SE=d4xgE[R16G+12()2+V()]S_E = \int d^4x \sqrt{g_E} \left[ -\frac{R}{16\pi G} + \frac{1}{2} (\nabla \phi)^2 + V(\phi) \right]
Here:
gEg_E is the Euclideanized metric tensor,
RR is the Ricci scalar in Euclidean signature.
The probability peaks for configurations where SES_E is minimized, favoring compact, nearly homogeneous 4-spheres as the dominant saddle points---mirroring Hartle--Hawking instantons.
3. From Instantons to Blinks: Discrete Emergence Events
Unlike the traditional view in which this quantum tunneling produces a single universe, the Blink model generalizes this mechanism by allowing multiple tunneling events, each corresponding to a "blink"---a discrete instantiation of a universe-like region. This leads to:
A multievent cosmogenesis, where different "blinks" may produce distinct spacetime patches, some causally disconnected.
Each blink seeds a layer in the Multilayer Multiverse (see Section II.2), defined by its initial conditions and local vacuum energy.
These events are non-sequential in coordinate time, but ordered probabilistically by their action weights and tunneling rates.
Let {Ui}\{ \mathcal{U}_i \} be the ensemble of universes blinking into existence. Then the partition function over the blinking cosmology is:
Zblink=ie2SE(i)Oi\mathcal{Z}_{\text{blink}} = \sum_i e^{-2 S_E^{(i)}} \mathcal{O}_i
Where:
Oi\mathcal{O}_i represents the observable content (e.g., curvature, field values) of the i-th universe layer.
4. Emergence of Spacetime from Informational Substrate
Underlying the blink process is an informational vacuum---a pre-spacetime regime characterized not by geometry but by configuration entropy and potential field arrangements. Following recent developments in quantum information theory and emergent gravity (e.g., Padmanabhan, Verlinde), we reinterpret the emergence of spacetime as a transition from an entropy-minimizing ensemble of quantum microstates.
Let the microstates be labeled by i\psi_i, and define the entropy functional:
