THE VACUUM STATE IN THE HETEROTIC SUPERSTRING THEORY

2007 ◽  
Vol 16 (04) ◽  
pp. 591-618 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Cosmological Constant ◽  
Functional Dependence ◽  
Gauge Coupling ◽  
Vacuum State ◽  
De Sitter Space ◽  
Small Radius ◽  
Internal Space ◽  
Quadratic Term ◽  
De Sitter ◽  
Superstring Theory

The gravitational vacuum state of the heterotic superstring theory is derived by substituting the maximally symmetric D-space [Formula: see text], where [Formula: see text] is the cosmological constant, into the classical field equations obtained from the effective ten-Lagrangian including quartic higher-derivative terms, [Formula: see text]. If the theory is reduced to the physical dimensionality D = 4, as required by supersymmetry and phenomenology, the ground state, due to [Formula: see text] and [Formula: see text], is anti-de Sitter space with [Formula: see text], where [Formula: see text] is the inverse gauge coupling and κ2 ≡ 8πG N is the gravitational coupling, G N being the Newton constant. The term [Formula: see text], derived from the Euler-number density [Formula: see text], is a total divergence and the quadratic term [Formula: see text], derived from [Formula: see text], vanishes identically, while the quadratic anomaly [Formula: see text], which alone would give rise to a positive Λ(anom), is ignorable for the reduced [Formula: see text] heterotic string, containing n v = 488 vector fields, because Λ( anom ) ≳ -Λ unless n v ≳ 7,000. For hypothetical reduction to the higher dimensonalities D = 5, 9, 10, [Formula: see text] has the effect of augmenting the Boulware–Deser, anti-de Sitter space vacuum due to [Formula: see text], which becomes exact when D = 8, for which [Formula: see text] vanishes identically, but leads to a de Sitter space for D = 6, 7 thus justifying the Ricci-flat vacuum state for the six-dimensional internal space. For simplicity, we assume compactification onto a toroidal internal space when D ≥ 5, so that all contributions of the form [Formula: see text] vanish. The remaining terms [Formula: see text] and [Formula: see text] are then almost comparable in effect, bringing into question the convergence of the Lagrangian power series [Formula: see text] in the Einstein space, and consequently the validity of the results obtained. Without knowledge of the yet higher-order terms [Formula: see text], n ≥ 6, however, no further analysis is possible. As they stand the results constitute a realization of the limiting-curvature hypothesis of Frolov et al., and are also discussed from the viewpoint of causality. Finally, the dimensional parameter a, introduced by Volkov and Akulov to define the non-linear global supersymmetry transformations, gives rise to a negative cosmological constant -κ2/a, which can therefore be identified with Λ (which has the functional dependence [Formula: see text] found by Freedman and Das for extended supergravity). This leads to the estimate B r ~ 2 for the dimensionless radius-squared of the internal space, implying a small radius of compactification, in agreement with previous estimates obtained via supersymmetry, and provides a realization of the super-Higgs effect.

GOLDSTONE FIELDS IN THE SUPERSTRING THEORY

2008 ◽  
Vol 17 (01) ◽  
pp. 81-94 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Cosmological Constant ◽  
Goldstone Boson ◽  
Gauge Coupling ◽  
Einstein Equations ◽  
Level Gauge ◽  
Tree Level ◽  
Internal Space ◽  
Spin Component ◽  
Additional Contribution ◽  
Superstring Theory

If global supersymmetry is broken by gaugino condensation in the hidden sector of the [Formula: see text] heterotic superstring theory after compactification, then the auxiliary field FB of the modulus B ≡ (B r , B i ) attains a finite value, while that of the dilaton A ≡ (A r , A i ) vanishes, FA = 0, the Goldstone fermion being the modulino [Formula: see text], the spin-½ component of the complex chiral supermultiplet [Formula: see text]. The Goldstone boson of the scale symmetry that is broken when the radius of the internal space is fixed at a constant value is B r , which is determined from the goldstino Lagrangian, compared term by term with the superstring Lagrangian, including higher-derivative gravitational terms [Formula: see text] and [Formula: see text], after linking the space–time curvature to the energy–momentum tensor of the goldstino via the Einstein equations. This non-linear formulation of supersymmetry, due to Volkov and Akulov, is expressed in terms of the goldstino alone, whose Lagrangian contains a negative cosmological constant, which can be cancelled by the super-Higgs mechanism of Deser and Zumino to make the gravitino massive and break supersymmetry at the level [Formula: see text] GeV, while [Formula: see text]. Here, the modulus has been scaled to the Hagedorn value for the heterotic superstring theory, [Formula: see text], and A r , identified with the inverse square of the tree-level gauge coupling, has been scaled to the calculation in the minimal supersymmetric standard model due to Weinberg, that g-2 = 1.39 at the unification mass MX = 2.2 × 1016 GeV, assuming three generations of elementary particles and two Higgs doublets. In the presence of gravitino condensation in the internal space, however, there is an arbitrary additional contribution to the cosmological constant, facilitating reduction of m s to ~ 100 TeV, say, and m3/2 to ~ 1 eV.

scholarly journals p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

2002 ◽  
Vol 17 (10) ◽  
pp. 1413-1433 ◽  
Author(s):  
GORAN S. DJORDJEVIĆ ◽  
BRANKO DRAGOVICH ◽  
LJUBIŠA D. NEŠIĆ ◽  
IGOR V. VOLOVICH
Keyword(s):  
Quantum Mechanics ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Quantum Effects ◽  
De Sitter Space ◽  
Cosmological Models ◽  
De Sitter ◽  
Adelic Quantum Mechanics ◽  
Matter Fields

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle–Hawking proposal does not work in models with matter fields. p-adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models exhibit some discreteness of the minisuperspace and cosmological constant. In particular, discreteness of the de Sitter space and its cosmological constant is emphasized.

ON THE SUPERSTRING HAMILTONIAN IN THE FRIEDMANN SPACE–TIME

2006 ◽  
Vol 15 (06) ◽  
pp. 845-868 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Cosmological Solution ◽  
Vacuum State ◽  
Einstein Condensate ◽  
De Sitter ◽  
Superstring Theory ◽  
Bose Einstein Condensate ◽  
Higher Derivative ◽  
Effective Lagrangian ◽  
State Formula ◽  
De Sitter Vacuum

The ten-dimensional effective Lagrangian [Formula: see text] for the gravitational sector of the heterotic superstring theory is known up to quartic higher-derivative order [Formula: see text]. In cosmology, the reduced, four-dimensional line element assumes the Friedmann form ds2 = dt2 - a(t)2dx2, where t is comoving time and a(t) ≡ a0eα(t) is the radius function of the three-space dx2, whose curvature is k = 0, ± 1. The four-Lagrangian can then be expressed as the power-series [Formula: see text], where ˙ ≡ d/dt, from which the field equation can be derived by the method of Ostrogradsky. Here, we determine the coefficients Λ0, An, Bn, Cn, and Kn, which are all non-vanishing in general. We recover the previously obtained, high-curvature, anti-de Sitter vacuum state [Formula: see text] with effective cosmological constant Λ = {18/[175ζ(3) - 1/2]}1/3A r κ-2, whose existence makes it possible to envisage a singularity-free and horizon-free cosmological solution, stable to linear perturbations. It is interesting that all the coefficients of quartic origin arise from the near-cancellation of sums of opposite sign but magnitude f ≈ (28.6–369) times larger than the answer. They thus exhibit a slight asymmetry with regard to positive and negative energies, the anti-de Sitter vacuum being characterized by positive Nordström energy, and therefore only accessible at high curvatures. This vacuum state is a Bose–Einstein condensate of non-interacting gravitons at zero temperature, which, referred to comoving time, can only be formulated after the Wick rotation t → ±iτ, resulting in an imaginary horizon.

