Eduardo Guendelman

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• Ph.D
• Professor Emeritus Director of Bahamas Advanced Study Institute and Conferences at Ben-Gurion University of the Negev

In string theory, the consequences of replacing the measure of integration (-γ)1/2 d2x in the Polyakov action by Φ d2x, where Φ is a density built out of degrees of freedom independent of the metric γab defined in the string, are studied. The string tension appears as an integration constant of the equations of motion. The string tension can change...

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 = ∫L1Φd4cursive Greek chi + ∫L2√-gd4cursive Greek chi where Φ is a density built out of degrees of freedom, the "measure fields" independent of gμν and matter fields appearing in L1, L2. If L1 contai...

The string and brane tensions do not have to be put in by hand, they can be dynamically generated, as in the case when we formulate string and brane theories in the modified measure formalism. Then string and brane tensions appears, but as an additional dynamical degree of freedom . It can be seen however that these string or brane tensions are not...

In the modified measure formulation the string tension appear as an additional dynamical degree of freedom and these tensions are not universal, but rather each string generates its own tension, which can have a different value for each string. We consider new background field that can couple to these strings, the tension scalar is capable of chang...

Braneworld scenarios appear in dynamical string tension theories, where string tension is positive between two surfaces separated by a short distance and at the two surfaces themselves the string tensions become infinite, therefore producing an effective confinement of the strings and therefore of all matter and gravity to the space between these t...

The paper Dynamical String Tension Theories with target space scale invariance leading to 4D, uploaded before this note, has been accepted for publication in the European Physical Journal C

The string tensions can be dynamical, as we have studied in recent publications, for example in the case when we formulate string theories in the modified measure formalism. Then string and brane tensions appear, but as an additional dynamical degree of freedom. It can be seen however that these string or brane tensions may not be universal, but ra...

General Relativity is a highly non linear theory, but surprisingly a set of very important solutions, which we call thë vacuum type Black Holes¨which include Schwarzschild, Reissner Nordstrom, hedgehog black and a few others can be superposed linearly. We explain this linearity in terms of a symmetry of the space of solutions rather than of a parti...

comments on recent paper Dynamical string tension theories with target space scale invariance SSB and restoration March 2025The European Physical Journal C 276(85):1 DOI: 10.1140/epjc/s10052-025-13966-9

The string and brane tensions do not have to be put in by hand, they can be dynamically generated, as in the case when we formulate string and brane theories in the modified measure formalism. Then string and brane tensions appears, but as an additional dynamical degree of freedom. It can be seen however that these string or brane tensions are not...

The Raychaudhuri equation (RE) governs the evolution of geodesic congruences in curved spacetime. Here, we extend the classical RE by incorporating non-affine parametrization within the framework of k-essence scalar field dynamics. The non-affine parametrization introduces deviations from purely geodesic congruences (motion), allowing investigation...

This article investigates the modified Raychaudhuri Equation (RE) in the context of Non-Gravitating Vacuum Energy (NGVE) theory and its implications for various cosmological characteristics. The equation is formulated based on the NGVE framework, in which global scale invariance generates a unique geometry. The newly developed geometry introduces a...

In this paper we consider a new approach to unify inflation and the late universe with dark energy and dark matter formulated in a model that includes a non-Riemannian metric independent measure and a scalar field with spontaneously broken scale symmetry. Here first of all inflation is possible, which is then followed by a reheating oscillating per...

The unification of quantum mechanics and general relativity has long been elusive. Only recently have empirical predictions of various possible theories of quantum gravity been put to test, where a clear signal of quantum properties of gravity is still missing. The dawn of multi-messenger high-energy astrophysics has been tremendously beneficial, a...

In the present contribution to the proceedings of MG17, the main aim is to elucidate the physically important effects of a special nonlinear gauge field with a square-root of the standard Maxwell Lagrangian in its action, interacting with a specific non-canonical modified $f(R)= R + R^2$ gravity formulated in terms of metric-independent spacetime v...

We expect the final theory of gravity to have more symmetries than we suspect and our research points in this direction. To start with, standard general coordinate invariance can be extended to complex holomorphic general coordinate transformations. This is possible by introducing a non-Riemannian measure of integration (NRMI) and where we avoid th...

These are the talks at the parallel session Early Universe (EU) Inflation: perturbations, initial singularities and emergent universes EU1 of the Seventeenth Marcel Grossmann Meeting (7-12 July 2024) Chairpersons: Eduardo Guendelman and Stefano Ansoldi

A two scalar field model that incorporates non Riemannian Measures of integration or usually called Two Measures Theory (TMT) is introduced, in order to unify the early and present universe. In the Einstein frame, a K-essence is generated and as a consequence for the early universe, we can have an Inflation for the very early universe and then, aft...

We show by matching two flat spaces one in Minkowski coordinates ( empty space) and the other in Minkowski coordinates after a special conformal transformation (also empty space) through a bubble with positive and constant surface tension, that the motion of the bubble is hyperbolic. If the surface tension is very big the initial size of the bubble...

We show by matching two flat spaces one in Minkowski coordinates (empty space) and the other in Minkowski coordinates after a special conformal transformation (also empty space) through a bubble with positive and constant surface tension, that the motion of the bubble is hyperbolic.

We compare the structures of the theory of causal fermion systems (CFS), an approach to unify Quantum Theory with General Relativity, with those of modified measure theories (MMT), which are a set of modified gravity theories. Spacetimes with MMT can be obtained as the continuum limit of a CFS. This suggests that MMT could serve as effective descripti...

Cosmological solutions are studied in the context of the modified measure formulation of string theory, then the string tension is a dynamical variable and the string the tension is an additional dynamical degree of freedom and its value is dynamically generated. These tensions are then not universal, rather each string generates its own tension wh...

Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in real space time. In this context here spacetime is extended to complex spacetime and standard general coordinat...

In this work we investigate the relation between curved momentum space and momentum-dependent gauge fields. While the former is a classic idea that has been shown to be tied to minimal-length models, the latter constitutes a relatively recent development in quantum gravity phenomenology. In particular, the gauge principle in momentum space amounts...

The specific model studied is in the context of the modified measure formulation the string or branes where tension appear as an additional dynamical degree of freedom. We then consider the signed reparametrization invariant volume element formulation of dynamical strings and branes and find that the dynamical tension can produce positive tensions...

Standard general coordinate invariance is extended to general coordinate transformations that have a negative jacobian. This is possible by introducing a non Riemannian Measure of integration, which transforms according to the jacobian of the coordinate transformation, not the absolute value of the jacobian of the coordinate transformation as it is...

The specific model studied is in the context of the modified measure formulation the string or branes where tension appear as an additional dynamical degree of freedom . We then consider the signed reparametrization invariant formulation of dynamical strings and branes and find that the dynamical tension is given by a quadratic equation giving posi...

Standard general coordinate invariance is extended to general coordinate transformations that have a negative jacobian. This is possible by introducing a non Riemannian Measure of integration, which transforms according to the jacobian of the coordinate transformation, not the absolute value of the jacobian of the coordinate transformation as it is...

We compare the structures of the theory of causal fermion systems (CFS), an approach to unify Quantum Theory with General Relativity, with those of modified measure theories (MMT), which are a set of modified gravity theories. Spacetimes with MMT can be obtained as the continuum limit of a CFS. This suggests that MMT could serve as effective descri...

A two scalar field model that incorporates non Riemannian Measures of integration or usually called Two Measures Theory (TMT) is introduced, in order to unify the early and present universe. In the Einstein frame a K-essence is generated and as a consequence for the early universe, we can have a Non Singular Emergent universe followed by Inflation...

In this work, we present a gauge principle that starts with the momentum space representation of the position operator (x^i=iℏ∂∂pi), rather than starting with the position space representation of the momentum operator (p^i=−iℏ∂∂xi). This extension of the gauge principle can be seen as a dynamical version of Born’s reciprocity theory, which exchange...

Cosmological solutions are studied in the context of the modified measure formulation of string theory , then the string tension is a dynamical variable and the string the tension is an additional dynamical degree of freedom and its value is dynamically generated. These tensions are then not universal, rather each string generates its own tension w...

String tension fundamentally determines the properties of strings; yet its value is often assigned arbitrarily, creating a fine-tuning problem. We describe a mechanism for dynamically generating string tension in a flat or almost flat spacetime, using the ‘modified measures formalism’, which in turn naturally generates a new type of stringy branewo...

In this work we uncover the intimate relation between curved momentum space and momentum gauge fields. While the former concept has found consideration for some time and been shown to be tied to minimal-length models, the latter constitutes a relatively recent development in quantum gravity phenomenology. In particular, the gauge principle in momen...

