arXiv subjects
Publications and source records attributed to E. I. Guendelman.
The consequences of considering the measure of integration in the action to be defined by degrees of freedom independent of the metric are studied. Models without the cosmological constant problem, new ways of spontaneously breaking scale symmetry which have an interesting cosmology and theories of extended objects (string, branes) without a fundamental scale appear possible.
For superstrings, the consequences of replacing the measure of integration $\sqrt{-γ}d^2 x$ in the Polyakov's action by $Φd^2 x$ where $Φ$ is a density built out of degrees of freedom independent of the metric $γ_{ab}$ defined in the string are studied. As in Siegel reformulation of the Green Schwarz formalism the Wess-Zumino term is the square of supersymmetric currents. As opposed to the Siegel case, the compensating fields needed for this do not enter into the action just as in a total derivative. They instead play a crucial role to make up a consistent dynamics. The string tension appears as an integration constant of the equations of motion. The generalization to higher dimensional extended objects is also studied using in this case the Bergshoeff and Sezgin formalism with the associated additional fields, which again are dynamically relevant unlike the standard formulation. Also unlike the standard formulation, there is no need of a cosmological term on the world brane.
In string theory, the consequences of replacing the measure of integration $\sqrt{-γ}d^2 x$ in the Polyakov's action by $Φd^2 x$ where $Φ$ is a density built out of degrees of freedom independent of the metric $γ_{ab}$ defined in the string are studied. The string tension appears as an integration constant of the equations of motion. The string tension can change in different parts of the string due to the coupling of gauge fields and point particles living in the string. The generalization to higher dimensional extended objects is also studied. In this case there is no need of a fine tuned cosmological term, in sharp contrast to the standard formulation of the generalized Polyakov action for higher dimensional branes.
The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. Scale invariance is considered in the context of a gravitational theory where the action, in the first order formalism, is of the form $S = \int L_{1} Φd^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where $Φ$ is a density built out of degrees of freedom independent of the metric. For global scale invariance, a "dilaton" $ϕ$ has to be introduced, with non-trivial potentials $V(ϕ)$ = $f_{1}e^{αϕ}$ in $L_1$ and $U(ϕ)$ = $f_{2}e^{2αϕ}$ in $L_2$. This leads to non-trivial mass generation and a potential for $ϕ$ which is interesting for inflation. The model after ssb can be connected to the induced gravity model of Zee, which is a successful model of inflation. Models of the present universe and a natural transition from inflation to a slowly accelerated universe at late times are discussed.
The stability of our vacuum is analyzed and several aspects concerning this question are reviewed. 1) In the standard Glashow-Weinberg-Salam (GWS) model we review the instability towards the formation of a bubble of lower energy density and how the rate of such bubble formation process compares with the age of the Universe for the known values of the GWS model. 2) We also review the recent work by one of us (E.I.G) concerning the vacuum instability question in the context of a model that solves the cosmological constant problem. It turns out that in such model the same physics that solves the cosmological constant problem makes the vacuum stable. 3) We review our recent work concerning the instability of elementary particle embedded in our vacuum, towards the formation of an infinite Universe. Such process is not catastrophic. It leads to a "bifurcation type" instability in which our Universe is not eaten by a bubble (instead a baby universe is born). This universe does not replace our Universe rather it disconnects from it (via a wormhole) after formation.
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken somehow. We get to this conclusion by showing that the infrared behavior of the conserved currents is singular so that there are no conserved charges associated with the global scale symmetry. The scale symmetry plays nevertheless a crucial role in determining the structure of the theory and it implies that in some high field regions the potentials become flat.
Summary of abstract Field theory models including gauge theories with SSB are presented where the energy density of the true vacuum state (TVS) is zero without fine tuning. The above models are constructed in the gravitational theory where a measure of integration Φin the action is not necessarily \sqrt{-g} but it is determined dynamically through additional degrees of freedom. The ratio Φ/\sqrt{-g} is a scalar field which can be solved in terms of the matter degrees of freedom due to the existence of a constraint. We study a few explicit field theory models where it is possible to combine the solution of the cosmological constant problem with: 1) possibility for inflationary scenario for the early universe; 2) spontaneously broken gauge unified theories (including fermions). The models are free from the well known problem of the usual scalar-tensor theories in what is concerned with the classical GR tests. The only difference of the field equations in the Einstein frame from the canonical equations of the selfconsistent system of Einstein's gravity and matter fields, is the appearance of the effective scalar field potential which vanishes in TVS without fine tuning.
