IgeomCmin()\mathcal{I}_{\text{geom}} \sim \mathcal{C}_{\text{min}}(\rho_{\partial})
This is intimately related to tensor network descriptions of spacetime (e.g., MERA) and the encoding of curvature in entanglement patterns.
4. Why This Definition Matters in Our Theory
In Blink Genesis, the tunneling event is not defined by energy or temperature but by a critical informational transition (e.g., reaching a minimal non-zero Icrit\mathcal{I}_{\text{crit}} across a topological barrier).
In Multilayer Multiverse, different layers correspond to distinct informational densities and configurations. Layer transitions are unitary operations on the global state Universe|\Psi_{\text{Universe}}\rangle.
In Fractal Universe, the self-similarity is interpreted not just as spatial redundancy but as repeating informational motifs, i.e., the same "information code" iterated over scales with transformations akin to renormalization flows in information space.
In sum, our theory promotes information to a first-class physical entity, measurable via entanglement, bounded by geometry, and generative of all physical structure. This offers not only a resolution to the quantum-gravity duality but provides a new lens through which cosmic anomalies and genesis events can be unified.
Outline
I. Introduction
I.1. Observational Challenges to CDM Cosmology
Discuss current tensions and anomalies such as:
The Hubble tension, Cosmic isotropy violations, Early formation of massive galaxies, Large-scale anomalies in the cosmic microwave background (CMB).
I.2. Alternative Proposals in Literature
Review major alternative approaches that attempt to address these issues:
Inhomogeneous cosmologies (e.g., Lematre--Tolman--Bondi models),
Void-centered models and gigaparsec-scale underdensities,
Cosmologies with cyclic, bouncing, or emergent origins,
Universe-as-black-hole and holographic perspectives.
I.3. Motivation for a Unified Paradigm Shift
Introduce a novel composite cosmological framework integrating:
Blink Universe: A quantum tunneling origin model avoiding Big Bang singularity,
Multilayer Multiverse: A layered topological structure accounting for cosmic anisotropies and variable Hubble scales,
Fractal Universe: A nonlinear internal structure yielding scale-invariant distributions and early galaxy formation.
II. Theoretical Framework
II.1. Quantum Blink Genesis
 Formulate the concept of universe genesis as a quantum spacetime tunneling process ("blink"), drawing parallels with instanton-like transitions and no-boundary proposals.
II.2. Multilayered Topological Architecture
Introduce a generalization of FRW metric to accommodate layered void-Hubble structures.
Define inter-universe topological connectivity via field-theoretic boundary conditions.
II.3. Fractal Geometry of Cosmic Matter
Use fractal dimensional analysis (Hausdorff dimension) to describe internal structure.
Link galaxy clustering, dark matter distribution, and void self-similarity to observable anisotropies.
III. Mathematical Formulation
III.1. Multilayer Spacetime Metric Tensor
Develop the mathematical structure for nested cosmological layers with:
Varying local expansion rates (Hubble parameters),
Curvature-induced differential evolution across layers.
III.2. Quantum Potential Formulation for Blink Genesis
Define the quantum potential and tunneling action integral for universe creation events.
III.3. Fractal Matter Distribution Function
Model mass-energy density using non-integer power laws:
(r)rDH3\rho(r) \sim r^{D_H - 3}
where DHD_H is the Hausdorff dimension.
III.4. Topological Interference Fields
Describe interference and correlation of spacetime layers via:
interfexp(i(x))d4x\Phi_{\text{interf}} \sim \int \exp(i\theta(x)) \, d^4x
capturing cross-layer coupling through topological phases.
IV. Numerical Simulations
IV.1. Layer-Dependent Hubble Parameter H(r)H(r)
Simulate radial variation of H0H_0 using observationally informed density inputs.
IV.2. Fractal-Induced Angular Momentum Bias
Simulate galactic spin orientation distribution based on fractal initial conditions.
IV.3. Topological Field Interference
Model interaction patterns across adjacent layers and predict possible large-scale signatures.
V. Results and Observational Signatures
V.1. Explaining the Low Cosmological Constant Naturally
Show how void topology and fractal geometry induce effective vacuum energy suppression.
V.2. Predictive Power for Early Structure Formation
Account for:
Mature galaxies in early epochs,
Large-scale anisotropic voids,
Galactic rotation patterns without inflation.
V.3. Signatures Accessible to JWST, Euclid, and SKA
List potential observable anomalies and alignments detectable with current/future surveys.
VI. Discussion
