We introduce some algebraic geometric models in cosmology related to the "boundaries" of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers between aeons. We suggest to model the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a point $x$. This creates a boundary which consists of the projective space of tangent directions to $x$ and possibly of the light cone of $x$. We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary. The Mixmaster (Bianchi IX) model of the early history of the universe is neatly explained in this picture by postulating that the reverse Wick rotation follows a hyperbolic geodesic connecting imaginary time axis to the real one. Penrose's idea to see the Big Bang as a sign of crossover from "the end of previous aeon" of the expanding and cooling Universe to the "beginning of the next aeon" is interpreted as an identification of a natural boundary of Minkowski space at infinity with the Big Bang boundary.
The pre-big bang's kinetic driven inflationary mechanism is not an adequate form of inflation: the Planck length grows more rapidly than the scale factor. In order to explain our large universe, the resulting post-big bang universe requires the same unnatural constants (Planck problem) as those of any other non-inflationary big bang model.
The necessary and sufficient condition for the absence of particle horizons in a big bang Friedmann-Robertson-Walker universe is provided. It happens to be a "smooth big bang" initial condition: the proper time derivative of the expansion factor $a(t)$ must be finite at the big bang. Equivalently, the energy density must not diverge faster than $a^{-2}$ at the big bang. This is just an initial condition: only the scale factor asymptotic behavior at the very moment of the big bang matters. The causal connection between remote space regions could then take place immediately after the big bang. E…
In pre-big-bang string cosmology one uses a phase of dilaton-driven inflation to stretch an initial (microscopic) spatial patch to the (much larger) size of the big-bang fireball. We show that the dilaton-driven inflationary phase does not naturally iron out the initial classical tensor inhomogeneities unless the initial value of the string coupling is smaller than 10^(-35).
A recent cosmological model is recapitulated which deduces the correct mass, radius and age of the universe as also the Hubble constant and other well known apparently coincidental relations. It also predicts an ever expanding accelerating universe as is confirmed by latest supernovae observations. Finally the Big Bang model is recovered as a suitable limiting case.
We evaluate the physical viability and logical strength of an array of putative criteria for big bang singularity resolution in quantum cosmology. Based on this analysis, we propose a mutually consistent set of constitutive conditions, which we argue should be taken to jointly define `global' and `local' big bang singularity resolution in this context. Whilst the present article will focus exclusively on evaluating resolution criteria for big bang singularities in the context of finite dimensional models of quantum cosmology, it is also hoped that the core features of our analysis will be exte…
Singular spacetimes are a natural prediction of Einstein's theory. Most memorable are the singular centers of black holes and the big bang. However, dilatonic extensions of Einstein's theory can support nonsingular spacetimes. The cosmological singularities can be avoided by dilaton driven inflation. Furthermore, a nonsingular black hole can be constructed in two dimensions.
We give an exact solution of the five-dimensional field equations which describes a shock wave moving in time and the extra (Kaluza-Klein) coordinate. The matter in four-dimensional spacetime is a cosmology with good physical properties. The solution suggests to us that the 4D big bang was a 5D shock wave.
We investigate a particular regularization of big bang singularity, which remains within the domain of 4-dimensional general relativity but allowing for degenerate metrics. We study the geodesics and geodesic congruences in the modified Friedmann-Lemaître-Robertson-Walker universe. In particular, we calculate the expansion of timelike and null geodesic congruences. Based on these results, we also briefly discuss the cosmological singularity theorems.
The pre--big bang cosmological scenario is studied within the context of the Brans--Dicke theory of gravity. An epoch of superinflationary expansion may occur in the pre--big bang phase of the Universe's history in a certain region of parameter space. Two models are considered that contain a cosmological constant in the gravitational and matter sectors of the theory, respectively. Classical pre-- and post--big bang solutions are found for both models. The existence of a curvature singularity forbids a classical transition between the two branches. On the other hand, a quantum cosmological appr…
A 5-dimensional gravity theory, motivated by the brane world picture, with factorisable metric and with Kaluza scalar $G_{55}(r)$, is shown to give rise to a positive contribution to the Raychaudhuri equation. This inhibits the focusing of geodesics and possibly cause non-focusing of the geodesics. This feature is translated into the situation in which the universe has an infinite age and hence no beginning avoiding the big bang singularity.
The it Global Time Theory (GTT) is the further development of the General Relativity (GR). GTT significantly differs from GR in the general physical concepts, but retains 90% of the mathematical structure and main results. The dynamics equations are derived from Lagrangian, and the Hamiltonian of gravitation is nonzero. The quantum theory of gravitation can be built on the basis of the Schroedinger equation, as for other fields. The quantum model of the Big Bang is demonstrated.
We establish a formal relationship between stationary axisymmetric spacetimes and $T^3$ Gowdy cosmological models which allows us to derive several preliminary results about the generation of exact cosmological solutions and their possible behavior near the initial singularity. In particular, we argue that it is possible to generate a Gowdy model from its values at the singularity and that this could be used to construct cosmological solutions with any desired spatial behavior at the Big Bang.
We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result \cite{Xue:2014} that did not model random perturbations. This result implies that the extensi…
The Hamilton-Jacobi equation for the string cosmology is solved using the gradient expansion method. The zeroth order solution is taken to be the standard pre-big bang model and the second order solution is found for the dilaton and the three-metric. It indicates that corrections generated by inhomogeneities of the seed metric are suppressed near the singularity and are growing towards the asymptotic past, but corrections generated by the dilaton inhomogeneities are growing near the singularity and are suppressed in the past. Possible influences of initial metric inhomogeneities on the pre-big…
String theory can (in principle) describe gravity at all curvature scales, and can be applied to cosmology to look back in time beyond the Planck epoch. The duality symmetries of string theory suggest a cosmological picture in which the imprint of a primordial, pre-big bang phase could still be accessible to present observations. The predictive power of such a scenario relies, however, on our ability to connect in a smooth way the pre-big bang to the present cosmological regime. Classical radiation back reaction seems to play a key role to this purpose, by isotropizing and turning into a final…
Field theoretical scheme of regular Big Bang in 4-dimensional physical space-time, built in the framework of gauge approach to gravitation, is discussed. Regular bouncing character of homogeneous isotropic cosmological models is ensured by gravitational repulsion effect at extreme conditions without quantum gravitational corrections. The most general properties of regular inflationary cosmological models are examined. Developing theory is valid, if energy density of gravitating matter is positive and energy dominance condition is fulfilled.
We examine the string cosmology equations with a dilaton potential in the context of the Pre-Big Bang Scenario with the desired scale factor duality, and give a generic algorithm for obtaining solutions with appropriate evolutionary properties. This enables us to find pre-big bang type solutions with suitable dilaton behaviour that are regular at $t=0$, thereby solving the graceful exit problem. However to avoid fine tuning of initial data, an `exotic' equation of state is needed that relates the fluid properties to the dilaton field. We discuss why such an equation of state should be required…
We show that the big bang is a coordinate singularity for a large class of $k = -1$ inflationary FLRW spacetimes which we have dubbed 'Milne-like.' By introducing a new set of coordinates, the big bang appears as a past boundary of the universe where the metric is no longer degenerate -- a result which has already been investigated in the context of vacuum decay [12]. We generalize their results and approach the problem from a more mathematical perspective. Similar to how investigating the geometrical properties of the $r = 2m$ event horizon in Schwarzschild led to a better understanding of bl…
The R+S^2 theories of gravity, where S^2 denotes the quadratic torsion terms, are analyzed under three cases. In the first two cases, the matter fields are described by two different spin fluids which are not homogeneous and isotropic. In the third case, a homogeneous and isotropic torsion field is used. It is found that under all the three cases, the R+S^2 theories may avert the big-bang singularity of the Robertson--Walker universe, with three corresponding constraints on the parameters.
