arXiv subjects

Ali H. Chamseddine

Publications and source records attributed to Ali H. Chamseddine.

At least 19 recordsLinked to original sources

arXiv2026

Mimetic Dark Matter from Inflation

We investigate the coupling of mimetic dark matter to the Gauss-Bonnet topological term in addition to the Einstein-Hilbert action. We demonstrate that such interactions can naturally give rise to mimetic dark matter during the inflationary stage of the universe's evolution. By choosing an appropriate coupling between the mimetic field and the Gauss-Bonnet term, we find that at the end of inflation, the correct amount of dust-like dark matter is produced, with its energy density expressible in terms of the Hubble parameter at the end of inflation. Furthermore, depending on the form of the coupling, the post matter-radiation equality behavior of mimetic dark matter can experience slight modifications.

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arXiv2025

Hearing the Shape of the Universe: A Personal Journey in Noncommutative Geometry

This article surveys the noncommutative-geometric (NCG) approach to fundamental physics, in which geometry is encoded spectrally by a generalized Dirac operator and where dynamics arise from the spectral action. I review historically how the simple idea of marrying a Riemannian manifold to a two point space, progressed to lead to the uniqueness of the Standard Model and beyond. I explain how inner fluctuations of the Dirac operator reconstruct the full gauge-Higgs sector of the Standard Model on an almost-commutative space, fixing representations and hypercharges and naturally accommodating right-handed neutrinos and the see-saw mechanism. On the gravitational side, the heat-kernel expansion of the spectral action yields the cosmological constant, Einstein--Hilbert term, and higher-curvature corrections, with volume-quantized variants clarifying the status of $Λ$. I discuss the renormalization-group interpretation of the spectral action as a high-scale boundary condition, phenomenological implications for Higgs stability and neutrino masses. I present generalized Heisenberg equation leading to identify the NCG space at unification. I conclude by emphasizing that NCG provides a unified, testable, and geometrically principled quantum framework, linking matter, gauge fields, and gravity.

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arXiv2025

On the Dark-Energy Enigma

We present a model that offers an explanation for the presence of (Dark Matter and) Dark Energy in the universe. A key idea is to express the volume form of the Lorentzian metric on space-time in terms of a positive function of a new scalar field multiplying a certain four-form given by the wedge product of the differential of the mimetic scalar field and a certain closed three-form. An ansatz for this three-form related to one commonly used to determine the winding number of a map from a three-dimensional hypersurface to a three-sphere is discussed. An action functional depending on the space-time metric, the new scalar field, the mimetic scalar and the three-form is proposed, and the field equations are derived. Special solutions of these equations for a Friedmann-Lemaître universe are presented.

gr-qc↗

arXiv2024

Poincare Invariance in Discrete Gravity

A formulation of discrete gravity was recently proposed based on defining a lattice and a shift operator connecting the cells. Spinors on such a space will have rotational SO(d) invariance which is taken as the fundamental symmetry. Inspired by lattice QCD, discrete analogues of curvature and torsion were defined that go smoothly to the corresponding tensors in the continuous limit. In this paper, we show that the absence of diffeomorphism invariance could be replaced by requiring translational invariance in the tangent space by enlarging the tangent space from SO(d) to the inhomogeneous Lorentz group ISO(d) to include translations. We obtain the ISO(d) symmetry by taking instead the Lie group SO(d + 1) and perform on it Inonu-Wigner contraction. We show that, just as for continuous spaces, the zero torsion constraint converts the translational parameter to a diffeomorphism parameter, thus explaining the effectiveness of this formulation.

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arXiv2024

Curvature of an Arbitrary Surface for Discrete Gravity and for $d=2$ Pure Simplicial Complexes

We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the surface in question to its four closest neighbors, forming quads. We then focus on the simplices of $d=2$, or triangles embedded in these quads, which make up a pure simplicial complex with $d=2$. This allows us to numerically compute the local metric along with zweibeins, which subsequently leads to a derivation of discrete curvature defined at every triangle or face. We provide an efficient algorithm with $\mathcal{O}(N \log{N})$ complexity that first orients two-dimensional surfaces, solves the nonlinear system of equations of the spin-connections resulting from the torsion condition, and returns the value of curvature at each face.

gr-qc↗

arXiv2023

Black Hole in Discrete Gravity

We study the metric corresponding to a three-dimensional coset space $SO(4)/SO(3)$ in the lattice setting. With the use of three integers $n_1, n_2$, and $n_3$, and a length scale, $l_μ$, the continuous metric is transformed into a discrete space. The numerical outcomes are compared with the continuous ones. The singularity of the black hole is explored and different domains are studied.

hep-th↗

arXiv2023

Curvature Tensor in Discrete Gravity

We study numerically the curvature tensor in a three-dimensional discrete space. Starting from the continuous metric of a three-sphere, we transformed it into a discrete space using three integers $n_1, n_2$, and $n_3$. The numerical results are compared with the expected values in the continuous limit. We show that as the number of cells in the lattice increases, the continuous limit is recovered.

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arXiv2023

Mimetic Inflation and Self-reproduction

It is shown how self-reproduction can be easily avoided in the inflationary universe, even when inflation starts at Planck scales. This is achieved by a simple coupling of the inflaton potential with a mimetic field. In this case, the problem of fine-tuning of the initial conditions does not arise, while eternal inflation and the multiverse with all their widely discussed problems are avoided.

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arXiv2022

Noncommutativity and Physics: A non-technical review

We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain how in general noncommutativity yields a canonical time evolution, while at the same time allowing for the coexistence of discrete and continuous variables. The spectral approach to geometry is then explained to encompass two natural ingredients: the line element and the algebra. The relation between these two is dictated by so-called higher Heisenberg relations, from which both spin geometry and non-abelian gauge theory emerges. Our exposition indicates some of the applications in physics, including Pati--Salam unification beyond the Standard Model, the criticality of dimension 4, second quantization and entropy.

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arXiv2022

Scalar Curvature in Discrete Gravity

We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers, while in the second we consider the case where one of the coordinates is ignorable. The numerical results of both cases are then compared with the expected values in the continuous limit as the number of cells of the lattice becomes very large.

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arXiv2022

The role of the 1.5 order formalism and the gauging of spacetime groups in the development of gravity and supergravity theories

The 1.5 formalism played a key role in the discovery of supergravity and it has been used to prove the invariance of essentially all supergravity theories under local supersymmetry. It emerged from the gauging of the super Poincare group to find supergravity. We review both of these developments as well as the auxiliary fields for simple supergravity and its most general coupling to matter using the tensor calculus.

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arXiv2021

Supergravity with mimetic dark matter

We formulate a supersymmetric version of gravity with mimetic dark matter. The coupling of a constrained chiral multiplet to N=1 supergravity is made locally supersymmetric using the rules of tensor calculus. The chiral multiplet is constrained with a Lagrange multiplier multiplet that could be either a chiral multiplet or a linear multiplet. We obtain the fully supersymmetric Lagrangians in both cases. It is then shown that the system consisting of the supergravity multiplet, the chiral multiplet and the Lagrange multiplier multiplet can break supersymmetry spontaneously leading to a model of a graviton, massive gravitino and two scalar fields representing mimetic dark matter. The combination of the chiral multiplet and Lagrange multiplier multiplet can act as the hidden sector breaking local N=1 supersymmetry.

hep-th↗

arXiv2021

Discrete Gravity

We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of freedom per elementary volume. In such discrete spaces, each elementary cell is completely characterized by displacement operators connecting a cell to the neighboring cells and by the spin connection. We define the torsion and curvature of the discrete spaces and show that in the limiting case of vanishing elementary volume the standard results for the continuous curved differentiable manifolds are completely reproduced.

hep-th↗

arXiv2020

Spectral action in matrix form

Quantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang-Mills theory. We illustrate the procedure for the toy electroweak model.

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arXiv2019

Non-flat Universes and Black Holes in Asymptotically Free Mimetic Gravity

The recently proposed theory of "Asymptotically Free Mimetic Gravity" is extended to the general non-homogeneous, spatially non-flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this theory asymptotic freedom of gravity implies the existence of a minimal black hole with vanishing Hawking temperature. Introducing a spatial curvature dependent potential, we moreover obtain non-singular, bouncing modifications of spatially non-flat Friedmann and Bianchi universes.

hep-th↗

arXiv2019

Mimetic Horava Gravity

We show that the scalar field of mimetic gravity could be used to construct diffeomorphism invariant models that reduce to Horava gravity in the synchronous gauge. The gradient of the mimetic field provides a timelike unit vector field that allows to define a projection operator of four-dimensional tensors to three-dimensional spatial tensors. Conversely, it also enables us to write quantities invariant under space diffeomorphisms in fully covariant form without the need to introduce new propagating degrees of freedom.

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arXiv2019

Black Hole Remnants

We show that in asymptotically free mimetic gravity with limiting curvature the black hole singularity can be resolved and replaced by a static patch of de Sitter space. As a result of Hawking evaporation of these non-singular black holes, there remain stable remnants with vanishing Hawking temperature.

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arXiv2019

A survey of spectral models of gravity coupled to matter

This is a survey of the historical development of the Spectral Standard Model and beyond, starting with the ground breaking paper of Alain Connes in 1988 where he observed that there is a link between Higgs fields and finite noncommutative spaces. We present the important contributions that helped in the search and identification of the noncommutative space that characterizes the fine structure of space-time. The nature and properties of the noncommutative space are arrived at by independent routes and show the uniqueness of the Spectral Standard Model at low energies and the Pati-Salam unification model at high energies.

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