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Pre-inflation and Trans-Planckian Censorship

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Yong Cai, Yun-Song Piao

General Relativity and Quantum Cosmology · Submitted 27 Sep 2019 · 86 references

Pith's verdict: A clean, honest argument that TCC-compatible pre-inflation hands you the Bunch-Davies state; the derivation is textbook-correct, but the claim that it applies to generic past-complete pre-inflation is asserted rather than shown.

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arXiv ID1909.12719 (version 3)
Pith ID5IBISWSH, Pith's permanent record of this paper and its review
CitationYong Cai, Yun-Song Piao. "Pre-inflation and Trans-Planckian Censorship." arXiv:1909.12719 (2019). https://pith.science/paper/5IBISWSH
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The paper

The paper claims

A past-complete pre-inflation may hand inflation its Bunch-Davies vacuum for free, without violating the Trans-Planckian Censorship Conjecture.

The reading

Inflation is past-incomplete: run the clock backwards and every perturbation mode you can see in the cosmic microwave background was once squeezed below the Planck length, where the theory used to describe it breaks down. That is why simply declaring the modes to start in the Bunch-Davies vacuum, the lowest-energy state of de Sitter space, has always looked like an unjustified choice rather than a derivation. Cai and Piao ask what happens if the universe was not singular but had a past-complete pre-inflationary era, asymptotically Minkowski in the infinite past, so that a Minkowski vacuum state can honestly be imposed there. They then propagate each mode through the intervening phases and show that, at the start of inflation, modes whose wavelengths are much shorter than the Hubble scale but still longer than the Planck length come out with $|alpha_i| approx 1$ and $|beta_i| = O(1/(k tilde{tau}))$: a Bunch-Davies state up to a phase. The Trans-Planckian Censorship Conjecture enters as the reason the modes never have to cross into the sub-Planckian regime at all, so the derivation and the conjecture hold together rather than pulling against each other.

What carries the argument

The carrying object is the two-by-two transfer matrix that relates the Bogoliubov coefficients $(alpha_j, beta_j)$ of one phase to those of the next, built from Hankel functions $H^{(1,2)}_{nu_j}$ of order $nu_j = |n_j - 1/2|$ evaluated at the junction. Its content is that when $k tilde{tau}_{j,1}$ and $k tilde{tau}_{j,2}$ are both much greater than one, the off-diagonal entries are suppressed as $O(1/(k tilde{tau}))$ and the diagonal entries are pure phases. Composing the matrices from the asymptotic Minkowski phase to the start of inflation therefore leaves $|alpha|$ and $|beta|$ unchanged to leading order. The diagnostic $C(k) = k^2(u_k u_k^* + k^{-2} u_k' u_k^{*'}) + 1/2$ converts this into a single number that equals one exactly for the Bunch-Davies state and is plotted against $k/(a_{inf} H_{inf})$.

Extended reading notes

Core claim

The paper's claim is conditional but strong: if the pre-inflationary era is past-complete, then setting the perturbation modes to the Minkowski vacuum in the infinite past is legitimate, and the evolution itself delivers an approximately Bunch-Davies state at the beginning of inflation for every mode with $lambda ll 1/H_i$. The authors establish this by writing the pre-inflationary history as a sequence of phases in each of which $z_j = sqrt{2 a^2 Q_s} propto (tau_{R,j} - tau)^{n_j}$, solving the Mukhanov-Sasaki equation in Hankel functions, and matching across each junction. For modes that stay sub-horizon at every junction, the transfer matrix is diagonal up to $O(1/(k tilde{tau}))$, so the coefficients $alpha$ and $beta$ pick up only phases as they pass through. A numerical run on the stable bounce-inflation background of an earlier paper confirms $|C(k)| to 1$ for $k gg a_{inf} H_{inf}$. The paper also shows the converse failure mode: if any phase has $C_s^2 = (k/Lambda)^{2p} gg 1$, one crossing multiplies $alpha$ and $beta$ by $k^p/(2 Lambda^p)$, which is the standard trans-Planckian problem reappearing in the language of the transfer matrix.

Load-bearing premise

The derivation assumes that the modes of interest stay well inside the perturbation horizon at every junction between pre-inflationary phases, and that each phase has $z propto (tau_R - tau)^{n}$; the general claim is argued analytically but checked numerically only on one bounce model.

Editorial extensions

If this is right

  • Modes with wavelengths far shorter than the Hubble scale at the start of inflation are in the Bunch-Davies state, so the standard nearly scale-invariant scalar and tensor spectra follow without an extra assumption about initial conditions.
  • Modes comparable to or longer than the Hubble scale at that time remain non-Bunch-Davies and carry imprints of the pre-inflationary era, giving a possible origin for the low-multipole power deficit and the dip near $l sim 20$.
  • Because the Trans-Planckian Censorship Conjecture limits the number of inflationary e-folds, the pre-inflationary window is pushed toward observable scales rather than being erased by stretching.
  • The trans-Planckian problem is recast as a statement about whether any phase of the pre-inflationary history had $C_s^2 gg 1$ for the modes of interest; the answer depends on whether those modes ever reached $lambda lesssim 1/Lambda$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The argument turns a statement about initial conditions into a statement about the geometry of the pre-inflationary history, so any pre-inflation model that is past-complete and keeps the CMB modes above the cutoff can be tested on the same footing, not just the bounce model used here.
  • If the same transfer-matrix bookkeeping were applied to tensor modes and to the sound speed of a beyond-Horndeski bounce, one could ask whether the tensor-to-scalar ratio inherits any pre-inflationary suppression beyond the bound the conjecture already imposes.
  • A sharp observational handle would be a scale-dependent departure from Bunch-Davies near the Hubble scale at the start of inflation: the $O(1/(k tilde{tau}))$ corrections grow as $k$ falls, so the transition region is where a pre-inflationary origin would show up as non-Gaussianity or a running of the spectral index.
  • The result suggests that the phrase 'the initial state of inflation' may be a misnomer for what is really a matching problem across a sequence of contracting phases, which is a calculational stance that could be exported to ekpyrotic and matter-bounce models generally.
Original abstract