We study a five-dimensional cosmological model, which suggests that the universe bagan as a discontinuity in a (Higgs-type) scalar field, or alternatively as a conventional four-dimensional phase transition.
We study numerically the inhomogeneous pre-big-bang inflation in a spherically symmetric space-time. We find that a large initial inhomogeneity suppresses the onset of the pre-big-bang inflation. We also find that even if the pre-big-bang inflationary stage is realized, the initial inhomogeneities are not homogenized. Namely, during the pre-big-bang inflation ``hairs''(irregularities) do not fall, in sharp contrast to the usual (potential energy dominated) inflation where initial inhomogeneity and anisotropy are damped and thus the resulting universe is less sensitive to initial conditions.
We present a simplified dynamic-vacuum-energy model for a time-symmetric Milne-like universe. The big bang singularity in this simplified model, like the one in a previous model, is just a coordinate singularity with finite curvature and energy density. We then calculate the dynamic behavior of scalar metric perturbations and find that these perturbations destabilize the big bang singularity.
An inhomogeneous version of pre--Big Bang cosmology emerges, within string theory, from quite generic initial conditions, provided they lie deeply inside the weak-coupling, low-curvature regime. Large-scale homogeneity, flatness, and isotropy appear naturally as late-time outcomes of such an evolution.
We study the impact of non-Abelian T-duality transformations on a string based cosmological model. The implementation of the pre-big-bang scenario is investigated. We found a region of the dual phase where such a picture is possible.
The massive gravity cosmology is studied in the scenario of big bang nucleosynthesis. By making use of current bounds on the deviation from the fractional mass, we derive the constraints on the free parameters of the theory. The cosmological consequences of the model are also discussed in the framework of the PAMELA experiment.
We discuss a simple cosmological model derived from M-theory. Three assumptions lead naturally to a pre-big bang scenario: (a) 11-dimensional supergravity describes the low-energy world; (b) non-gravitational fields live on a three-dimensional brane; and (c) asymptotically past triviality.
We analyse numerically the onset of pre-big bang inflation in an inhomogeneous, spherically symmetric Universe. Adding a small dilatonic perturbation to a trivial (Milne) background, we find that suitable regions of space undergo dilaton-driven inflation and quickly become spatially flat ($Ω\to 1$). Numerical calculations are pushed close enough to the big bang singularity to allow cross checks against previously proposed analytic asymptotic solutions.
The large-$N$ master field of the Lorentzian IIB matrix model can, in principle, give rise to a particular degenerate metric relevant to a regularized big bang. The length parameter of this degenerate metric is then calculated in terms of the IIB-matrix-model length scale.
In this paper it is investigated whether torsion, which arises naturally in most theories of quantum gravity, has observable implications for the Big Bang nucleosynthesis. Torsion can lead to spin flips amongst neutrinos thus turning them into sterile neutrinos. In the early Universe they can alter the helium abundance which is tightly constrained by observations. Here I calculate to what extent torsion of the string theory type leads to a disagreement with the Big Bang nucleosynthesis predictions.
Quantum gravity may remove classical space-time singularities and thus reveal what a universe at and before the big bang could be like. In loop quantum cosmology, an exactly solvable model is available which allows one to address precise dynamical coherent states and their evolution in such a setting. It is shown here that quantum fluctuations before the big bang are generically unrelated to those after the big bang. A reliable determination of pre-big bang quantum fluctuations would require exceedingly precise observations.
I discuss the status of present knowledge about a possible background of relic gravitons left by an early, pre-big bang cosmological epoch, whose existence in the past of our Universe is suggested by the duality symmetries of string theory.
Dark matter could be composed by black-hole remnants formed before the big-bang era in a bouncing cosmology. This hypothetical scenario has major implications on the issue of the arrow of time: it would upset a common attribution of past low entropy to the state of the geometry, and provide a concrete realisation to the perspectival interpretation of past low entropy.
