[Paper Review] Cosmological expansion and contraction from Pauli exclusion principle in $M0$-branes

Alireza Sepehri, Ahmed Farag Ali+6 more|arXiv (Cornell University)|Aug 27, 2016

Black Holes and Theoretical Physics41 references3 citations

TL;DR

This paper proposes that cosmological expansion and contraction arise from the Pauli exclusion principle in a system of M0-branes that form M1-brane pairs, leading to symmetry breaking and emergent gravity. The imbalance between degrees of freedom in bulk and boundary due to spin-dependent curvatures—driven by anti-parallel vs. parallel spins—results in effective repulsive gravity upon compactification, inducing cyclic universe dynamics on an M3-brane.

ABSTRACT

We show that the Pauli exclusion principle in a system of $M0$-branes can give rise to the expansion and contraction of the universe which is located on an $M3$-brane. We start with a system of $M0$-branes with high symmetry, which join mutually and form pairs of $M1$-anti-$M1$-branes. The resulting symmetry breaking creates gauge fields that live on the $M1$-branes and play the role of graviton tensor modes, which induce an attractive force between the $M1$ and anti-$M1$ branes. Consequently, the gauge fields that live on the $M1$-branes, and the scalar fields which are attached symmetrically to all parts of these branes, decay to fermions that attach anti-symmetrically to the upper and lower parts of the branes, and hence the Pauli exclusion principle emerges. By closing $M1$-branes mutually, the curvatures produced by parallel spins will be different from the curvatures produced by anti-parallel spins, and this leads to an inequality between the number of degrees of freedom on the boundary surface and the number of degrees of freedom in the bulk region. This behavior is inherited in the $M3$-brane on which the universe is located, and hence this leads to the emergence of the universe expansion and contraction. In this sense, the Pauli exclusion principle rules the cosmic dynamics.

Motivation & Objective

• To explain the origin of cosmic expansion and contraction within a brane cosmology framework.
• To link the Pauli exclusion principle to emergent gravitational dynamics in M-theory.
• To show how symmetry breaking in M0-brane systems leads to gauge and fermionic excitations on M1-branes.
• To connect differences in degrees of freedom between bulk and boundary to the Padmanabhan mechanism for cosmic dynamics.
• To derive a brane action where compactification reverses gravity sign via spin-dependent curvature terms.

Proposed method

• Starting from a high-symmetry system of M0-branes, the model considers their joining into M1-anti-M1-brane pairs.
• Symmetry breaking generates gauge fields on M1-branes that act as graviton tensor modes, mediating attractive forces.
• Scalar and gauge fields decay into fermions that attach anti-symmetrically to upper and lower M1-brane parts, enforcing Pauli exclusion.
• The model distinguishes curvature contributions from parallel vs. anti-parallel spins, leading to unequal degrees of freedom in bulk and boundary.
• A Lagrangian is derived for compactified Mp-branes, with terms sensitive to spin alignment and graviton mass.
• The total action is constructed from summed curvatures of free and bound fermions on M1-branes, showing sign reversal under compactification.

Experimental results

Research questions

• RQ1 How can the Pauli exclusion principle emerge from brane dynamics in M-theory?
• RQ2 What role do spin configurations (parallel vs. anti-parallel) play in generating curvature imbalances?
• RQ3 How does compactification of M1-branes lead to a reversal of gravitational behavior?
• RQ4 Can the difference in degrees of freedom between bulk and boundary explain cosmic expansion and contraction?
• RQ5 How is the Padmanabhan mechanism of cosmic dynamics realized through M-brane systems?

Key findings

• The Pauli exclusion principle emerges from anti-symmetric fermion attachment on M1-branes after symmetry breaking from M0-brane joining.
• Anti-parallel spins produce different curvatures than parallel spins, leading to an imbalance between bulk and boundary degrees of freedom.
• Compactification of M1-branes causes a sign reversal in effective gravity, inducing repulsive forces and brane separation.
• The derived action for Mp-branes explicitly shows that curvature terms depend on spin alignment and graviton mass.
• The model realizes cyclic universe dynamics on an M3-brane due to alternating attractive and repulsive gravity from spin-dependent curvature differences.
• The Lagrangian (D.7) confirms that gravity changes from attractive to repulsive upon compactification, driven by spin-dependent curvature terms.