A Dark Sector Extension of the Almost-Commutative Standard Model

Stephan, Christoph A.

doi:10.1142/s0217751x14500055

Cited by 6 publications

(3 citation statements)

References 50 publications

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“…Other searches beyond the Standard Model with noncommutative geometry include [53,70,71,73,72,74], adopting a slightly different approach to almost-commutative manifolds as we do.…”

Section: Beyond the Standard Model With Noncommutative Geometrymentioning

confidence: 99%

A survey of spectral models of gravity coupled to matter

Chamseddine

Suijlekom

2019

Advances in Noncommutative Geometry

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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 spacetime. 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.2 Early days of the spectral Standard ModelThe first serious attempt to utilize the ideas of noncommutative geometry in particle physic was made by Alain Connes in 1988 in his paper "Essay on physics and noncommutative geometry" [28]. He observed that it is possible to change the structure of the (Euclidean) space-time so that the action functional gives the Weinberg-Salam model. The main emphasis was on the conceptual understanding of the Higgs field, which he calls, the black box of the standard model. The qualitative picture was taken to be of a twosheeted Euclidean space-time separated by a distance of the order of 10 −16 cm. In order to simplify the presentation, and to easily follow the historical development, we will use a uniform notation, representing old results in a new format. It is therefore more efficient to start with the basic definitions.

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“…Other searches beyond the Standard Model with noncommutative geometry include [53,70,71,73,72,74], adopting a slightly different approach to almost-commutative manifolds as we do.…”

Section: Beyond the Standard Model With Noncommutative Geometrymentioning

confidence: 99%

A survey of spectral models of gravity coupled to matter

Chamseddine

Suijlekom

2019

Advances in Noncommutative Geometry

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“…NCG is a generalization of Riemannian geometry which (amongst other applications) provides an elegant framework for describing gauge theories coupled to gravity. In this capacity, it's main physical interest is in constraining the allowed extensions of the standard model of particle physics [10,[16][17][18][19][20][21][22][23][24][25][26][27]. The basic idea of NCG is to replace the familiar manifold and metric data {M, g} of Riemannian geometry with a 'spectral triple' of data {A, H, D}, which consist of a 'coordinate' algebra A that provides topological information, a Dirac operator D which provides metric information, and a Hilbert space H that provides a place for A and D to interact.…”

Section: Product Non-commutative Geometriesmentioning

confidence: 99%

The graded product of real spectral triples

Farnsworth

2017

Journal of Mathematical Physics

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Forming the product of two geometric spaces is one of the most basic operations in geometry, but in the spectral-triple formulation of non-commutative geometry, the standard prescription for taking the product of two real spectral triples is problematic: among other drawbacks, it is non-commutative, non-associative, does not transform properly under unitaries, and often fails to define a proper spectral triple. In this paper, we explain that these various problems result from using the ungraded tensor product; by switching to the graded tensor product, we obtain a new prescription where all of the earlier problems are neatly resolved: in particular, the new product is commutative, associative, transforms correctly under unitaries, and always forms a well defined spectral triple

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“…As noted by Pruna [3], 'The Standard Model (SM) of particle physics ... does not satisfactorily explain the origin of matter, the nature of neutrino oscillations, the observation of dark matter and dark energy, and it does not accommodate gravity'. This list reflects the main directions by which physicists are trying to build extensions of the Standard Model [4]. Is there room for negative masses in these generalizations?…”

Section: Introductionmentioning

confidence: 99%

A unifying hypothesis of dark energy and dark matter: negative masses, imaginary charges and dark minus-photons

Tretyakov¹,

Terletsky²

2020

Phys. Scr.

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The idea of a new model explaining the coherent nature of dark matter and dark energy is proposed. Recent works by Farnes (2018) and Socas-Navarro (2019) proposed a cosmological model and its critical analysis in which both dark matter and dark energy are replaced with a single fluid of negative mass. This paper presents a modification of this idea using the hypothesis about the existence of so-called imaginary charges and electromagnetic fields with negative energy density (‘minus-fields’) proposed by Ya.Terletsky (1991) and derived by us from a commutative generalization of the U(1) gauge symmetry group. It is shown that dark photons could be a partial source of the observed late-time cosmological acceleration, saying that dark energy, or part of it could be not cosmological constant or scalar field (quintessence), but photons with negative energy instead. The unusual properties of imaginary charges ensure the existence of dark matter structures. The Friedmann equation, in case when minus-photons give considerable contribution to the energy balance of the Universe, gives the following condition for the accelerated expansion: . It is found that even a relatively small density of dark negative radiation can lead to a significant change in the expansion dynamics of the Universe and new effects are predicted. Last, we assert the need to develop a new type of detectors that can detect particles and waves with negative energy.

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A Dark Sector Extension of the Almost-Commutative Standard Model

Cited by 6 publications

References 50 publications

A survey of spectral models of gravity coupled to matter

A survey of spectral models of gravity coupled to matter

The graded product of real spectral triples

A unifying hypothesis of dark energy and dark matter: negative masses, imaginary charges and dark minus-photons

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