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Emergence of Dark Energy from topology and chiral spinors

J. Lorca Espiro, Yerko Vásquez, M. Le Delliou

TL;DR

The paper introduces a torsionful Einstein–Cartan gravity on a Lorentzian 4-manifold with internal boundaries and shows that a harmonic 1-form $\\theta$ detected by the topology (captured by $H^1(\\mathcal{M})$ and related to π_3) acts as a source of contortion, generating a dynamical dark-energy–like term. By decomposing the connection into a Levi-Civita part and a contortion generated by $\\theta$, and imposing an Ehresmann parallel spinor hypothesis, the authors derive a chain of relations linking a topological current $J$ to the boundary data via a Dirichlet-to-Neumann operator $\\Lambda$, ultimately leading to a generalized Einstein equation with a positive term $|\\theta|^2_g$ that acts as dynamical dark energy. The framework ties the dark energy density to topology and boundary conditions (through $\\Lambda$ and boundary values $\\xi$) and provides a holographic flavor by showing the boundary data controls bulk cosmological dynamics. This topological mechanism offers a falsifiable route to explain dark energy without introducing new fundamental fields, and it invites cosmological applications and observational tests. The key mathematical objects are the harmonic form $\\theta$, the Dirac current $J$, the Nieh–Yan structure, and the boundary-to-bulk coupling mediated by $\\Lambda$.

Abstract

Under the existence of a massless spinor with respect to the total connection in a spacetime modeled as a Lorentzian manifold with internal boundaries, such as finite volume semi-classical Black Holes, we show that a topological mechanism naturally induces terms in the Einstein-Cartan gravitational action that can be interpreted as General Relativity with dark energy. This may alleviate the problems of dark energy. The topological information is carried by a harmonic 1-form associated to the first co-holomology group of the spacetime, which induces a spacetime contortion acting on the horizontal bundle.

Emergence of Dark Energy from topology and chiral spinors

TL;DR

The paper introduces a torsionful Einstein–Cartan gravity on a Lorentzian 4-manifold with internal boundaries and shows that a harmonic 1-form detected by the topology (captured by and related to π_3) acts as a source of contortion, generating a dynamical dark-energy–like term. By decomposing the connection into a Levi-Civita part and a contortion generated by , and imposing an Ehresmann parallel spinor hypothesis, the authors derive a chain of relations linking a topological current to the boundary data via a Dirichlet-to-Neumann operator , ultimately leading to a generalized Einstein equation with a positive term that acts as dynamical dark energy. The framework ties the dark energy density to topology and boundary conditions (through and boundary values ) and provides a holographic flavor by showing the boundary data controls bulk cosmological dynamics. This topological mechanism offers a falsifiable route to explain dark energy without introducing new fundamental fields, and it invites cosmological applications and observational tests. The key mathematical objects are the harmonic form , the Dirac current , the Nieh–Yan structure, and the boundary-to-bulk coupling mediated by .

Abstract

Under the existence of a massless spinor with respect to the total connection in a spacetime modeled as a Lorentzian manifold with internal boundaries, such as finite volume semi-classical Black Holes, we show that a topological mechanism naturally induces terms in the Einstein-Cartan gravitational action that can be interpreted as General Relativity with dark energy. This may alleviate the problems of dark energy. The topological information is carried by a harmonic 1-form associated to the first co-holomology group of the spacetime, which induces a spacetime contortion acting on the horizontal bundle.
Paper Structure (24 sections, 61 equations, 2 figures, 1 table)

This paper contains 24 sections, 61 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction.
  2. Structure and Generalities.
  3. Principal bundle and boundary of spacetime.
  4. The total action and its field equations.
  5. Summary of the section
  6. Scalar field and spacetime topology.
  7. Co-homology and boundary value problems.
  8. The boundary Value Problem and " theoretical topological probes".
  9. Summary of the section
  10. Spin connection and Contortion.
  11. General form of the Contortion and Torsion.
  12. The spin field equation and explicit Lie symmetry
  13. Summary of the section
  14. Ehresmann parallel spinor hypothesis
  15. Killing equation and spinor effective mass.
  16. ...and 9 more sections

Figures (2)

  • Figure 1: A two-dimensional representation of the space-time manifold $\mathcal{M}$. The boundary of the manifold is internal and defined by $\partial \mathcal{M} \simeq \partial \mathcal{X}$.
  • Figure 2: A typical closed parallel transport $\partial C$ measuring the holonomy with base point $x_0$ of the total connection $\text{Hol}_{x_0} \left( \bar{\omega} \right)$.