We investigate the implication of Trans-Planckian Censorship Conjecture (TCC) for the initial state of primordial perturbations. It is possible to set the state of perturbation modes in the infinite past as the Minkowski vacuum, only if the pre-inflationary era is past-complete. We calculate the evolution of the perturbation modes in such a pre-inflationary era and show that at the beginning of inflation the perturbation modes with wavelengths much shorter than the Hubble scale (but still larger than the Planck length scale) will behave as they are in the Bunch-Davis state. Therefore, a past-complete pre-inflationary evolution may automatically prepare the initial state required for the inflationary perturbations at the CMB window while obeying the TCC.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,746 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We investigate the implication of Trans-Planckian Censorship Conjecture (TCC) for the initial state of primordial perturbations. It is possible to set the state of perturbation modes in the infinite past as the Minkowski vacuum, only if the pre-inflationary era is past-complete. We calculate the evolution of the perturbation modes in such a pre-inflationary era and show that at the beginning of inflation the perturbation modes with wavelengths much shorter than the Hubble scale (but still larger than the Planck length scale) will behave as they are in the Bunch-Davis state. Therefore, a past-complete pre-inflationary evolution may automatically prepare the initial state required for the inflationary perturbations at the CMB window while obeying the TCC.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We investigate the implication of Trans-Planckian Censorship Conjecture (TCC) for the initial state of primordial perturbations. contribution 0.89 0.86 0.05 unclear 0.52
s1 It is possible to set the state of perturbation modes in the infinite past as the Minkowski vacuum, only if the pre-inflationary era is past-complete. result 0.79 0.34 0.13 hedged possibility 0.90
s2 We calculate the evolution of the perturbation modes in such a pre-inflationary era and show that at the beginning of inflation the perturbation modes with wavelengths much shorter than the Hubble scale (but still larger than the Planck length scale) will behave as they are in the Bunch-Davis state. result 0.92 0.94 0.14 asserted 1.00
s3 Therefore, a past-complete pre-inflationary evolution may automatically prepare the initial state required for the inflationary perturbations at the CMB window while obeying the TCC. interpretation 0.98 0.70 0.84 hedged possibility 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1: Causal patch of the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe with in
Figure 2. FIG. 2: Causal patch of the FLRW universe in the bounce inflation scenario, where
Figure 4. FIG. 4: The evolution of the Hubble parameter

Showing 3 of the paper's 4 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:1909.12719 by the authors.

References
How the literature uses it

34 arXiv papers cite this in 40 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 24 sentences without a confident label

Uses its method or tool 1 paper
Compares with it 1 paper
  • We emphasize some similarity between this picture and other scenarios with a trans-Planckian cut-off For instance, some authors have formulated a trans-Planckian Censorship Conjecture [ref] , arguing that modes with a length scale smaller than the Planck length must be shielded from classicalizing, in analogy with the Penrose's argument that solutions of GR with naked singularities cannot arise in a full theory.

    Unattainability of the Trans-Planckian regime in Nonlocal Quantum Gravity · Conclusions · 0.95

Cites it as support 1 paper
Cites it as background 12 papers

What it cites · 73 sentences without a confident label

Uses the method or tool of 1 paper
Cites as support 3 papers
  • It will be significantly different from $1/H$, if $Q_s$ is rapidly changing, see also [ref] .] as long as $a_f/a_b<M_P/H_f$ and $a_b$ is sufficiently large (see also [ref] ),

    A Galileon Design of Slow Expansion · Minkowski in past-complete pre-inflation · 0.96

  • It will be significantly different from $1/H$, if $Q_s$ is rapidly changing, see also [ref] .] as long as $a_f/a_b<M_P/H_f$ and $a_b$ is sufficiently large (see also [ref] ),

    Trans-Planckian Censorship and Inflationary Cosmology · Minkowski in past-complete pre-inflation · 0.96

  • As showed recently in [ref] , the pre-inflationary bounce might be responsible for the power deficit of the CMB TT-spectrum at low multipoles and the dip at $l∼20$.

    Primordial perturbations with pre-inflationary bounce · Conclusion · 0.96

Cites as background 12 papers
  • Recently, Bedroya and Vafa proposed the Trans-Planckian Censorship Conjecture (TCC) [ref] , which requires that the sub-Planckian fluctuations should never cross their Hubble scale to become classical, otherwise the corresponding EFT belongs to the swampland [ref] .

    Trans-Planckian Censorship and the Swampland · On TCC · 0.91

  • Recently, Bedroya and Vafa proposed the Trans-Planckian Censorship Conjecture (TCC) [ref] , which requires that the sub-Planckian fluctuations should never cross their Hubble scale to become classical, otherwise the corresponding EFT belongs to the swampland [ref] .

    De Sitter Space and the Swampland · On TCC · 0.91

  • Recently, Bedroya and Vafa proposed the Trans-Planckian Censorship Conjecture (TCC) [ref] , which requires that the sub-Planckian fluctuations should never cross their Hubble scale to become classical, otherwise the corresponding EFT belongs to the swampland [ref] .

    On the Cosmological Implications of the String Swampland · On TCC · 0.91

Discussion

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