A unified multiscalar field model with three flat regions is discussed. The three flat regions are the inflation, early- and late dark energy epochs. The potential is obtained by a spontaneous breaking of scale invariance generated by non-Riemannian measures of integration (or two measures theories (TMT)). We define the scale invariant couplings of...

In this work we present a gauge principle that starts with the momentum space representation of the position operator (${\hat x}_i = i \hbar \frac{\partial}{\partial p_i}$) rather than starting with the position space representation of the momentum operator (${\hat p}_i = -i \hbar \frac{\partial}{\partial x_i}$). We discuss some simple examples wit...

This book describes Relativistic Quantum Mechanics, starting from the free field equations for spin-zero particles and for spin-one-half particles, leading to the Klein–Gordon equation and Dirac equations. Interactions of these particles with the electromagnetic field through minimal coupling are introduced as well as other interactions between par...

String tension fundamentally determines the properties of strings; yet its value is often assigned arbitrarily, creating a fine-tuning problem. We describe a mechanism for dynamically generating string tension in a flat or almost flat spacetime, using the modified measures formalism, which in turn naturally generates a new type of stringy brane-wor...

An extension to the Einstein–Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, represented by a time-like axial vector $$S^\mu $$ S μ . The dynamics of torsion is invoked by a novel kinetic term. Here we show that this kinetic term gives rise to...

There is great interest in the construction of brane worlds, where matter and gravity are forced to be effective only in a lower dimensional surface , the brane . How these could appear as a consequence of string theory is a crucial question and this has been widely discussed. Here we will examine a distinct scenario that appears in dynamical tensi...

hThere is great interest in the construction of brane worlds, where matter and gravity are forced to be effective only in a lower dimensional surface , the brane. How these could appear as a consequence of string theory is a crucial question and this has been widely discussed. Here we will examine a distinct scenario that appears in dynamical tensi...

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give u...

A two scalar field model that incorporates the Two Measures Theory (TMT) is introduced, in order to unify the early and present universe. We define the scale invariant couplings of the scalar fields to the different measures through exponential potentials. Spontaneous breaking of scale invariance takes place when integrating the fields that define...

The string tension does not have to be put in by hand, it can be dynamically generated, as in the case when we formulate string theory in the modified measure formalism, and other formulations as well. Then string tension appears, but as an additional dynamical degree of freedom. It can be seen however that this string tension is not universal, but...

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give u...

A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going to an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider the addition of a linear contribution to the gravitational potential \(\phi \) which can be used to cancel the gravitational field induced by going to the...

The string tension does not have to be put in by hand, it can be dynamically generated, as in the case when we formulate string theory in the modified measure formalism, and other formulations as well. Then string tension appears, but as an additional dynamical degree of freedom . It can be seen however that this string tension is not universal, bu...

There is great interest in the construction of brane worlds, where matter and gravity are forced to be effective only in a lower dimensional surface, the brane . How these could appear as a consequence of string theory is a crucial question and this has been widely discussed. Here we will examine a distinct scenario that appears in dynamical string...

An extension to the Einstein-Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, and written by of a vector $S^\mu$. Then this torsion model, compliant with the Cosmological Principle, is made dynamical by introducing its quadratic, totally anti-s...

Recently a new kind of quintessential inflation coming from the Lorentzian distribution has been introduced in [1,2]. The model leads to a very simple potential, which basically depends on two parameters, belonging to the class of α-attractors and depicting correctly the early and late time accelerations of our universe. The potential emphasizes a...

An exponential kind of quintessential inflation potential motivated by supergravity is studied. This type belongs to the class of α-attractor models. The model was studied for the first time by Dimopoulos and Owen in [J. Cosmol. Astropart. Phys. 06 (2017) 027], in which the authors introduced a negative cosmological constant in order to ensure a ze...

The instant preheating mechanism in the framework of a scale invariant two measures theory is studied. We introduce this mechanism into a nonoscillating inflationary model as another possible solution to the reheating of the Universe in this theory. In this framework, we consider that the model includes two scalar matter fields, the first is a dila...

In this paper, we analytically present an exact confining charged black hole solution to the $4$-dimensional ($4D$) novel Einstein Gauss-Bonnet (EGB) gravity coupled to non-linear gauge theory containing $\sqrt{-F^{2}}$ term. Part of the importance of using a non-trivial $4D$ theory of Gauss-Bonnet gravity is that it is proven the absence of the Os...

