Does σ-model conformal invariance imply a Robertson-Walker universe?

Diamandis, G.A.; Georgalas, B.C.; Lahanas, A.B.

doi:10.1016/0370-2693(92)91878-d

Cited by 4 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us now turn to our original desire to find a minisuperspace Lagrangian. The usual way of seeking such a reduced Lagrangian is to insert the metric (15) and the potential ( 16) into the Einstein's-Hilbert's + Electromagnetic action. This is not working here due to a fact that, as we have already discussed, in the class of pp-wave spacetimes all the curvature scalars are zero.…”

Section: Class a (410)mentioning

confidence: 99%

“…The authors of [14] have cast Newton's equations for N non-relativistic interacting particles, according to the inverse square law, in the form of equations for null geodesics in a (3N + 2)-dimensional generalized pp-wave spacetime. In [15] the authors have proven that the conformal invariance of a σmodel does not imply only a Robertson-Walker universe but also a special kind of a pp-wave metric. For a bosonic string in a specially chosen pp-wave spacetime the conformal anomaly vanishes as it was shown in [16], while pp-waves are shown to be suitable, up to conditions, for providing string vacua for the sigma model perturbation expansion, at all orders [17].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Classical and quantum analysis of 3D electromagnetic pp-wave spacetime

Pailas

Dimakis

Karagiorgos

et al. 2019

Class. Quantum Grav.

View full text Add to dashboard Cite

The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A classification is presented based on the symmetry group. To the best of our knowledge, the solution corresponding to only one of the Classes is known. The dynamics of some of the Classes was also derived from a minisuperspace Lagrangian which has been constructed. This Lagrangian contains a degree of freedom (the lapse) which can be considered either as dynamical or non-dynamical (indicating a singular or a regular Lagrangian correspondingly). Surprisingly enough, on the space of classical solutions, an equivalence of these two points of view can be established. The canonical quantization is then used in order to quantize the system for both the singular and regular Hamiltonian. A subsequent interpretation of quantum states is based on a Bohm-like analysis. The semi-classical trajectories deviate from the classical only for the regular Hamiltonian and in particular for a superposition of eigenstates (a Gaussian initial state has been used). Thus, the above mentioned equivalence is broken at the quantum level. It is noteworthy that the semi-classical trajectories tend to the classical ones in the limit where the initial wavepacket is widely spread. Hence, even with this simple superposition state, the classical solutions are acquired as a limit of the semi-classical. *

show abstract

Section: Class a (410)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Classical and quantum analysis of 3D electromagnetic pp-wave spacetime

Pailas

Dimakis

Karagiorgos

et al. 2019

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…In string theory there were a lot of attempts to develop a consistent theory of string cosmology,in which inflation plays a dominant rôle. There were found solutions to the non-linear σ-model equations for the graviton,dilaton and antisymmetric tensor in a Friedman-Robertson-Walker (FRW) background.Then the FRW spaces were interpreted as conformal field theories capable of being embedded in consistent string theories [2,3]. The advandange of this string cosmological model is,that at tree level, does not depend on a scalar potential,so any inflationary solution will depend on the dynamics of the scalar field,and on its couplings to the other massless string modes.…”

Section: Introductionmentioning

confidence: 99%

On `graceful exit' from inflationary phase in two-dimensional Liouville string cosmology

et al. 1999

Self Cite

View full text Add to dashboard Cite

Within the context of a super-critical (Liouville) string, we discuss (target-space) twodimensional string cosmology. A numerical analysis indicates that the identification of time with the Liouville mode results in an expanding universe with matter which exhibits an inflationary phase, and 'graceful exit' from it, tending asymptotically to a flat-metric fixed point. This fixed point is characterized by a dilaton configuration which, depending on the initial conditions, either decreases linearly with the cosmic time, or is a finite constant. This implies that, in contrast to the critical string case, the string coupling remains bounded during the exit from the inflationary phase, and, thus, the pertinent dynamics can be reliably described in terms of a tree-level string effective action. The rôle of matter in inducing such phenomena is emphasized. It is also interesting to note that the asymptotic value of the vacuum energy, which in the σ-model framework is identified with the 'running' central charge deficit, depends crucially on the set of initial conditions. Thus, although preliminary, this toy model seems to share all the features expected to characterize a phenomenologically acceptable cosmological string model.

show abstract

Cosmological string solutions in 4 dimensions from 5d black holes

Behrndt¹,

Förste

1994

Physics Letters B

View full text Add to dashboard Cite

We obtain cosmological four dimensional solutions of the low energy effective string theory by reducing a five dimensional black hole, and black hole-de Sitter solution of Einstein gravity down to four dimensions. The appearance of a cosmological constant in the five dimensional Einstein-Hilbert action produces a special dilaton potential in the four dimensional effective string action. Cosmological scenarios implemented by our solutions are discussed.To describe strings propagating in nontrivial background there are two different approaches. First, one can start with a conformal field theory, e.g. (gauged) WZW, FeiginFuchs or Liouville theory, and rewrite this as a string σ model. Although the gauged WZW model is an exact conformal field theory it is possible to obtain the σ model background only perturbatively. The reason is that in general the 2d gauge field can be eliminated only in an α ′ expansion. One example for which one got an exact result is the SL(2, R)/U(1) WZW model [1,2]. In the second approach one starts with the low energy effective action and tries to find solutions in an α ′ expansion. In terms of both approaches some cosmological solutions have been obtained so far. Exact solutions, e.g. , are given by the gauged WZW model based on SL(2, R)/SO(1, 1) × R 2 [3] or the combination of the SU(2) WZW model with a Feigin-Fuchs part [4,5]. In the second or "phenomenological" approach cosmological solutions have been discussed in [6] and [7]. In all these solutions the metric is either time independent like the SU(2) WZW in the string frame a or spatially flat or the dilaton is constant. In the present paper we use the second approach and find time dependent solutions (metric and dilaton) which are spatially not flat. We use the following procedure. We neglect all terms O(α ′2 ) and consider only curvature and dilaton terms. Then we will rewrite the effective string action in four dimensions (4d) as *

show abstract

Does σ-model conformal invariance imply a Robertson-Walker universe?

Cited by 4 publications

References 8 publications

Classical and quantum analysis of 3D electromagnetic pp-wave spacetime

Classical and quantum analysis of 3D electromagnetic pp-wave spacetime

On `graceful exit' from inflationary phase in two-dimensional Liouville string cosmology

Cosmological string solutions in 4 dimensions from 5d black holes

Contact Info

Product

Resources

About