Abstract
I critically discuss a controversial ‘trans-Planckian censorship’ conjecture, which has recently been introduced to researchers working at the intersection of fundamental physics and cosmology. My focus explicitly avoids any appeals to contingent research within string theory (the sociological origins of the conjecture) or regarding the more general (quantum) gravitational ‘swampland’. Rather, I concern myself with the conjecture’s foundations in our current, well-trodden physics of quantized fields, spacetime, and (classical) gravity. In doing so, I locate what exactly within trans-Planckian censorship amounts to a departure from current physics—identifying what is, ultimately, so conjectural about the conjecture.
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Notes
The upper bound on the duration of rapid expansion allowed (e.g. in an inflationary epoch in the early universe) depends on fixing a class of models, given further empirical constraints (e.g. the amplitude of the CMB power spectrum downstream of the inflationary epoch). On this point, as summarized in [8, p. 7], bounds on inflation that are due to trans-Planckian censorship:
... are only consistent if inflation takes place at a very low energy scale of \(V^{\frac{1}{4}}< 10^9\)GeV, assuming an almost constant value of [Hubble radius] during inflation and instantaneous reheating. This is a very severe constraint on canonical single scalar field models of inflation. The bound can be relaxed by allowing a substantial time dependence of [Hubble radius] during inflation or by modifying the post-inflation cosmology. On the other hand, the bound is strengthened if there is a period of radiation domination before the onset of inflation.
Or, more carefully put: a principle along the lines of trans-Planckian censorship is evidently what would ensure, in a model-independent way, that there is a finite upper bound in each cycle—so that, especially, it might thus be reasonable to go ‘beyond the standard model’ in late-stage cosmology, favoring end conditions consistent with a cyclic model instead. (In Sect. 3.1 of the paper cited in text, the model included for illustrative purposes builds in the finiteness by hand, though the authors do explicitly note that facts about the dark energy density are what, in the model, matters to that finiteness.) I thank Anna Ijjas for correspondence on this topic.
In this exposition, I am being purposefully quiet about whence the demand for a quantum gravity theory that is, specifically, ‘UV’. It suffices to say that, in the wake of GR, there are conceptual challenges spelling out adequacy criteria for any fundamental quantum gravity theory, if that theory is not apt for use above the Planck scale. But this subtlety is a tangent in the present context.
This is, in fact, a subtle point about the physics implicated in trans-Planckian censorship. At face value, the statement of the TCC only involves reference to that part of the physics circumscribed by low-energy quantum gravity (which is, after all, an effective theory defined perturbatively, relative to any suitable choice of background, including that which will feature shortly in Sect. 2.1). But as evidenced by the later discussion in Sect. 2.3, there is more physical reasoning involved than just the effective field theoretic dynamics of material field modes interacting with low-energy quantum gravity, situated on a background.
See [15] for a classic foundational treatment of the latter. Note that, in this rough analogy, it is very likely not the case that the underlying topological and smoothness structure of a spacetime corresponds to a global charge. Causally perverse spacetimes defined on trivial underlying smooth manifolds, e.g. Gödel spacetime, complicate the story [35]. If, though, we are restricted to globally hyperbolic spacetimes (as discussed presently), it seems plausible that (smoothly) foliated manifolds are what may stand in that rough analogy.
Another avenue of research in QFTCS sets aside semiclassical gravity, in order to focus on the phenomenology of quantized fields merely subject to specific model spacetime backgrounds selected for their applications [6]. But this will not suffice for our purposes: as will become clear below, it is crucial to the TCC that we consider the material quantum field on the expanding background as gravitationally coupled, such that expansion is itself an apt mean-field description of the gravitational state of the total system, including small perturbations.
For more details on de Sitter spacetime and its many cousins, see [4] and references therein—especially [33] and [11]. The ‘flat FLRW patch’ is called the ‘cosmological patch’ in [4], and the de Sitter metric within that patch can, in four spacetime dimensions, be written as the familiar flat FLRW metric \(ds^2=-dt^2+e^{2t}(dx_1^2+dx_2^2+dx_3^2+dx_4^2)\). Although the flat FLRW patch is naturally understood in terms of the exponential expansion of space through a de Sitter observer’s proper time, the intersection of the flat FLRW patch generated by that observer with the causal past of the same observer (i.e. the observer’s backward lightcone) gives rise to the ‘static patch’ relative to them. As the name suggests, within the static patch, the line element of the de Sitter metric can be written so that the spatial components are time-independent. This is clearly untrue with respect to the larger flat FLRW patch, and is as well untrue in de Sitter spacetime, considered globally.
How this would go is, unfortunately, not immediately clear. In particular: this other notion of low-energy description would, presumably, also be tasked with explaining why the EFT toolkit is, in nearly every (other) context, sufficient for what is demanded of it. One suggestion, motivated by an objection to trans-Planckian censorship developed in [13], is to appeal to a more rigorous notion of scale decoupling in fundamental physics, which might recover the EFT toolkit in the latter’s more ordinary applications. One notable challenge, in such a case, would be locating independent support for that particular rigorous notion in the context of UV quantum gravity beyond field theory.
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Acknowledgements
I would like to thank Feraz Azhar, Nick Huggett, and an anonymous reviewer for helpful comments. This article was produced while I was a postdoctoral researcher on the Beyond Spacetime project, funded by a ‘Cosmology Beyond Spacetime’ grant from the John Templeton Foundation
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Schneider, M.D. A (Strictly) Contemporary Perspective on Trans-Planckian Censorship. Found Phys 52, 76 (2022). https://doi.org/10.1007/s10701-022-00593-7
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DOI: https://doi.org/10.1007/s10701-022-00593-7