An exponential kind of quintessential inflation potential motivated by supergravity is studied. This type belongs to the class of $\alpha$-attractor models. The model was studied for the first time in [1] where the authors introduced a Cosmological Constant in order to ensure quintessence at late times. However, in this note we disregard this Cosmo...

Recently a new kind of quintessential inflation coming from the Lorentzian distribution has been introduced in [1,2]. The model leads to a very simple potential, which basically depends on two parameters, belonging to the class of $\alpha$-attractors and depicting correctly the early and late time accelerations of our universe. The potential emphas...

A concise description is presented in the basic features of the formalism of non-canonical spacetime volume forms and its application in modified gravity theories and cosmology. The well-known unimodular gravity theory appears as a very special case. Concerning the hot issues facing cosmology now, we specifically briefly outline the construction of...

The standard ΛCDM model of cosmology is formulated as a simple modified gravity coupled to a single scalar field (“darkon”) possessing a nontrivial hidden nonlinear Noether symmetry. The main ingredient in the construction is the use of the formalism of non-Riemannian spacetime volume-elements. The associated Noether conserved current produces stre...

A covariant canonical gauge theory of gravity free from torsion is studied. Using a metric conjugate momentum and a connection conjugate momentum, which takes the form of the Riemann tensor, a gauge theory of gravity is formulated, with form-invariant Hamiltonian. Through the introduction of the metric conjugate momenta, a correspondence between th...

We present a concise description of the basic features of gravity-matter models based on the formalism of non-canonical spacetime volume-forms in its two versions: (a) the method of non-Riemannian volume-forms (metric-independent covariant volume elements) and (b) the dynamical spacetime formalism. Among the principal outcomes we briefly discuss: (...

The connection between the Cosmological Principle and the Newtonian Dynamics is formulated via Noether Symmetry (NS). [1] formulates the symmetry that connects two different frames with relative acceleration, without an action formulation. Here, this symmetry is derived from a classical particles system that governed by the potential {\phi}. The ac...

From the assumption that the slow-roll parameter 𝜖 has a Lorentzian form as a function of the e-folds number N, a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of 𝜖 to 1 at the e...

The Local Group (LG) is an appropriate test system for Modified Newtonian Dynamics, since the acceleration of M31 galaxy is fully in the deep MOND regime a≪a0. We model the LG as a two body problem of M31 and the Milky Way (MW) galaxies. Extending previous studies, we also include the Cosmological Constant. The assumption that in the big bang the g...

The Local Group (LG) is {an appropriate} test system for Modified Newtonian Dynamics, since the acceleration of M31 galaxy is fully in the deep MOND regime $a \ll a_0$. We model the LG as a two body problem of $M31$ and the Milky Way (MW) galaxies. {Extending previous studies, we also include the Cosmological Constant.} The assumption that in the b...

Starting with a simple two-scalar field system coupled to a modified measure that is independent of the metric, we, first, find a Born–Infeld dynamics sector of the theory for a scalar field and second, show that the initial scale invariance of the action is dynamically broken and leads to a scale charge nonconservation, although there is still a c...

From the assumption that the slow roll parameter $\epsilon$ has a Lorentzian form as a function of the e-folds number $N$, a successful model of a quintessential inflation is obtained, as succinctly studied in \cite{Benisty:2020xqm}. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs and satisfies the c...

A concise description is presented of the basic features of the formalism of non-canonical spacetime volume-forms and its application in modified gravity theories and cosmology. The well known unimodular gravity theory appears as a very special case. Concerning the hot issues facing cosmology now, we specifically briefly outline the construction of...

From the assumption that the slow-roll parameter \(\varepsilon \) has a Lorentzian form as a function of the e-fold number N, a successful model of a quintessential inflation is obtained, as succinctly studied in [1]. The form corresponds to the vacuum energy both in the inflationary and in the dark-energy epochs and satisfies the condition to clim...

The instant preheating mechanism in the framework of a scale invariant two measures theory is studied. We introduce this mechanism into a non oscillating inflationary model as another possible solution to the reheating of the universe in this theory. In this framework, we consider that the model includes two scalar matter fields, the first a dilato...

First, we propose a scale-invariant modified gravity interacting with a neutral scalar inflaton and a Higgs-like SU(2)×U(1) iso-doublet scalar field based on the formalism of non-Riemannian (metric-independent) spacetime volume-elements. This model describes, in the physical Einstein frame, a quintessential inflationary scenario driven by the “infl...