scholarly journals TURBULENT INSTABILITY OF ANTI-DE SITTER SPACE–TIME

2013 ◽  
Vol 28 (22n23) ◽  
pp. 1340020 ◽  
Author(s):  
MACIEJ MALIBORSKI ◽  
ANDRZEJ ROSTWOROWSKI
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Numerical Study ◽  
De Sitter Space ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Field System ◽  
Technical Details

In these lecture notes, we discuss recently conjectured instability of anti-de Sitter space, resulting in gravitational collapse of a large class of arbitrarily small initial perturbations. We uncover the technical details used in the numerical study of spherically symmetric Einstein-massless scalar field system with negative cosmological constant that led to the conjectured instability.

THERMODYNAMICS OF de SITTER SPACE–TIME IN YORK'S FORMALISM

2001 ◽  
Vol 16 (23) ◽  
pp. 1487-1492 ◽  
Author(s):  
BO-BO WANG ◽  
CHAO-GUANG HUANG
Keyword(s):  
Black Holes ◽  
Cosmological Constant ◽  
Path Integral ◽  
De Sitter Space ◽  
Space Time ◽  
Integral Approach ◽  
De Sitter ◽  
First Law Of Thermodynamics ◽  
Path Integral Approach ◽  
Thermodynamics Of Black Holes

The York's formalism of path-integral approach to the thermodynamics of black holes is applied to de Sitter space–time. The first law of thermodynamics for de Sitter space–time is given, which includes a "work term" with respect to the cosmological constant.

scholarly journals Evaluation of the Cosmological Constant in Inflation with a Massive Nonminimal Scalar Field

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Jung-Jeng Huang
Keyword(s):  
Scalar Field ◽  
Dispersion Relation ◽  
Energy Density ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Vacuum State ◽  
Energy Scale ◽  
Quantum Evolution ◽  
Vacuum Energy Density ◽  
De Sitter

In Schrödinger picture we study the possible effects of trans-Planckian physics on the quantum evolution of massive nonminimally coupled scalar field in de Sitter space. For the nonlinear Corley-Jacobson type dispersion relations with quartic or sextic correction, we obtain the time evolution of the vacuum state wave functional during slow-roll inflation and calculate explicitly the corresponding expectation value of vacuum energy density. We find that the vacuum energy density is finite. For the usual dispersion parameter choice, the vacuum energy density for quartic correction to the dispersion relation is larger than for sextic correction, while for some other parameter choices, the vacuum energy density for quartic correction is smaller than for sextic correction. We also use the backreaction to constrain the magnitude of parameters in nonlinear dispersion relation and show how the cosmological constant depends on the parameters and the energy scale during the inflation at the grand unification phase transition.

Nonsingular Metric Elastic Universe

1996 ◽  
Vol 168 ◽  
pp. 571-572
Author(s):  
Alexander Gusev
Keyword(s):  
Phase Space ◽  
Minkowski Space ◽  
Vacuum State ◽  
De Sitter Space ◽  
Space Time ◽  
Phase Portraits ◽  
De Sitter ◽  
Deformation State ◽  
Image Position ◽  
The Universe

