The Higgs boson is often compared to a small ripple on a vast, calm ocean. This "ocean" is the universal Higgs vacuum expectation value, approximate to 246 GeV, permeating all space and generating particle masses. Its remarkable uniformity reflects the large-scale nature of the universe. Here I argue that the Higgs field plays a far deeper role. In regions of extreme gravity near singularities, it becomes a non-perturbative, space-time-dependent field that creates new space-time domains beyond gravitational singularities-new regions governed by antigravity. This mechanism produces dramatic dynamics inside black holes and in the earliest universe, including restoration of the electroweak symmetry SU(2)& times;U(1) at singularities. The adjoining gravity and antigravity regions form a geodesically complete space-time bridged by traversable singularities-absent in the Standard Model coupled to general relativity or its extensions such as string theory. In such a framework, the black hole information paradox admits a new, manifestly unitary resolution. Details of computations are developed in the companion paper [1]; here, only a brief outline is given.

The Higgs field is conventionally treated as a small local perturbation atop a large, constant vacuum value that uniformly permeates the Universe. I propose instead that in regions of extreme gravitational intensity-such as near gravitational singularities-the Higgs field behaves in a profoundly non-perturbative manner. In such environments, spacetime and the Higgs field engage in a dynamic interplay that extends spacetime beyond the singularity, achieving geodesic completeness. The continuation beyond the singularity is dominated by antigravity effects, reshaping the causal structure of spacetime and enabling novel flows of matter and information, including traversal through singularities. In its standard form, the combined framework of the Standard Model (SM) and general relativity (GR), as well as most of its extensions, fails to capture these phenomena due to its geodesic incompleteness. By contrast, a refined, locally conformal-symmetric formulation-denoted i(SM + GR)-naturally incorporates these effects. GR is not an optional component of i(SM + GR) but an essential ingredient. This framework preserves the empirical success of SM + GR in the low-energy regime while predicting striking new phenomena in extreme gravitational settings, including within black holes (on both sides of the singularity) and in pre-big bang cosmology. At the classical field theory level, i(SM + GR) offers fresh perspectives on the black hole information puzzle and provides a platform for locally scale-invariant generalizations, such as geodesically complete quantum field theory, string theory, and unified models of fundamental interactions. This paper presents the detailed derivations and explanations that underlie a condensed letter version recently published in Itzhak Bars, Higgs field as architect of a geodesically complete universe and agent for new physics in interiors of black holes, arXiv:2509.07346.

The traditional Chern-Simons (CS) terms in 3+1 dimensions that modify general relativity (GR), quantum chromodynamics (QCD), and quantum electrodynamics (QED), typically lack scale invariance. However, a locally scale invariant and geodesically complete framework for the Standard Model (SM) coupled to GR was previously constructed by employing a tailored form of local scale (Weyl) symmetry. This refined SM+GR model closely resembles the conventional SM in subatomic realms where gravitational effects are negligible. Nevertheless, it offers an intriguing prediction: the emergence of new physics beyond the traditional SM and GR near spacetime singularities, characterized by intense gravity and substantial deviations in the Higgs field. In this study, we expand upon the enhanced SM+GR by incorporating Weyl invariant CS terms for gravity, QCD, and QED in 3+1 dimensions, thereby integrating CS contributions within the locally scale-invariant and geodesically complete paradigm. Additionally, we establish a holographic correspondence between the new CS terms in 3+1 dimensions and novel (4+2)-dimensional CS-type actions within 2T physics. We demonstrate that the Weyl transformation in 3+1 dimensions arises from 4+2 general coordinate transformations, which unify the hidden extra 1+1 large (not curled up) dimensions with the evident 3+1 dimensions. By leveraging the newfound local conformal symmetry, the augmented and geodesically complete SM+GR+CS introduces innovative tools and perspectives for exploring classical field theory aspects of black hole and cosmological singularities in 3+1 dimensions, while the (4+2)-dimensional connection unveils deeper facets of spacetime. Published by the American Physical Society 2024

The traditional Chern-Simons (CS) terms in 3 + 1 dimensions that modify general relativity (GR), quantum chromodynamics (QCD), and quantum electrodynamics (QED), typically lack scale invariance. However, a locally scale invariant and geodesically complete framework for the Standard Model (SM) coupled to GR was previously constructed by employing a tailored form of local scale (Weyl) symmetry. This refined SM + GR model closely resembles the conventional SM in subatomic realms where gravitational effects are negligible. Nevertheless, it offers an intriguing prediction: the emergence of new physics beyond the traditional SM and GR near spacetime singularities, characterized by intense gravity and substantial deviations in the Higgs field. In this study, we expand upon the enhanced SM + GR by incorporating Weyl invariant CS terms for gravity, QCD, and QED in 3 + 1 dimensions, thereby integrating CS contributions within the locally scale-invariant and geodesically complete paradigm. Additionally, we establish a holographic correspondence between the new CS terms in 3 + 1 dimensions and novel (4 + 2)-dimensional CS-type actions within 2T physics. We demonstrate that the Weyl transformation in 3 + 1 dimensions arises from 4 + 2 general coordinate transformations, which unify the hidden extra 1 + 1 large (not curled up) dimensions with the evident 3 + 1 dimensions. By leveraging the newfound local conformal symmetry, the augmented and geodesically complete SM + GR + CS introduces innovative tools and perspectives for exploring classical field theory aspects of black hole and cosmological singularities in 3 + 1 dimensions, while the (4 + 2)-dimensional connection unveils deeper facets of spacetime.

The relation between motion in $-1/r$ and $r^{2}$ potentials, known since Newton, can be demonstrated by the substitution $r\rightarrow r^{2}$ in the classical/quantum radial equations of the Kepler/Hydrogen problems versus the harmonic oscillator. This suggests a duality-type relationship between these systems. However, when both radial and angular components of these systems are included the possibility of a true duality seems to be remote. Indeed, investigations that explored and generalized Newton's radial relation, including algebraic approaches based on noncompact groups such as SO(4,2), have never exhibited a full duality consistent with Newton's. On the other hand, 2T-physics predicts a host of dualities between pairs of a huge set of systems that includes Newton's two systems. These dualities take the form of rather complicated canonical transformations that relate the full phase spaces of these respective systems in all directions. In this paper we focus on Newton's case by imposing his radial relation to find an appropriate basis for 2T-physics dualities, and then construct the full duality. Using the techniques of 2T-physics, we discuss the hidden symmetry of the actions (beyond the symmetry of Hamiltonians) for the Hydrogen atom in $D$-dimensions and the harmonic oscillator in $\bar{D}$ dimensions. The symmetries lead us to find the one-to-one relation between the quantum states, including angular degrees of freedom, for specific values of $\left( D,\bar{D}\right) $, and construct the explicit quantum canonical transformation in those special cases. We find that the canonical transformation has itself a hidden gauge symmetry that is crucial for the respective phase spaces to be dual even when $D\neq\bar{D}$. In this way we display the surprising beautiful symmetry of the full duality that generalizes Newton's radial duality.

This is the first of a series of papers in which we use analyticity properties of quantum fields propagating on a spacetime to uncover a new multiverse geometry when the classical geometry has horizons and/or singularities. The nature and origin of the multiverse idea presented in this paper, that is shared by the fields in the standard model coupled to gravity, is different from other notions of a multiverse. Via analyticity we are able to establish definite relations among the universes. In this paper we illustrate these properties for the extended Rindler space, while black hole spacetime and the cosmological geometry of mini-superspace (see Appendix B) will appear in later papers. In classical general relativity, extended Rindler space is equivalent to flat Minkowski space; it consists of the union of the four wedges in (u,v) light-cone coordinates as in Fig.(1). In quantum mechanics, the wavefunction is an analytic function of (u,v) that is sensitive to branch points at the horizons u=0 or v=0, with branch cuts attached to them. The wavefunction is uniquely defined by analyticity on an infinite number of sheets in the cut analytic (u,v) spacetime. This structure is naturally interpreted as an infinite stack of identical Minkowski geometries, or universes, connected to each other by analyticity across branch cuts, such that each sheet represents a different Minkowski universe when (u,v) are analytically continued to the real axis on any sheet. We show in this paper that, in the absence of interactions, information doesn't flow from one Rindler sheet to another. By contrast, for an eternal black hole spacetime, which may be viewed as a modification of Rindler that includes gravitational interactions, analyticity shows how information is lost due to a flow to other universes, enabled by an additional branch point and cut due to the black hole singularity.

In this paper I will first outline an effective field theory for cosmology (EFTC) that is based on the Standard Model coupled to General Relativity and improved with Weyl symmetry. There are no new physical degrees of freedom in this theory, but what is new is an enlargement of the domain of the existing physical fields and of spacetime via the larger symmetry, thus curing the geodesic incompleteness of the traditional theory. Invoking the softer behavior of an underlying theory of quantum gravity, I further argue that it is reasonable to ban higher curvature terms in the effective action, thus making this EFTC mathematically well behaved at gravitational singularities, as well as geodesically complete, thus able to make new physics predictions. Using this EFTC, I show some predictions of surprising behavior of the universe at singularities including a unique set of big-bang initial conditions that emerge from a dynamical attractor mechanism. I will illustrate this behavior with detailed formulas and plots of the classical solutions and the quantum wavefunction that are continuous across singularities for a cosmology that includes the past and future of the big bang. The solutions are given in the geodesically complete global mini-superspace that is similar to the extended spacetime of a black hole or extended Rindler spacetime. The analytic continuation of the quantum wavefunction across the horizons describes the passage through the singularities. This analytic continuation solves a long-standing problem of the singular (-1/r^2) potential in quantum mechanics that dates back to Von Neumann. The analytic properties of the wavefunction also reveal an infinite stack of universes sewn together at the horizons of the geodesically complete space. Finally a critique of recent controversial papers using the path integral approach in cosmology is given.

String theories on a background manifold with torsion are discussed. Candidate vacuum configurations are discussed for ten-dimensional superstrings. These are compactified on M/sub 4/ x K, where M/sub 4/ is four-dimensional and K is some compact six-dimensional manifold. Solutions with non-zero torsion on K are emphasized. The compactification problem is approached both from the effective field theory point of view and directly using string considerations. The construction of string theories in curved space with torsion is then discussed. Particular emphasis is put on the constraints on space-time supersymmetry in the Green-Schwarz approach. Two-dimensional non-linear sigma models are used to describe the propagation of strings in background geometries with torsion. (LEW)

Abstract We develop a new background independent Moyal star formalism in bosonic open string field theory, rendering it into a more transparent and computationally more efficient theory. The new star product is formulated in a half-phase-space, and because phase space is independent of any background fields that the string propagates in, the interactions expressed with the new star product are background independent. The interaction written in this basis has a large amount of symmetry, including a supersymmetry OSp(d|2) that acts on matter and ghost degrees of freedom, and simplifies computations. The BRST operator that defines the quadratic kinetic term of string field theory may be regarded as the solution of the equation of motion Ā ⋆ Ā = 0 of a purely cubic background independent string field theory. We find an infinite number of non-perturbative solutions to this equation, and are able to associate them to the BRST operator of conformal field theories on the worldsheet. Thus, the background emerges from a spontaneous-type breaking of a purely cubic highly symmetric theory. The form of the BRST field breaks the symmetry in a tractable way such that the symmetry continues to be useful in practical perturbative computations as an expansion around some background. The new Moyal basis is called the σ-basis, where σ is the worldsheet parameter of an open string. A vital part of the new star product is a natural and crucially needed mid-point regulator in this continuous basis, so that all computations are finite. The regulator is removed after renormalization and then the theory is finite only in the critical dimension. Boundary conditions for D-branes at the endpoints of the string are naturally introduced and made part of the theory as simple rules in algebraic computations. The formalism is tested by computing some perturbative quantities and finding agreement with previous methods. We are now prepared for new non-perturbative computations. A byproduct of our approach is an astonishing suggestion of the formalism: the roots of ordinary quantum mechanics may originate in the rules of non-commutative interactions in string theory.

