The emergence of our Universe

TL;DR

Ambjørn and Watabiki propose that our Universe emerges from symmetry breaking of a multicomponent $W_3$ algebra whose components form a Jordan algebra, enabling a knitting process that assembles one-dimensional flavored universes into an extended four-dimensional spacetime. The resulting dynamics are governed by a modified Friedmann equation, with a special singular point on an associated algebraic curve setting a natural cosmic scale; the $H_3(C)$ and $H_3(O)$ models yield distinct patterns of extended versus compact dimensions, and the Coleman mechanism drives the bare cosmological constant to zero while wormhole webs generate a small effective coupling $g$. The framework explains large dimensionless number coincidences, provides a dynamical rationale for the smallness of $g$, and predicts a discretized spacetime with Planck-scale wormhole webs, a dynamically low-entropy initial state, and a scale-invariant primordial spectrum arising from pre-knitting fluctuations. Collectively, the work links deep algebraic structures to observable cosmological features, offering a novel path to explain late-time acceleration and the near scale invariance of fluctuations without invoking conventional inflation.

Abstract

We show how our Universe can emerge from a symmetry breaking of a multicomponent $W_3$ algebra, where the components in addition form a Jordan algebra. We discuss how symmetry breaking related to the Jordan algebras $H_3(C)$ and $H_3(O)$ over the complex and octonion numbers can lead to an extended four-dimensional spacetime, where the expansion of the Universe is governed by a modified Friedmann equation. We finally discuss how this modified Friedmann equation might explain a number of puzzling cosmological observations.

Figures (5)

• Figure 1: Points of two one-dimensional universes with different flavors (here different colors) are identified via knitting, i.e. by exchange of wormholes. In this way the two $T^1$ spatial universes merge into a a two-dimensional $T^2$ universe that propagates in time (the direction of the arrow). For combinatorial convenience a point on the entrance loop of each of the two universes is marked (see al1w1 for a discussion of this).
• Figure 2: On the left picture three one-dimensional universes with different flavors (here different colors) are identified via knitting, i.e. by exchange of wormholes. The wormholes forms a tree-diagram made possible by the cubic interaction term of the $\alpha^{(0)}$ mode in (\ref{['ClifordNdimTypeModel1WoperatorInteraction']}) . In this way three $T^1$ spatial universes merge into $T^3$, a three-dimensional toroidal universe. The generalization to higher dimensional toroidal universes is shown on the right picture, where tree-diagrams of wormholes connect the universes of different flavors. A $d$-dimensional universe is formed from tree diagrams with $N_{\rm edge} = d$ external vertices and thus $N_{\rm wh} = 2d-3$ wormholes, interacting at $N_{\rm vertex} = d-2$ vertices.
• Figure 3: The figure is similar to Fig. \ref{['fig1']}, except that the interaction (\ref{['f9']}) will allow for the flavor to change during the propagation. Here we have only considered the oscillation between two flavors where the "wormhole" has a third flavor, but the structure constants $d_{iI\tilde{I}}$ allow for more complicated exchange patterns during the propagation.
• Figure 4: The algebraic curve (\ref{['g8']}) plotted in the $(\lambda,h)$ plane. The branch of the curve parametrized by negative $p$ starts at the left at $(\lambda,h) \to (-\infty,\infty)$ for $p \to -0$ and move to the right for decreasing $p$. The branch of the curve parametrized by positive $p$ goes to $(\infty,\infty)$ for $p \to +0$, and to $(\infty, -\infty)$ for $p \to \infty$. The two branches intersect in (1,1).
• Figure 5: The graphical representation of Eq. (\ref{['KnittingCC0']}), which describes the knitting mechanism from the viewpoint of the wormhole web (magenta tree graph). Here each thick magenta segment represents a cylindrical one--dimensional universe connected through wormholes, even though it is drawn as a line in the figure. The full magenta network corresponds to a single wormhole web with quantum weight $A$. The Planck--scale wormhole web occupies a spacetime cell of temporal extent $t_{\rm unit}$ and spatial size $L_{\rm unit}$, both of which are dynamically generated by the two--dimensional quantum gravity dynamics. In particular, $t_{\rm unit} = t_{\rm planck} \sim L_{\rm wh}$ and $L_{\rm unit} = L_{\rm planck} \sim L_{\rm wh} = 1/\sqrt{\mu_{\rm wh}}$, so that the web lives in a Planck--scale spacetime cell. $\mu_{\rm wh}$ denotes the wormhole cosmological constant. The numbers of vertices, edges, and internal lines in the magenta tree graph are $N_{\rm vertex}=d-2$, $N_{\rm edge}=d$, and $N_{\rm wh}=2d-3$, respectively.