The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. The realizations of scale invariance which are considered, are in the context of a gravitational theory where the action, in the first order formalism, is of the form $S = \int L_{1} Φd^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where $Φ$ is a density built out of degrees of freedom independent of gravity, which we call the "measure fields". For global scale invariance, a "dilaton" $ϕ$ has to be introduced, with non-trivial potentials $V(ϕ)$ = $f_{1}e^{αϕ}$ in $L_1$ and $U(ϕ)$ = $f_{2}e^{2αϕ}$ in $L_2$. This leads to non-trivial mass generation and potential for $ϕ$. Mass terms for an arbitrary matter field can appear in a scale invariant form both in $L_1$ and in $L_2$ where they are coupled to different exponentials of the field $ϕ$. Implications of these results for cosmology having in mind in particular inflationary scenarios, models of the late universe and modified gravitational theories are discussed.
We consider a model of an elementary particle as a 2 + 1 dimensional brane evolving in a 3 + 1 dimensional space. Introducing gauge fields that live in the brane as well as normal surface tension can lead to a stable "elementary particle" configuration. Considering the possibility of non vanishing vacuum energy inside the bubble leads, when gravitational effects are considered, to the possibility of a quantum decay of such "elementary particle" into an infinite universe. Some remarkable features of the quantum mechanics of this process are discussed, in particular the relation between possible boundary conditions and the question of instability towards Universe formation is analyzed.
Realizations of scale invariance are studied in the context of a gravitational theory where the action (in the first order formalism) is of the form $S = \int L_{1} Φd^{4}x$ + $\int L_{2}\sqrt{-g}d^{4}x$ where $Φ$ is a density built out of degrees of freedom, the "measure fields" independent of $g_{μν}$ and matter fields appearing in $L_{1}$, $L_{2}$. If $L_{1}$ contains the curvature, scalar potential $V(ϕ)$ and kinetic term for $ϕ$, $L_{2}$ another potential for $ϕ$, $U(ϕ)$, then the true vacuum state has zero energy density, when theory is analyzed in the conformal Einstein frame (CEF), where the equations assume the Einstein form. Global Scale invariance is realized when $V(ϕ)$ = $f_{1}e^{αϕ}$ and $U(ϕ)$ = $f_{2}e^{2αϕ}$. In the CEF the scalar field potential energy $V_{eff}(ϕ)$ has in, addition to a minimum at zero, a flat region for $αϕ\to\infty$, with non zero vacuum energy, which is suitable for either a New Inflationary scenario for the Early Universe or for a slowly rolling decaying $Λ$-scenario for the late universe, where the smallness of the vacuum energy can be understood as a kind of see-saw mechanism.
We study field theory models in the context of a gravitational theory based on the requirement that the measure of integration in the action is not necessarily \sqrt{-g} but it is determined dynamically through additional degrees of freedom, like four scalar fields ϕ_{a}. We study three possibilities for the general structure of the theory: (A) The total action has the form S=\intΦLd^{4}x where the measure Φis built from the scalars ϕ_{a} in such a way that the transformation L\to L+const does not effect equations of motion. Then an infinite dimensional shifts group of the measure fields (SGMF) ϕ_{a} by arbitrary functions of the Lagrangian density L is a symmetry group of the action. (B) The total action has the form S=S_{1}+S_{2}, S_{1}=\intΦL_{1}d^{4}x, S_{2}=\int\sqrt{-g}L_{2}d^{4}x which is the only model different from (A) and invariant under SGMF (but now with f_{a}= f_{a}(L_{1})). Similarly, now only S_{1} satisfies the requirement that the transformation L_{1}\to L_{1}+const does not effect equations of motion. Both in the case (A) and in the case (B) it is assumed that L, L_{1}, L_{2} do not depend on ϕ_{a}. (C) The action includes a term which breaks the SGMF symmetry. It is shown that in the first order formalism in cases (A) and (B) the CCP is solved: the effective potential vanishes in a true vacuum state (TVS) without fine tuning. In the case (C), the breaking of the SGMF symmetry induces a nonzero energy density for the TVS.
We consider an action which consists of two terms: the first S_{1}=\int L_{1}Φd^{4}x and the second S_{2}=\int L_{2}\sqrt{-g}d^{4}x where Φis a measure which has to be determined dynamically. S_{1} satisfies the requirement that the transformation L_{1}\to L_{1}+const does not effect equations of motion. In the first order formalism, a constraint appears which allows to solve χ=Φ/\sqrt{-g}. Then, in a true vacuum state (TVS), χ\to\infty and in the conformal Einstein frame no singularities are present, the energy density of TVS is zero without fine tuning of any scalar potential in S_{1} or S_{2}. When considering only a linear potential for a scalar field ϕin S_{1}, the continuous symmetry ϕ\toϕ+const is respected. Surprisingly, in this case SSB takes place while no massless ("Goldstone") boson appears.