Geodesic incompleteness is a problem in both general relativity and string theory. The Weyl-invariant Standard Model coupled to general relativity ($\mathrm{SM}+\mathrm{GR}$), and a similar treatment of string theory, are improved theories that are geodesically complete. A notable prediction of this approach is that there must be antigravity regions of spacetime connected to gravity regions through gravitational singularities such as those that occur in black holes and cosmological bang/crunch. Antigravity regions introduce apparent problems of ghosts that raise several questions of physical interpretation. It was shown that unitarity is not violated, but there may be an instability associated with negative kinetic energies in the antigravity regions. In this paper we show that the apparent problems can be resolved with the interpretation of the theory from the perspective of observers strictly in the gravity region. Such observers cannot experience the negative kinetic energy in antigravity directly, but can only detect in and out signals that interact with the antigravity region. This is no different from a spacetime black box for which the information about its interior is encoded in scattering amplitudes for in/out states at its exterior. Through examples we show that negative kinetic energy in antigravity presents no problems of principles but is an interesting topic for physical investigations of fundamental significance.

We present the geodesical completion of the Schwarzschild black hole in four dimensions which covers the entire space in (u,v) Kruskal-Szekeres coordinates, including the spacetime behind the black and white hole singularities. The gravitational constant switches sign abruptly at the singularity, thus we interpret the other side of the singularity as a region of antigravity. The presence of such sign flips is a prediction of local (Weyl) scale invariant geodesically complete spacetimes which improve classical general relativity and string theory. We compute the geodesics for our new black hole and show that all geodesics of a test particle are complete. Hence, an ideal observer, that starts its journey in the usual space of gravity, can reach the other side of the singularity in a finite amount of proper time. As usual, an observer outside of the horizon cannot verify that such phenomena exist. However, the fact that there exist proper observers that can see this, is of fundamental significance for the construction of the correct theory and the interpretation of phenomena pertaining to black holes and cosmology close to and beyond the singularities.

In the conventional formalism of physics, with 1-time, systems with different Hamiltonians or Lagrangians have different physical interpretations and are considered to be independent systems unrelated to each other. However, in this paper we construct explicitly canonical maps in 1T phase space (including timelike components, specifically the Hamiltonian) to show that it is appropriate to regard various 1T-physics systems, with different Lagrangians or Hamiltonians, as being duals of each other. This concept is similar in spirit to dualities discovered in more complicated examples in field theory or string theory. Our approach makes it evident that such generalized dualities are widespread. This suggests that, as a general phenomenon, there are hidden relations and hidden symmetries that conventional 1T-physics does not capture, implying the existence of a more unified formulation of physics that naturally supplies the hidden information. In fact, we show that 2T-physics in (d+2)-dimensions is the generator of these dualities in 1T-physics in d-dimensions by providing a holographic perspective that unifies all the dual 1T systems into one. The unifying ingredient is a gauge symmetry in phase space. Via such dualities it is then possible to gain new insights toward new physical predictions not suspected before, and suggest new methods of computation that yield results not obtained before. As an illustration, we will provide concrete examples of 1T-systems in classical mechanics that are solved analytically for the first time via our dualities. These dualities in classical mechanics have counterparts in quantum mechanics and field theory, and in some simpler cases they have already been constructed in field theory. We comment on the impact of our approach on the meaning of spacetime and on the development of new computational methods based on dualities.

String theory was developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend that open string field theory is a fully consistent definition of the theory – it is at least a self-consistent sector. Then we find in its structure that the rules of quantum mechanics emerge from the non-commutative nature of the basic string joining/splitting interactions. Thus, rather than assuming the quantum commutation rules among the usual canonical variables we derive them from the physical process of string interactions. Morally we could apply such an argument to M-theory to cover quantum mechanics for all physics. If string or M-theory really underlies all physics, it seems that the door has been opened to an explanation of the origins of quantum mechanics from the physical processes point of view.

We develop a new background independent Moyal star formalism in bosonic open string field theory. The new star product is formulated in a half-phase-space, and because phase space is independent of any background fields, the interactions are background independent. In this basis there is a large amount of symmetry, including a supersymmetry OSp(d|2) that acts on matter and ghost degrees of freedom, and simplifies computations. The BRST operator that defines the quadratic kinetic term of string field theory may be regarded as the solution of the equation of motion A*A=0 of a purely cubic background independent string field theory. We find an infinite number of non-perturbative solutions to this equation, and are able to associate them to the BRST operator of conformal field theories on the worldsheet. Thus, the background emerges from a spontaneous-type breaking of a purely cubic highly symmetric theory. The form of the BRST field breaks the symmetry in a tractable way such that the symmetry continues to be useful in practical perturbative computations as an expansion around some background. The new Moyal basis is called the $σ$-basis, where $σ$ is the worldsheet parameter of an open string. A vital part of the new star product is a natural and crucially needed mid-point regulator in this continuous basis, so that all computations are finite. The regulator is removed after renormalization and then the theory is finite only in the critical dimension. Boundary conditions for D-branes at the endpoints of the string are naturally introduced and made part of the theory as simple rules in algebraic computations. A byproduct of our approach is an astonishing suggestion of the formalism: the roots of ordinary quantum mechanics may originate in the rules of non-commutative interactions in string theory.

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 crunch and bang. Recently, some authors rediscovered a few of these divergences and concluded based on their existence alone that the theories cannot be geodesically complete. In this note, we show that this conclusion is invalid. Using conserved quantities we explicitly construct the complete set of geodesics and show that they pass continuously through the big crunch-big bang transition.

The fundamental string length, which is an essential part of string theory, explicitly breaks scale invariance. However, in field theory we demonstrated recently that the gravitational constant, which is directly related to the string length, can be promoted to a dynamical field if the standard model coupled to gravity (SM+GR) is lifted to a locally scale (Weyl) invariant theory. The higher gauge symmetry reveals previously unknown field patches whose inclusion turn the classically conformally invariant SM+GR into a geodesically complete theory with new cosmological and possibly further physical consequences. In this paper this concept is extended to string theory by showing how it can be Weyl lifted with a local scale symmetry acting on target space background fields. In this process the string tension (fundamental string length) is promoted to a dynamical field, in agreement with the parallel developments in field theory. We then propose a string theory in a geodesically complete cosmological stringy background which suggests previously unimagined directions in the stringy exploration of the very early universe.

We show how to lift a generic non-scale-invariant action in Einstein frame into a locally conformally invariant (or Weyl-invariant) theory and present a new general form for Lagrangians consistent with Weyl symmetry. Advantages of such a conformally invariant formulation of particle physics and gravity include the possibility of constructing geodesically complete cosmologies. We present a conformal-invariant version of the standard model coupled to gravity, and show how Weyl symmetry may be used to obtain unprecedented analytic control over its cosmological solutions. Within this new framework, generic Friedmann-Robertson-Walker cosmologies are geodesically complete through a series of big crunch--big bang transitions. We discuss a new scenario of cosmic evolution driven by the Higgs field in a ``minimal'' conformal standard model, in which there is no new physics beyond the standard model at low energies, and the current Higgs vacuum is metastable as indicated by the latest LHC data.

Recent measurements at the LHC suggest that the current Higgs vacuum could be metastable with a modest barrier (height (1010–12GeV)4) separating it from a ground state with negative vacuum density of order the Planck scale. We note that metastability is problematic for standard bang cosmology but is essential for cyclic cosmology in order to end one cycle, bounce, and begin the next. In this Letter, motivated by the approximate scaling symmetry of the standard model of particle physics and the primordial large-scale structure of the universe, we use our recent formulation of the Weyl-invariant version of the standard model coupled to gravity to track the evolution of the Higgs in a regularly bouncing cosmology. We find a band of solutions in which the Higgs field escapes from the metastable phase during each big crunch, passes through the bang into an expanding phase, and returns to the metastable vacuum, cycle after cycle after cycle. We show that, due to the effect of the Higgs, the infinitely cycling universe is geodesically complete, in contrast to inflation.

A unique description of the Big Crunch-Big Bang transition is given at the classical gravity level, along with a complete set of homogeneous, isotropic, analytic solutions in scalar-tensor cosmology, with radiation and curvature. All solutions repeat cyclically; they have been obtained by using conformal gauge symmetry (Weyl symmetry) as a powerful tool in cosmology, and more generally in gravity. The significance of the Big Crunch-Big Bang transition is that it provides a model independent analytic resolution of the singularity, as an unambiguous and unavoidable solution of the equations at the classical gravitational physics level. It is controlled only by geometry (including anisotropy) and only very general features of matter coupled to gravity, such as kinetic energy of a scalar field, and radiation due to all forms of relativistic matter. This analytic resolution of the singularity is due to an attractor mechanism created by the leading terms in the cosmological equation. It is unique, and it is unavoidable in classical relativity in a geodesically complete geometry. Its counterpart in quantum gravity remains to be understood.