scholarly journals BUILDING COSMOLOGICAL MODELS VIA NONCOMMUTATIVE GEOMETRY

2011 ◽  
Vol 08 (05) ◽  
pp. 1131-1168 ◽  
Author(s):  
MATILDE MARCOLLI
Keyword(s):  
Noncommutative Geometry ◽  
Particle Physics ◽  
Group Analysis ◽  
Cosmological Models ◽  
Action Functional ◽  
Ongoing Research ◽  
Renormalization Group Analysis ◽  
Spectral Action ◽  
Physics Model ◽  
Nonperturbative Calculation

This is an overview of new and ongoing research developments aimed at constructing cosmological models based on noncommutative geometry, via the spectral action functional, thought of as a modified gravity action, which includes the coupling with matter when computed on an almost commutative geometry. This survey is mostly based on recent results obtained in collaboration with Elena Pierpaoli and Kevin Teh. We describe various aspects of cosmological models of the very early universe, developed by the author and Pierpaoli, based on the asymptotic expansion of the spectral action functional and on renormalization group analysis of the associated particle physics model (an extension of the standard model with right-handed neutrinos and Majorana mass terms previously developed in collaboration with Chamseddine and Connes). We also describe nonperturbative results, more recently obtained by Pierpaoli, Teh, and the author, which extend to the more modern universe, which show that, for different candidate cosmic topologies, the form of the slow-roll inflation potentials obtained from the nonperturbative calculation of the spectral action are strongly coupled to the underlying geometry and topology. We discuss some ongoing directions of research and open questions in this new field of "noncommutative cosmology". The paper is based on the talk given by the author at the conference "Geometry and Quantum Field Theory" at the MPI, in honor of Alan Carey.

scholarly journals NONCOMMUTATIVE GEOMETRY SPECTRAL ACTION AS A FRAMEWORK FOR UNIFICATION: INTRODUCTION AND PHENOMENOLOGICAL/COSMOLOGICAL CONSEQUENCES

2011 ◽  
Vol 20 (05) ◽  
pp. 785-804 ◽  
Author(s):  
MAIRI SAKELLARIADOU
Keyword(s):  
Standard Model ◽  
Noncommutative Geometry ◽  
Particle Physics ◽  
Geometrical Model ◽  
Energy Scale ◽  
Noncommutative Space ◽  
Geometrical Approach ◽  
Neutrino Mixing ◽  
Spectral Triples ◽  
Spectral Action

I will summarize Noncommutative Geometry Spectral Action, an elegant geometrical model valid at unification scale, which offers a purely gravitational explanation of the Standard Model, the most successful phenomenological model of particle physics. Noncommutative geometry states that close to the Planck energy scale, spacetime has a fine structure and proposes that it is given as the product of a four-dimensional continuum compact Riemaniann manifold by a tiny discrete finite noncommutative space. The spectral action principle, a universal action functional on spectral triples which depends only on the spectrum of the Dirac operator, applied to this almost commutative product geometry, leads to the full Standard Model, including neutrino mixing which has Majorana mass terms and a see-saw mechanism, minimally coupled to gravity. It also makes various predictions at unification scale. I will review some of the phenomenological and cosmological consequences of this beautiful and purely geometrical approach to unification.

scholarly journals THE B – L/ELECTROWEAK HIERARCHY IN SMOOTH HETEROTIC COMPACTIFICATIONS

2010 ◽  
Vol 25 (13) ◽  
pp. 2631-2677 ◽  
Author(s):  
MICHAEL AMBROSO ◽  
BURT A. OVRUT
Keyword(s):  
Gauge Symmetry ◽  
Particle Physics ◽  
Vector Bundles ◽  
Group Analysis ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Supersymmetric Particle ◽  
Renormalization Group Analysis ◽  
Standard Models ◽  
M Theory

E8 × E8 heterotic string and M-theory, when appropriately compactified, can give rise to realistic, N = 1 supersymmetric particle physics. In particular, the exact matter spectrum of the MSSM, including three right-handed neutrino supermultiplets, one per family, and one pair of Higgs–Higgs conjugate superfields is obtained by compactifying on Calabi–Yau manifolds admitting specific SU(4) vector bundles. These "heterotic standard models" have the SU (3)C × SU (2)L × U (1)Y gauge group of the standard model augmented by an additional gauged U (1)B – L. Their minimal content requires that the B – L gauge symmetry be spontaneously broken by a vacuum expectation value of at least one right-handed sneutrino. In a previous paper, we presented the results of a renormalization group analysis showing that B – L gauge symmetry is indeed radiatively broken with a B – L/electroweak hierarchy of [Formula: see text] to [Formula: see text]. In this paper, we present the details of that analysis, extending the results to include higher order terms in tan β-1 and the explicit spectrum of all squarks and sleptons.

scholarly journals ASYMPTOTIC SAFETY, HYPERGEOMETRIC FUNCTIONS, AND THE HIGGS MASS IN SPECTRAL ACTION MODELS

2013 ◽  
Vol 10 (07) ◽  
pp. 1350036 ◽  
Author(s):  
CHRISTOPHER ESTRADA ◽  
MATILDE MARCOLLI
Keyword(s):  
Particle Physics ◽  
Hypergeometric Functions ◽  
Higgs Mass ◽  
Action Functional ◽  
Renormalization Group Flow ◽  
Spectral Action ◽  
Linear Ode ◽  
Action Models ◽  
Group Flow ◽  
Correction Terms

We study the renormalization group flow for the Higgs self-coupling in the presence of gravitational correction terms. We show that the resulting equation is equivalent to a singular linear ODE, which has explicit solutions in terms of hypergeometric functions. We discuss the implications of this model with gravitational corrections on the Higgs mass estimates in particle physics models based on the spectral action functional.

scholarly journals Xenon-1T excess as a possible signal of a sub-GeV hidden sector dark matter

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Amin Aboubrahim ◽  
Michael Klasen ◽  
Pran Nath
Keyword(s):  
Dark Matter ◽  
Particle Physics ◽  
Small Mass ◽  
Big Bang ◽  
Mass Splitting ◽  
Recoil Energy ◽  
Dirac Fermions ◽  
Dark Sector ◽  
Dark Photon ◽  
Physics Model

Abstract We present a particle physics model to explain the observed enhancement in the Xenon-1T data at an electron recoil energy of 2.5 keV. The model is based on a U(1) extension of the Standard Model where the dark sector consists of two essentially mass degenerate Dirac fermions in the sub-GeV region with a small mass splitting interacting with a dark photon. The dark photon is unstable and decays before the big bang nucleosynthesis, which leads to the dark matter constituted of two essentially mass degenerate Dirac fermions. The Xenon-1T excess is computed via the inelastic exothermic scattering of the heavier dark fermion from a bound electron in xenon to the lighter dark fermion producing the observed excess events in the recoil electron energy. The model can be tested with further data from Xenon-1T and in future experiments such as SuperCDMS.

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