This essay elucidates recent achievements of the "nongravitating vacuum energy" (NGVE) theory" which has the feature that a shift of the Lagrangian density by a constant does not affect dynamics. In the first order formalism, a constraint appears that enforces the vanishing of the cosmological constant Λ. Standard dynamics of gauge unified theories (including fermions) and their SSB appear if a four index field strength condensate is present. At a vacuum state there is exact balance to zero of the gauge fields condensate and the original scalar fields potential. As a result it is possible to combine the solution of the Λproblem with inflation and transition to a Λ=0 phase without fine tuning after a reheating period. The model opens new possibilities for a solution of the hierarchy problem.
In this paper we use a non-covariant gauge which makes some of the YM features manifest which otherwise do not appear explicitly in the Landau gauge used by Nielsen and Olesen.We show, in fact, that the unstable mode which makes a large contribution to the vacuum energy is non-perturbative even classically.
We show that it is possible to obtain inflation and also solve the cosmological constant problem. The theory is invariant under changes of the Lagrangian density $L$ to $L+const$. Then the constant part of a scalar field potential $V$ cannot be responsible for inflation. However, we show that inflation can be driven by a condensate of a four index field strength. A constraint appears which correlates this condensate to $V$. After a conformal transformation, the equations are the standard GR equations with an effective scalar field potential $V_{eff}$ which has generally an absolute minimum $V_{eff}=0$ independently of $V$ and without fine tuning. We also show that, after inflation, the usual reheating phase scenario (from oscillations around the absolute minimum) is possible.
We study gauge theories in the context of a gravitational theory without the cosmological constant problem (CCP). The theory is based on the requirement that the measure of integration in the action is not necessarily $\sqrt{-g}$ but it is determined dynamically through additional degrees of freedom. Realization of these ideas in the framework of the first order formalism solves the CCP. Incorporation of a condensate of a four index field strength allows, after a conformal transformation to the Einstein frame, to represent the system of gravity and matter in the standard GR form. Now, however, the effective potential vanishes at a vacuum state due to the exact balance to zero of the gauge fields condensate and the original scalar fields potential. As a result it is possible to combine the solution of the CCP with: a) inflation and transition to a $Λ=0$ phase without fine tuning after a reheating period; b) spontaneously broken gauge unified theories (including fermions). The model opens new possibilities for a solution of the hierarchy problem.
We showed that the principle of nongravitating vacuum energy, when formulated in the first order formalism, solves the cosmological constant problem. The most appealing formulation of the theory displays a local symmetry associated with the arbitrariness of the measure of integration. This can be motivated by thinking of this theory as a direct coupling of physical degrees of freedom with a "space - filling brane" and in this case such local symmetry is related to space-filling brane gauge invariance. The model is formulated in the first order formalism using the metric and the connection as independent dynamical variables. An additional symmetry (Einstein - Kaufman symmetry) allows to eliminate the torsion which appears due to the introduction of the new measure of integration. The most successful model that implements these ideas is realized in a six or higher dimensional space-time. The compactification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic masses. It turns out that remaining four dimensional space-time must have effective zero cosmological constant.
We develop the principle of nongravitating vacuum energy, which is implemented by changing the measure of integration from $\sqrt{-g}d^{D}x$ to an integration in an internal space of $D$ scalar fields $ϕ_{a}$. As a consequence of such a choice of the measure, the matter Lagrangian $L_{m}$ can be changed by adding a constant while no cosmological term is induced. Here we develop this idea to build a new theory which is formulated through the first order formalism, i.e. using vielbein $e_{a}^μ$ and spin connection $ω_μ^{ab}$ (a,b=1,2,...D) as independent variables. The equations obtained from the variation of $e_{a}^μ$ and the fields $ϕ_{a}$ imply the existence of a nontrivial constraint. This approach can be made consistent with invariance under arbitrary diffeomorphisms in the internal space of scalar fields $ϕ_{a}$ (as well as in ordinary space-time), provided that the matter model is chosen so as to satisfy the above mentioned constraint. If the matter model is not chosen so as to satisfy automatically this constraint, the diffeomorphism invariance in the internal space is broken. In this case the constraint is dynamically implemented by the degrees of freedom that become physical due to the breaking of the internal diffeomorphism invariance. However, this constraint always dictates the vanishing of the cosmological constant term and the gravitational equations in the vacuum coincide with vacuum Einstein's equations with zero cosmological constant. The requirement that the internal diffeomorphisms be a symmetry of the theory points towards the unification of forces in nature like in the Kaluza-Klein scheme.