We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantisation to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t=0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.
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.
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 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.
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.
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 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.
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.
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.
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 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 …
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.
A review is attempted of physical motivations, theoretical and phenomenological aspects, as well as outstanding problems, of the pre-big bang scenario in string cosmology.
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.
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.
We describe how cosmology has converged towards a beautiful model of the Universe: the Big Bang Universe. We praise this model, but show there is a dark side to it. This dark side is usually called ``the cosmological problems'': a set of coincidences and fine tuning features required for the Big Bang Universe to be possible. After reviewing these ``riddles'' we show how they have acted as windows into the very early Universe, revealing new physics and new cosmology just as the Universe came into being. We describe inflation, pre Big Bang, and varying speed of light theories. At the end of the …
This short review is addressed to cosmologists. General relativity predicts that space-time comes to an end and physics comes to a halt at the big-bang. Recent developments in loop quantum cosmology have shown that these predictions cannot be trusted. Quantum geometry effects can resolve singularities, thereby opening new vistas. Examples are: The big bang is replaced by a quantum bounce; the `horizon problem' disappears; immediately after the big bounce, there is a super-inflationary phase with its own phenomenological ramifications; and, in presence of a standard inflaton potential, initial …
Some long standing issues concerning the quantum nature of the big bang are resolved in the context of homogeneous isotropic models with a scalar field. Specifically, the known results on the resolution of the big bang singularity in loop quantum cosmology are significantly extended as follows: i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the `emergent time' idea; ii) the physical Hilbert space, Dirac observables and semi-classical states are constructed rigorously; iii) the Hamiltonian constraint is solved numerically to show that the…
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.
In a recent series of papers, we have shown that theories with scalar fields coupled to gravity (e.g., the standard model) can be lifted to a Weyl-invariant equivalent theory in which it is possible to unambiguously trace the classical cosmological evolution through the transition from big crunch to big bang. The key was identifying a sufficient number of finite, Weyl-invariant conserved quantities to uniquely match the fundamental cosmological degrees of freedom across the transition. In so doing we had to account for the well-known fact that many Weyl-invariant quantities diverge at the crun…
The quantum fluctuations of a homogeneous, isotropic, open pre-big bang model are discussed. By solving exactly the equations for tensor and scalar perturbations we find that particle production is negligible during the perturbative Pre-Big Bang phase.
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.
The equations of motion and junction conditions for a gravi-dilaton brane world scenario are studied in the string frame. It is shown that they allow Kasner-like solutions on the brane, which makes the dynamics of the brane very similar to the low curvature phase of pre-big bang cosmology. Analogies and differences of this scenario with the Randall-Sundrum one and with the standard bulk pre-big bang dynamics are also discussed.
A simple, non-technical introduction to the pre-big bang scenario is given, emphasizing physical motivations, considerations, and consequences over formalism.
We describe spontaneous creation of the Brane World in $AdS_{5}$ with external field. The resulting Brane World consists of a flat 4d spatially finite expanding Universe and curved expanding "regulator" branes. No negative tension branes are involved.
Important open questions in cosmology require a better understanding of the Big Bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like Big Bang models, presenting both solved and open problems.
