II.1. Quantum Blink Genesis
In this section, we develop the formal basis for the "Blink Universe" concept: a cosmological genesis scenario in which spacetime emerges via a quantum tunneling event from a pre-geometric regime. This framework offers a singularity-free alternative to the classical Big Bang, while retaining compatibility with semiclassical and quantum gravity principles.
1. Conceptual Foundations: From Singular Genesis to Probabilistic Emergence
Standard CDM cosmology traces cosmic evolution back to a spacetime singularity of infinite density and curvature---a breakdown of classical general relativity. To overcome this conceptual and mathematical impasse, several quantum cosmological proposals have been developed, notably:
The Hartle--Hawking "no-boundary" wavefunction, wherein the universe emerges from a compact, Euclidean spacetime with no initial boundary.
Vilenkin's tunneling wavefunction, describing the universe's spontaneous nucleation from 'nothing' (a state with no classical spacetime).
Instanton transitions, describing nonperturbative quantum tunneling between vacua in Euclidean spacetime.
The Blink Universe builds on these foundations, proposing that universes can blink into existence via tunneling from a pre-spacetime informational vacuum---a state devoid of classical geometry but rich in potential configurations of quantum fields.
We model this transition as nonunitary but probabilistic, governed by a Euclidean action integral over a set of pre-geometric topologies, with a dominant contribution from saddle-point instantons corresponding to spacetime seeds.
2. Mathematical Formalism: Tunneling from a Quantum Pre-Geometry
We define the tunneling probability P\mathcal{P} for the emergence of a universe with classical spacetime metric gg_{\mu\nu} and scalar field content \phi, from an informational vacuum state \emptyset, as:
Pe2SE[g,]\mathcal{P} \sim e^{-2 S_E[g_{\mu\nu}, \phi]}
Where:
SES_E is the Euclidean action of the instanton solution mediating the tunneling,
The exponential suppression encodes the quantum barrier separating non-spacetime and spacetime configurations.
For a simplified minisuperspace model with FRW metric and a scalar field \phi with potential V()V(\phi), the Euclidean action becomes:
