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Asselmeyer-Maluga, Torsten; Król, Jerzy

doi:10.1016/j.dark.2017.12.002

Cited by 23 publications

(34 citation statements)

References 48 publications

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“…Another interesting result in this direction is [1]. In their paper the authors show how the cosmological constant may arise from a topological quantity via Chern-Simons invariants.…”

Section: Summary Of Resultsmentioning

confidence: 99%

The Big Bang is a Coordinate Singularity for $$k = -1$$ Inflationary FLRW Spacetimes

Ling

2020

Found Phys

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We show the big bang is a coordinate singularity for a large class of k = −1 inflationary FLRW spacetimes which we have dubbed 'Milne-like.' By introducing a new set of coordinates, the big bang appears as a past boundary of the universe where the metric is no longer degenerate. In fact this past boundary is just the future lightcone at the origin of a spacetime conformal to Minkowski space. Similar to how investigating the geometrical properties of the r = 2m event horizon in Schwarzschild led to a better understanding of black holes, we believe that investigating the geometrical properties of the big bang coordinate singularity for Milne-like spacetimes will lead to a better understanding of cosmology. We show how the mathematics of these spacetimes may help illuminate certain issues associated with dark energy, dark matter, and the universe's missing antimatter.

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“…Another interesting result in this direction is [1]. In their paper the authors show how the cosmological constant may arise from a topological quantity via Chern-Simons invariants.…”

Section: Summary Of Resultsmentioning

confidence: 99%

The Big Bang is a Coordinate Singularity for $$k = -1$$ Inflationary FLRW Spacetimes

Ling

2020

Found Phys

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“…This simple idea opens the door to explicit calculations. In case of the transition S 3 → ∂A = Σ(2, 5, 7), the corresponding results can be found in [39]. If one assumes a Planck-size (L P ) 3-sphere at the Big Bang, then the scale a of Σ(2, 5, 7) changes like a = L P · exp 3 2 · CS(Σ(2, 5, 7)) with the Chern-Simons invariant CS(Σ(2, 5, 7)) = 9 4 · (2 · 5 · 7) = 9 280 and the Planck scale of order 10 −34 m changes to 10 −15 m. Obviously, this transition has an exponential or inflationary behavior.…”

Section: Reconstructing a Spacetime: The Ksurface And Particle Physicsmentioning

confidence: 93%

“…The embedding of the Akbulut cork is essential for the following results. In [39], it was shown that the embedded cork admits a hyperbolic geometry if the underlying K3 surface has an exotic smoothness structure. This simple property has far-reaching consequences.…”

Section: Reconstructing a Spacetime: The Ksurface And Particle Physicsmentioning

confidence: 99%

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Braids, 3-Manifolds, Elementary Particles: Number Theory and Symmetry in Particle Physics

Asselmeyer-Maluga

2019

Symmetry

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In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston's geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement C(K) = S 3 \ (K × D 2 ) of a knot K carrying a hyperbolic geometry) and bosons as torus bundles. In particular, hyperbolic 3-manifolds have a close connection to number theory (Bloch group, algebraic K-theory, quaternionic trace fields), which will be used in the description of fermions. Here, we choose the description of 3-manifolds by branched covers. Every 3-manifold can be described by a 3-fold branched cover of S 3 branched along a knot. In case of knot complements, one will obtain a 3-fold branched cover of the 3-disk D 3 branched along a 3-braid or 3-braids describing fermions. The whole approach will uncover new symmetries as induced by quantum and discrete groups. Using the Drinfeld-Turaev quantization, we will also construct a quantization so that quantum states correspond to knots. Particle properties like the electric charge must be expressed by topology, and we will obtain the right spectrum of possible values. Finally, we will get a connection to recent models of Furey, Stoica and Gresnigt using octonionic and quaternionic algebras with relations to 3-braids (Bilson-Thompson model).

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“…By general arguments (see [15,16]) the complement C(K + ) admits a hyperbolic structure, i.e. it is a homogenous space of constant negative curvature.…”

Section: Small Exotic Rmentioning

confidence: 99%

Hyperbolic groups, 4-manifolds and Quantum Gravity

Asselmeyer-Maluga

2019

J. Phys.: Conf. Ser.

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4-manifolds have special topological properties which can be used to get a different view on quantum mechanics. One important property (connected with exotic smoothness) is the natural appearance of 3-manifold wild embeddings (Alexanders horned sphere) which can be interpreted as quantum states. This relation can be confirmed by using the Turaev-Drinfeld quantization procedure. Every part of the wild embedding admits a hyperbolic geometry uncovering a deep connection between quantum mechanics and hyperbolic geometry. Then the corresponding symmetry is used to get a dimensional reduction from 4 to 2 for infinite curvatures. Physical consequences will be discussed. At the end we will obtain a spacetime representation of a quantum state of geometry by a non-singular fractal space (wild embedding) which is stable in the limit of infinite curvatures.

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How to obtain a cosmological constant from small exotic R4

Cited by 23 publications

References 48 publications

The Big Bang is a Coordinate Singularity for $$k = -1$$ Inflationary FLRW Spacetimes

The Big Bang is a Coordinate Singularity for $$k = -1$$ Inflationary FLRW Spacetimes

Braids, 3-Manifolds, Elementary Particles: Number Theory and Symmetry in Particle Physics

Hyperbolic groups, 4-manifolds and Quantum Gravity

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