We study a quotient Conformal Field Theory, which describes a 3+1 dimensional cosmological spacetime. Part of this spacetime is the Nappi-Witten (NW) universe, which starts at a ``big bang'' singularity, expands and then contracts to a ``big crunch'' singularity at a finite time. The gauged WZW model contains a number of copies of the NW spacetime, with each copy connected to the preceeding one and to the next one at the respective big bang/big crunch singularities. The sequence of NW spacetimes is further connected at the singularities to a series of non-compact static regions with closed tim…
A simple model for a scalar field and gravity admits homogeneous isotropic cosmological solutions which cross the Big Bang singularity. In the scaling frame with field dependent effective Planck mass these solutions are regular. They become singular in the Einstein frame with fixed Planck mass. This field singularity arises since the field transformation of the metric to the Einstein frame is singular at the crossing point of a vanishing scalar field. No physical singularity is present for these solutions. Within general models with no more than two derivatives we find that the possibility of …
Our universe appears to have been created not out of nothing but from a strange space-time dust. Quantum geometry (loop quantum gravity) makes it possible to avoid the ominous beginning of our universe with its physically unrealistic (i.e. infinite) curvature, extreme temperature, and energy density. This could be the long sought after explanation of the big-bang and perhaps even opens a window into a time before the big-bang: Space itself may have come from an earlier collapsing universe that turned inside out or inverted and began to expand again. - Key words: Loop quantum cosmology, Wheeler…
The consequences of holography hypothesis are investigated for the Pre-big-bang string cosmological models. The evolution equations are obtained from the tree level string effective action. It is shown that $S/A$ is bounded by a constant in each case, $S$ being the entropy within the volume bounded by the horizon of area $A$.
We compute the amount of inflation required to solve the horizon problem of cosmology in the pre-big-bang scenario. First we give a quick overview of string cosmology as developed by Veneziano and collaborators. Then we show that the amount of inflation in this background solves the horizon problem. We discuss fine-tuning.
Starting from the Janus solution and its gauge theory dual, we obtain the dual gauge theory description of the cosmological solution by procedure of the double anaytic continuation. The coupling is driven either to zero or to infinity at the big-bang and big-crunch singularities, which are shown to be related by the S-duality symmetry. In the dual Yang-Mills theory description, these are non singular at all as the coupling goes to zero in the N=4 Super Yang-Mills theory. The cosmological singularities simply signal the failure of the supergravity description of the full type IIB superstring th…
In this note, we investigate the possibility of avoiding the Big Bang singularity with a single scalar field which couples non-minimally to gravity. We show that in the case that gravity couples linearly to the field, some severe conditions on the field's potential have to be imposed. However, in non-linear case, it is quite generic to avoid the singularity with single scalar field.
We re-examine the graceful exit problem in the pre-big bang scenario of string cosmology, by considering the most general time-dependent classical correction to the Lagrangian with up to four derivatives. By including possible forms for quantum loop corrections we examine the allowed region of parameter space for the coupling constants which enable our solutions to link smoothly the two asymptotic low-energy branches of the pre-big bang scenario, and observe that these solutions can satisfy recently proposed entropic bounds on viable singularity free cosmologies.
We point out a new phenomenon which seems to be generic in 4d effective theories of scalar fields coupled to Einstein gravity, when applied to cosmology. A lift of such theories to a Weyl-invariant extension allows one to define classical evolution through cosmological singularities unambiguously, and hence construct geodesically complete background spacetimes. An attractor mechanism ensures that, at the level of the effective theory, generic solutions undergo a big crunch/big bang transition by contracting to zero size, passing through a brief antigravity phase, shrinking to zero size again, …
We study Big Crunch/Big Bang cosmologies that correspond to exact world-sheet superconformal field theories of type II strings. The string theory spacetime contains a Big Crunch and a Big Bang cosmology, as well as additional ``whisker'' asymptotic and intermediate regions. Within the context of free string theory, we compute, unambiguously, the scalar fluctuation spectrum in all regions of spacetime. Generically, the Big Crunch fluctuation spectrum is altered while passing through the bounce singularity. The change in the spectrum is characterized by a function $Δ$, which is momentum and time…
We find pp wave solutions in string theory with null-like linear dilatons. These provide toy models of big bang cosmologies. We formulate Matrix String Theory in these backgrounds. Near the big bang ``singularity'', the string theory becomes strongly coupled but the Yang-Mills description of the matrix string is weakly coupled. The presence of a second length scale allows us to focus on a specific class of non-abelian configurations, viz. fuzzy cylinders, for a suitable regime of parameters. We show that, for a class of pp waves, fuzzy cylinders which start out big at early times dynamically s…
We argue that in the tensionless phase of string theory where the stringy gauge symmetries are unbroken, (at least some) cosmological singularities can be understood as gauge artefacts. We present two conceptually related, but distinct, pieces of evidence: one relying on spacetime and the other on worldsheet.
