Defining cosmological probabilities in quantum cosmology

Determine a precise and operational meaning for cosmological probabilities in quantum cosmology, particularly in single-universe settings where frequentist interpretations fail, in order to assess the role of state normalizability for candidates such as the Chern–Simons–Kodama state.

Background

In discussing normalizability of the CSK state, the authors point out that probabilistic interpretations in cosmology are subtle: if there is only one universe, frequentist probability may not apply. They note that, absent a clear probabilistic framework, the centrality of normalizability as a physical criterion becomes questionable.

This highlights a conceptual gap: a rigorous definition of cosmological probabilities is needed to clarify whether normalizability should be required for wavefunctionals like the CSK state.

References

Note, however, that it is not entirely clear in what sense one can define cosmological probabilities at all.

— Quantum Gravity, de Sitter Space, and Normalizability  (2511.05417 - Alexander et al., 7 Nov 2025) in Section 3.1 (Normalizability and the Inner Product), footnote

The problem is that the complex solutions might not contribute to the vacuum persistence, as it is unclear whether regular solutions with spherical topology and a complex, evolving scalar field exist. Thus, these solutions raise the question of whether the sum over all possible evolutions would yield a total probability of unity, or a value slightly larger. The total would not be much larger than unity, as these complex no-boundary instantons are exponentially suppressed compared to the vacuum persistence calculated above, but the question should certainly be clarified. We leave this for future work and note, for now, that the cleanest case is the one where the scalar is real valued throughout.

— Connected Geometries in Gravitational Path Integrals, and Normalized No-Boundary Probabilities  (2610.08596 - Lehners, 6 Oct 2026) in Section 2, discussion of complex scalar fields