In the RTFD(Gusev (1986)) the conception of a Sakharov - Wheeler Metric Elasticity(SWME)(Sakharov (1967), Wheeler (1970)) had been worked out. On the basis of the exact solutions of Einstein equations and qualitative analysis RTFD the global evolution have been studied and the phase portraits of the early Universe is being constructed. An analysis of phase portraits show on the possibility description of spontaneous creation of Universe from an initial Minkowskian's vacuum to an inflationary de Sitter space-time in the frame of phenomenological non-quantum theory (Guth (1991)). During the past decade, a radically new picture of cosmology has emerged. The present homogeneous expanding Universe would have stated out with a de Sitter phase. The purpose of this paper is to shown that the geometry-dynamical approach to the Einstein's gravitation theory in the frame RTFD also is leaded to the nonsingular cosmological models (Brandenberger (1993)). Let us to propose that before the some moment of time the Universe is at the vacuum state and is described the geometry of Minkowskian's space. Deformations of vacuum state, identifying with empty Mikowskian's space are described by the deformations tensor, An arising of deformation ∊αβis leaded to appearance of the stress tensor ∊αβand the energy-momentumTαβ(∊γδ) which is connected with “creating” particles in the Universe. Here we are considered the deformations of Minkowskian's space (the initial vacuum state with∞αβ = 0) at the linear theory (~ ∊) of finite deformations. The final deformation stategαβare searched in the metric class of Friedmann's cosmological spaces. In the comoving reference systemUα(0, 0, 0, 1) the Friedmann's equations have form (Narlikar & Padmanabhan (1983), and Gusev (1989)):where R(t) is so called the expansion factor at the Robertson - Walker line element, k is the curvature parameter with the possible values −1, 0, + 1, P is pressure,k1,k2are the some combination from a Lame coefficients,l02is a “initial radius” Universe, a free parameter model. The phase space of this model is the two-dimensional (R,Ṙ) plane. We note that there is only two singular points (Ṙ= 0,Ṙ= 0) in the phase plane. The one of those points isR=l0,Ṙ= 0 and corresponds to Minkowski space - time. There are two classes trajectories which are asymptotically de Sitter. Those starting at large positive values ofṘgo off toṘ= + ∞, reaching their asymptotic value of H from above. Those starting with large negative values ofṘtend toR= + ∞ withṘ> 0. For small values ofṘand R we can see that there are periodic solutions about Minkowski space. The corresponding solutions oscillate with frequency given byH0(which is possible equal planck scale) about Minkowski space. Based on the preceding discussion of asymptotic solutions we see that there is a separatrix (Gusev, (1989)) in phase space dividing solutions which tend toR= + ∞ from those which oscillate or tend toR=l0. The above analyses of the phase portraits is an indication that in our theory Minkowski space may be unstable toward homogeneous deformations. We stress that all the general features of the phase portrait analyses are true for quadratic deformations of gravitational vacuum. Our model incorporates a very important feature: in the asymptotic de Sitter region, the quadratic deformations and temperature effects does not have an important effect on the geometry. The effective gravitational constant of coupling goes to zero as space - time approaches de Sitter space. In this sense the model is asymptotically free (gravitational confinement Linde, (1990)). At the late times the solutions are described a evolution of the de Sitter UniverseR~expHt(Hoyle et al. (1993)).

scholarly journals SPONTANEOUS DECAY OF THE EFFECTIVE COSMOLOGICAL CONSTANT

1998 ◽  
Vol 13 (07) ◽  
pp. 571-580 ◽  
Author(s):  
MURAT ÖZER ◽  
M. O. TAHA
Keyword(s):  
Cosmological Constant ◽  
De Sitter Space ◽  
Space Time ◽  
Time Dependent ◽  
Spontaneous Decay ◽  
Quantum Fields ◽  
De Sitter ◽  
Initial Value ◽  
Effective Time ◽  
Effective Cosmological Constant

We discuss the notion that quantum fields may induce an effective time-dependent cosmological constant which decays from a large initial value. It is shown that such cosmological models are viable in a non-de Sitter space–time.

Verifying the universe is another way to ds space-time

2021 ◽  
Author(s):  
Wen-Xiang Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Cosmological Constant ◽  
Uncertainty Principle ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
The Given ◽  
The Universe

In this paper, it is explained that the role of the cosmological constant in the De Sitter space is similar to that of the preset boundary conditions in the superradiation phenomenon. In the previous literature, superradiance at a given boundary condition can cause the uncertainty principle to be less extreme, and so the uncertainty principle to be less extreme without the given boundary condition, might be one way to prove that the universe is ds spacetime.

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