Big bang of the Friedmann-Robertson-Walker (FRW)-brane universe is studied. In contrast to the spacelike initial singularity of the usual FRW universe, the initial singularity of the FRW-brane universe is point-like from the viewpoint of causality including gravitational waves propagating in the bulk. Existence of null singularities (seam singuralities) is also shown in the flat and open FRW-brane universe models.
We point out that algebraically special Einstein fields with twisting rays exhibit the basic properties of conformal Universes considered recently by Roger Penrose.
The possibility of avoiding the big bang singularity by means of a generalized uncertainty principle is investigated. In relation with this matter, the statistical mechanics of a free-particle system obeying the generalized uncertainty principle is studied and it is shown that the entropy of the system has a finite value in the infinite temperature limit. It is then argued that negative temperatures and negative pressures are possible in this system. Finally, it is shown that this model can remove the big bang singularity.
We analyze the quantum cosmology of the simplest pre--big--bang model without dilaton potential. In addition to the minisuperspace variables we include inhomogeneous dilaton fluctuations and determine their wave function on a semiclassical background. This wave function is used to calculate the reduced density matrix and to find criteria for the loss of decoherence. It is shown that coherence between different backgrounds can always be achieved by a specific choice of vacua though generically decoherence can be expected. In particular, we discuss the implications of these results on the ``exit…
The Standard Model Extension formulated by Colladay and Kostelecký is reviewed in the framework of the $^4He$ primordial abundance. Upper bounds on coefficients for the Lorentz violation are derived using the present observational data.
Following up on earlier work on the regularization of the singular Schwarzschild solution, we now apply the same procedure to the singular Friedmann solution. Specifically, we are able to remove the divergences of the big bang singularity, at the price of introducing a 3-dimensional spacetime defect with a vanishing determinant of the metric. This particular regularization also suggests the existence of a "pre-big-bang" phase.
We look at the possibility of superinflationary behavior in a class of anisotropic Type-IIB superstring cosmologies in the context of Pre-big Bang scenario and find that there exists a rather narrow range of parameters for which these models inflate. We then show that, although in general this behavior is left untouched by the introduction of a Ramond-Ramond axion field through a SL(2,R) rotation, there exists a particular class of axions for which inflation disappears completely. Asymptotic past initial conditions are briefly discussed, and some speculations on the possible extension of Pre-b…
The Pre-Big Bang cosmology inspired generations of cosmologists in attempts to cure the initial Big Bang singularity using a fundamental length scale as proposed by String Theory. The existence of a phase of collapse/inflation with increasing curvature followed by a cosmic bounce has been proposed as an alternative to standard inflation in the solution of the horizon and curvature problems. However the generation of a nearly scale-invariant spectrum of perturbations is not an automatic prediction of such scenarios. In this paper I review some general statements about the evolution of perturbat…
The t<0 branch of pre-big bang cosmological scenarios is subject to a gravitational wave instability. The unstable behaviour of tensor perturbations is derived in a very simple way in Hwang's covariant and gauge-invariant formalism developed for extended theories of gravity. A simple interpretation of this instability as the effect of an "antifriction" is given, and it is argued that a universe must eventually enter the expanding phase.
We solve exactly the (linear order) equations for tensor and scalar perturbations over the homogeneous, isotropic, open pre-big bang model recently discussed by several authors. We find that the parametric amplification of vacuum fluctuations (i.e. particle production) remains negligible throughout the perturbative pre-big bang phase.
We consider a contracting universe and its transition to expansion through the big bang singularity with a time varying equation of state $w$, where $w$ approaches $1$ as the universe contracts to the big bang. We show that this singularity is non-regularizable. That is, there is no unique extension of the physical quantities after the transition, but rather infinitely many. This is entirely different from the case of $w > 1$ studied in \cite{Xue:2014}, where $w$ approaches a constant value $w_c > 1$ as the universe contracts. In that case a continuous transition through the big bang to yield …
We confront the big bang for the beginning of the universe with an equivalent picture of a slow freeze - a very cold and slowly evolving universe. In the freeze picture the masses of elementary particles increase and the gravitational constant decreases with cosmic time, while the Newtonian attraction remains unchanged. The freeze and big bang pictures both describe the same observations or physical reality. We present a simple "crossover model" without a big bang singularity. In the infinite past space-time is flat. Our model is compatible with present observations, describing the generation …
After a brief review of current scenarios for the resolution and/or avoidance of the Big Bang, an alternative hypothesis is put forward implying an infinite increase in complexity towards the initial singularity. This may result in an effective non-calculability which would present an obstruction to actually reaching the beginning of time. This proposal is motivated by the appearance of certain infinite-dimensional duality symmetries of indefinite Kac--Moody type in attempts to unify gravity with the fundamental matter interactions, and deeply rooted in properties of Einstein's theory.
Robertson-Walker spacetimes within a large class are geometrically extended to larger cosmologies that include spacetime points with zero and negative cosmological times. In the extended cosmologies, the big bang is lightlike, and though singular, it inherits some geometric structure from the original spacetime. Spacelike geodesics are continuous across the cosmological time zero submanifold which is parameterized by the radius of Fermi space slices, i.e, by the proper distances along spacelike geodesics from a comoving observer to the big bang. The continuous extension of the metric, and the …
This paper considers the structure and physical processes in the transition region at the border between the regions of false and physical vacuums in a cavitation model of the inflationary stage of the Big Bang. It is shown that in the process of the formation of physical vacuum bubbles in a false vacuum, conditions for the formation of a narrow layer filled with matter arise in the transition region, which is the precursor to bridges in the observed large-scale cellular structure of the universe.
We present a short introduction to a non-standard cosmological scenario motivated by the duality symmetries of string theory, in which the big bang singularity is replaced with a "big bounce" at high but finite curvature. The bouncing epoch is prepared by a long (possibly infinitely extended) phase of cosmic evolution, starting from an initial state asymptotically approaching the string perturbative vacuum.
This note is a summary of the work reported in hep-th/9801073. We give a brief discussion of the fine tuning problem in pre-big bang cosmology. We use the flatness problem as our test case, and in addition to the exact numerical limits on initial conditions, we highlight the differences between pre-big bang and standard inflation. The main difference is that in pre-big bang the universe must be smooth and flat in an exponentially large domain already at the beginning of the dilaton-driven inflation.
I review various aspects of the pre-big-bang scenario and of its main open problems, with emphasis on the role played by the dilaton. Since the dilaton is a compelling consequence of string theory, tests of this scenario are direct tests of string theory and also, more generally, of Planck scale physics.
When quantum gravity is used to discuss the big bang singularity, the most important, though rarely addressed, question is what role genuine quantum degrees of freedom play. Here, complete effective equations are derived for isotropic models with an interacting scalar to all orders in the expansions involved. The resulting coupling terms show that quantum fluctuations do not affect the bounce much. Quantum correlations, however, do have an important role and could even eliminate the bounce. How quantum gravity regularizes the big bang depends crucially on properties of the quantum state.
In a recent article, we propose a general geometric notion of initial data on big bang singularities. This notion is of interest in its own right. However, it also serves the purpose of giving a unified perspective on many of the results in the literature. In the present article, we give a partial justification of this statement by rephrasing the results concerning Bianchi class A orthogonal stiff solutions and solutions in the $\mathbb{T}^{3}$-Gowdy symmetric vacuum setting in terms of our general geometric notion of initial data on the big bang singularity.
The scenario that the Universe contracts towards a big crunch and then undergoes a transition to expanding Universe in envisaged in the quantum string cosmology approach. The Wheeler-De Witt equation is solved exactly for an exponential dilaton potential. S-duality invariant cosmological effective action, for type IIB theory, is considered to derive classical solutions and solve WDW equations.
We present classical and quantum dynamics of a test particle in the compactified Milne space. Background spacetime includes one compact space dimension undergoing contraction to a point followed by expansion. Quantization consists in finding a self-adjoint representation of the algebra of particle observables. Our model offers some insight into the nature of the cosmic singularity.
