The proposed multilayer metric structure predicts several testable phenomena:
Apparent Hubble variance between line-of-sight directions intersecting different layers with Hi0\Delta H_i \neq 0,
Large-scale anisotropies due to directional sampling of inhomogeneous curvature profiles,
Redshift distortions and integrated Sachs--Wolfe signals modified by inter-layer lensing potentials,
Possible echoes or mirroring of structures across symmetrically embedded layers.
The Multilayer Spacetime Metric Tensor defines a novel class of cosmological models wherein the universe is stratified into interconnected geometric layers, each evolving with its own expansion rate and curvature. This framework embeds within a higher-dimensional manifold, where inter-layer coupling and information flow generate rich phenomenology, capable of explaining a host of CDM anomalies---most notably the Hubble tension and cosmic anisotropies. It further forms the geometric backbone upon which the fractal cosmic matter distribution (Section II.3) and quantum blink origin (Section II.1) are coherently unified.
III.2. Quantum Potential Formulation for Blink Genesis
To model the creation of universes as a "blink"---a spontaneous, non-singular emergence from an information-theoretic vacuum---we develop a formulation grounded in quantum cosmology, combining elements from the Wheeler--DeWitt equation, Bohmian quantum potential, and instanton-inspired tunneling actions.
This framework treats the origin of a universe as a quantum tunneling process through a classically forbidden region of the gravitational configuration space, avoiding both the initial singularity and the need for external time.
1. Minisuperspace Setup and the Wheeler--DeWitt Equation
We consider the simplified minisuperspace of homogeneous, isotropic geometries, described by the scale factor aa and a scalar field \phi as the only degrees of freedom.
The Wheeler--DeWitt equation (WDW) in the minisuperspace reads:
[22a2+222+a6V()a4k](a,)=0\left[ -\hbar^2 \frac{\partial^2}{\partial a^2} + \hbar^2 \frac{\partial^2}{\partial \phi^2} + a^6 V(\phi) - a^4 k \right] \Psi(a, \phi) = 0
Here:
(a,)\Psi(a, \phi) is the wavefunction of the universe,
V()V(\phi) is the scalar field potential (which may include inflationary or tunneling features),
k{1,0,+1}k \in \{-1, 0, +1\} encodes spatial curvature.
We focus on the semi-classical WKB regime, where the wavefunction may be approximated as:
