the nonlinear corrections of the magnetic field.

Physical Review D, 2015

Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the nontrivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter fNL (which is of order unity before the bounce phase) is enhanced during the bounce phase if the curvature fluctuations grow. Hence, in such nonsingular bounce models with matter given by a single scalar field, there appears to be a tension between obtaining a small enough tensor-to-scalar ratio and not obtaining a value of fNL in excess of the current upper bounds. This conclusion may be considered as a "no-go" theorem that rules out any single field matter bounce cosmology starting with vacuum initial conditions for the fluctuations.

Physical Review D, 2017

We revisit nonsingular cosmologies in which the limiting curvature hypothesis is realized. We study the cosmological perturbations of the theory and determine the general criteria for stability. For the simplest model, we find generic Ostrogradski instabilities unless the action contains the Weyl tensor squared with the appropriate coefficient. When considering two specific nonsingular cosmological scenarios (one inflationary and one genesis model), we find ghost and gradient instabilities throughout most of the cosmic evolution. Furthermore, we show that the theory is equivalent to a theory of gravity where the action is a general function of the Ricci and Gauss-Bonnet scalars, and this type of theory is known to suffer from instabilities in anisotropic backgrounds. This leads us to construct a new type of curvature-invariant scalar function. We show that it does not have Ostrogradski instabilities, and it avoids ghost and gradient instabilities for most of the interesting background inflationary and genesis trajectories. We further show that it does not possess additional new degrees of freedom in an anisotropic spacetime. This opens the door for studying stable alternative nonsingular very early Universe cosmologies.

Journal of Cosmology and Astroparticle Physics, 2020

Finding effective theories of modified gravity that can resolve cosmological singularities and avoid other physical pathologies such as ghost and gradient instabilities has turned out to be a rather difficult task. The concept of limiting curvature, where one bounds a finite number of curvatureinvariant functions thanks to constraint equations, is a promising avenue in that direction, but its implementation has only led to mixed results. Cuscuton gravity, which can be defined as a special subclass of k-essence theory for instance, is a minimal modification of gravity since it does not introduce any new degrees of freedom on a cosmological background. Importantly, it naturally incorporates the idea of limiting curvature. Accordingly, models of cuscuton gravity are shown to possess non-singular cosmological solutions and those appear stable at first sight. Yet, various subtleties arise in the perturbations such as apparent divergences, e.g., when the Hubble parameter crosses zero. We revisit the cosmological perturbations in various gauges and demonstrate that the stability results are robust even at those crossing points, although certain gauges are better suited to analyze the perturbations. In particular, the spatially-flat gauge is found to be ill defined when H = 0. Otherwise, the sound speed is confirmed to be generally close to unity in the ultraviolet, and curvature perturbations are shown to remain essentially constant in the infrared throughout a bounce phase. Perturbations for a model of extended cuscuton (as a subclass of Horndeski theory) are also studied and similar conclusions are recovered.

Physical Review D, 2021

Over 30 years ago, Barrow and Tipler proposed the principle according to which the action integrated over the entire four-manifold describing the universe should be finite. Here we explore the cosmological consequences of a related criterion, namely, that semiclassical transition amplitudes from the early universe up to current field values should be well defined. On a classical level, our criterion is weaker than the Barrow-Tipler principle, but it has the advantage of being sensitive to quantum effects. We find significant consequences for early universe models, in particular, eternal inflation and strictly cyclic universes are ruled out. Within general relativity, the first phase of evolution cannot be inflationary, and it can be ekpyrotic only if the scalar field potential is trustworthy over an infinite field range. Quadratic gravity eliminates all nonaccelerating backgrounds near a putative big bang (thus imposing favorable initial conditions for inflation), while the expected infinite series of higher-curvature quantum corrections eliminates Lorentzian big bang spacetimes altogether. The scenarios that work best with the principle of finite amplitudes are the no-boundary proposal, which gives finite amplitudes in all dynamical theories that we have studied, and string-inspired loitering phases. We also comment on the relationship of our proposal to the swampland conjectures.

Physical Review D, 2020

We propose a class of theories that can limit scalars constructed from the extrinsic curvature. Applied to cosmology, this framework allows us to control not only the Hubble parameter but also anisotropies without the problem of Ostrogradsky ghost, which is in sharp contrast to the case of limiting spacetime curvature scalars. Our theory can be viewed as a generalization of mimetic and cuscuton theories (thus clarifying their relation), which are known to possess a structure that limits only the Hubble parameter on homogeneous and isotropic backgrounds. As an application of our framework, we construct a model where both anisotropies and the Hubble parameter are kept finite at any stage in the evolution of the universe in the diagonal Bianchi type I setup. The universe starts from a constant-anisotropy phase and recovers Einstein gravity at low energies. We also show that the cosmological solution is stable against a wide class of perturbation wave numbers, though instabilities may remain for arbitrary initial conditions.