We propose a new approach to investigate inflation in a model-independent way, and in particular to elaborate the involved observables, through the introduction of the “scale factor potential”. Through its use one can immediately determine the inflation end, which corresponds to its first (and global) minimum. Additionally, we express the inflation...

First, we propose a scale-invariant modified gravity interacting with a neutral scalar inflaton and a Higgs-like SU(2) × U(1) iso-doublet scalar field based on the formalism of non-Riemannian (metric-independent) spacetime volume-elements. This model describes in the physical Einstein frame a quintessential inflationary scenario driven by the “infl...

From the assumption that the slow roll parameter $\epsilon$ has a Lorentzian form as a function of the e-folds number $N$, a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of $\ep...

A correspondence between the equivalence principle and the homogeneity of the universe is discussed. In Newtonian gravity, translation of co-moving coordinates in a uniformly expanding universe defines an accelerated frame. A consistency condition for the invariance of this transformation which requires a well-defined transformation for the Newtoni...

The standard $\Lambda$CDM model of cosmology is formulated as a simple modified gravity coupled to a single scalar field ("darkon") possessing a non-trivial hidden nonlinear Noether symmetry. The main ingredient in the construction is the use of the formalism of non-Riemannian spacetime volume-elements. The associated Noether conserved current prod...

Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the forma...

First, we propose a scale-invariant modified gravity interacting with a neutral scalar "inflaton" and a Higgs-like SU(2)xU(1) iso-doublet scalar field based on the formalism of non-Riemannian (metric-independent) spacetime volume-elements. This model describes in the physical Einstein frame a quintessential inflationary scenario driven by the "infl...

DOI:https://doi.org/10.1103/PhysRevD.101.049901

Our primary objective is to construct a plausible unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, where all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalis...

Our primary objective is the formulation of a plausible cosmological inflationary model entirely in terms of a pure modified gravity without any a priori matter couplings within the formalism of non-Riemannian spacetime volume elements. The non-Riemannian volume elements dynamically create in the physical Einstein frame a canonical scalar matter fi...

We consider a simple model of modified gravity interacting with a single scalar field φ with weakly coupled exponential potential within the framework of non-Riemannian spacetime volume-form formalism. The specific form of the action is fixed by the requirement of invariance under global Weyl-scale symmetry. Upon passing to the physical Einstein fr...

We consider string meson and string baryon models in the framework of the modified measure theory, the theory that does not use the determinant of the metric to construct the invariant volume element. As the outcome of this theory, the string tension is not placed ad hoc but is derived. When the charges are presented, the tension undergoes alterati...

The Running Vacuum Model (RVM) has been a candidate to solve the tension between the Hubble constant from the early and the late universe data fit. However the model does consider a Lagrangian formulation directly. In this paper we formulate an action principle that approaches the RMV from the second type, with a scalar field model for the whole da...

We propose a new approach to investigate inflation in a model-independent way, and in particular to elaborate the involved observables, through the introduction of the "scale factor potential". Through its use one can immediately determine the inflation end, which corresponds to its first (and global) minimum. Additionally, we express the inflation...

We propose a simple modified gravity model without any initial matter fields in terms of several alternative non-Riemannian spacetime volume elements within the metric (second order) formalism. We show how the non-Riemannian volume-elements, when passing to the physical Einstein frame, create a canonical scalar field and produce dynamically a non-t...

A model of inflation realization driven by fermions with curvature-dependent mass is studied. Such a term is derived from the covariant canonical gauge theory of gravity (CCGG) incorporating Dirac fermions. We obtain an initial de Sitter phase followed by a successful exit, and moreover we acquire the subsequent thermal history, with an effective m...

The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable...

We consider a simple model of modified gravity interacting with a single scalar field $\varphi$ with weakly coupled exponential potential within the framework of non-Riemannian spacetime volume-form formalism. The specific form of the action is fixed by the requirement of invariance under global Weyl-scale symmetry. Upon passing to the physical Ein...

Cosmological solutions for covariant canonical gauge theories of gravity are presented. The underlying covariant canonical transformation framework invokes a dynamical spacetime Hamiltonian consisting of the Einstein–Hilbert term plus a quadratic Riemann tensor invariant with a fundamental dimensionless coupling constant g1. A typical time scale re...