The beautiful scenario of pre-big-bang cosmology is appealling not only because it is more or less derived from string theory, but also because it separates clearly the problem of the initial conditions for the universe from that of high curvatures. Recently, the pre-big-bang program was subject to attack from on the grounds that pre-big-bang cosmology does not solve the horizon and flatness problems in a ``natural'' way, as customary exponential ``new'' inflation does. In particular, it appears that an arbitrarily small deviation from perfect flatness in the initial state can not be accommoda…
One of the simplest time-dependent solutions of M theory consists of nine-dimensional Euclidean space times 1+1-dimensional compactified Milne space-time. With a further modding out by Z_2, the space-time represents two orbifold planes which collide and re-emerge, a process proposed as an explanation of the hot big bang. When the two planes are near, the light states of the theory consist of winding M2-branes, describing fundamental strings in a particular ten-dimensional background. They suffer no blue-shift as the M theory dimension collapses, and their equations of motion are regular across…
We argue that the Big Bang can be understood as a type of mirror. We show how reflecting boundary conditions for spinors and higher spin fields are fixed by local Lorentz and gauge symmetry, and how a temporal mirror (like the Bang) differs from a spatial mirror (like the AdS boundary), providing a possible explanation for the observed pattern of left- and right-handed fermions. By regarding the Standard Model as the limit of a minimal left-right symmetric theory, we obtain a new, cosmological solution of the strong $CP$ problem, without an axion.
We study D-branes in a two-dimensional Lorentzian orbifold R^{1,1}/Γwith a discrete boost Γ. This space is known as Misner or Milne space, and includes big crunch/big bang singularity. In this space, there are D0-branes in spiral orbits and D1-branes with or without flux on them. In particular, we observe imaginary parts of partition functions, and interpret them as the rates of open string pair creation for D0-branes and emission of winding closed strings for D1-branes. These phenomena occur due to the time-dependence of the background. Open string 2 -> 2 scattering amplitude on a D1-brane is…
We study the leading quantum effects in the recently introduced Matrix Big Bang model. This amounts to a study of supersymmetric Yang-Mills theory compactified on the Milne orbifold. We find a one-loop potential that is attractive near the Big Bang. Surprisingly, the potential decays very rapidly at late times, where it appears to be generated by D-brane effects. Usually, general covariance constrains the form of any effective action generated by renormalization group flow. However, the form of our one-loop potential seems to violate these constraints in a manner that suggests a connection bet…
We analyze the problem of graceful exit from superinflationary pre-big bang phase of string cosmology within the context of lowest-order string effective action. The previous no go theorems are generalized for the case when higher genus terms of general form and additional matter fields are included. It is shown that the choice of the E-frame essentially simplifies the consideration. For the example of pure gravi-dilaton case the comparison of E-frame and string frame approaches, based on phase space analysis, is carried out.
The origins of matter and radiation in the universe lie in a Hot Big Bang. We present a number of well-motivated cosmologies in which the Big Bang occurs through a strong first order phase transition -- either at the end of inflation, after a period of kination ("Kination-Induced Big Bang"), or after a second period of vacuum-domination in the early universe ("Supercooled Big Bang"); we also propose a "Dark Big Bang" where only the dark matter in the Universe is created in a first-order phase transition much after inflation. In all of these scenarios, the resulting gravitational radiation can …
We consider quantum field theory on a spacetime representing the Big Crunch/Big Bang transition postulated in the ekpyrotic or cyclic cosmologies. We show via several independent methods that an essentially unique matching rule holds connecting the incoming state, in which a single extra dimension shrinks to zero, to the outgoing state in which it re-expands at the same rate. For free fields in our construction there is no particle production from the incoming adiabatic vacuum. When interactions are included the total particle production for fixed external momentum is finite at tree level. We …
