Initial-State and Trans-Planckian Interfaces

Quantum-cosmology proposals can select or motivate an inflationary initial state, but observable deviations are most cleanly parameterized as a bounded Bogoliubov or boundary-EFT deformation. Power-spectrum or bispectrum sensitivity does not identify its ultraviolet origin; backreaction, adiabaticity, cutoff support, and degeneracy with ordinary initial-state physics must be tested.

Required background. Trans-Planckian Initial-State Sensitivity supplies the QFT calculation. Quantum-Cosmology Observables and the Problem of Time supplies interpretation.

Helpful background. Initial Density Matrices and Boundary EFT, Power Spectra, Horizon Crossing, and Freeze-Out, and Cross-Regime Trans-Planckian Sensitivity and Universality supply controls.

Bogoliubov initial data

At initial conformal time $\eta_0$, write

$$u_k=\alpha_k u_k^{\mathrm{BD}} +\beta_k u_k^{\mathrm{BD}*}, \qquad |\alpha_k|^2-|\beta_k|^2=1.$$

In a convention where the late growing mode is proportional to $\alpha_k+\beta_k$,

$$\mathcal P_\zeta(k)= \mathcal P_{\mathrm{BD}}(k)|\alpha_k+\beta_k|^2.$$

For small $\beta_k$, the leading oscillatory correction is $2\operatorname{Re}\beta_k$ including its phase.

Application: bounded deformation and backreaction

Choose $\beta_k=\beta_0e^{-(k/a_0\Lambda)^2}e^{2ik\eta_0}$. Its excitation energy is approximately

$$\rho_\beta(\eta_0) =\frac{1}{a_0^4}\int\frac{d^3k}{(2\pi)^3} k|\beta_k|^2.$$

Require $\rho_\beta\ll\epsilon M_{\mathrm P}^2H^2$ and physical support $k/a_0\lesssim\Lambda$. Propagate the same state through the in-in contour to the bispectrum; folded configurations can be enhanced, but the phase, switching, and boundary counterterms must be consistent Holman and Tolley 2008.

Adversarial origin test

Construct a boundary-EFT density matrix with the same $\alpha_k,\beta_k$ as a no-boundary, tunneling, or bounce proposal. Their late correlators agree at this order, so the signal does not identify the UV program. Vary $\eta_0$, cutoff profile, and phase; enforce adiabatic falloff and backreaction after each variation.

Scope

This interface turns a state proposal into falsifiable correlator parameters while preserving the claim ceiling. It neither proves trans-Planckian sensitivity nor singularity resolution. The complete semiclassical-status assessment follows on Semiclassical Recovery, Decoherence, Obstructions, and Status.

The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.

For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.

References

• Collins, H., and R. Holman. “Renormalization of Initial Conditions and the Trans-Planckian Problem of Inflation.” Physical Review D 71 (2005): 085009. DOI.
• Holman, R., and A. J. Tolley. “Enhanced Non-Gaussianity from Excited Initial States.” Journal of Cosmology and Astroparticle Physics 2008, 5 (2008): 001. DOI.