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Register a new userCosmic Censorship of Trans-Planckian Field Ranges in Gravitational Collapse
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A classical solution where the (scalar) field value moves by an ${cal O}(1)$ range in Planck units is believed to signal the breakdown of Effective Field Theory (EFT). One heuristic argument for this is that such a field will have enough energy to be inside its own Schwarzschild radius, and will result in collapse. In this paper, we consider an inverse problem: what kind of field ranges arise during the gravitational collapse of a classical field? Despite the fact that collapse has been studied for almost a hundred years, most of the discussion is phrased in terms of fluid stress tensors, and not fields. An exception is the scalar collapse made famous by Choptuik. We re-consider Choptuik-like systems, but with the emphasis now on the evolution of the scalar. We give strong evidence that generic spherically symmetric collapse of a massless scalar field leads to super-Planckian field movement. But we also note that in every such supercritical collapse scenario, the large field range is hidden behind an apparent horizon. We also discuss how the familiar perfect fluid models for collapse like Oppenheimer-Snyder and Vaidya should be viewed in light of our results.
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It was recently proposed that a field theory cannot be consistent with quantum gravity if it allows a mode shorter than the Planck length to exit the Hubble horizon. This is called the Trans-Planckian Censorship Conjecture (TCC). We discuss the implications of the TCC on the possible shape of the inflaton potential in single-field slow-roll inflation. We point out that (1) there is generically an initial condition in which the total e-folding number $N_text{total}$ is doubled or more compared to the e-folds necessary for the cosmic microwave background fluctuations, and (2) a sizable negative running of spectral index is generically expected to make $N_text{total}$ small. In concrete setups, we find a stringent constraint on the inflationary energy scale, $V_text{inf}^{1/4} < mathcal{O}(10) , text{TeV}$ with $r < mathcal{O}(10^{-50})$, and the running parameter is bounded above as $alpha_text{s} lesssim - 4 times 10^{-3}$.
If the inflationary phase lasted longer than the minimal period, the length scales observed today originate from modes that were smaller than the Planck length during inflation. It was recently argued that this trans-Planckian problem can never arise in a consistent string theory framework, which places a stringent constraint on the energy scale of inflation, $V^{1/4}lesssim 10^9$ GeV. In this paper, we show that this requirement corresponds to a very small Hubble scale during inflation, $H_{rm inf}lesssim 1$ GeV, and therefore has serious consequences on scenarios where the dark matter density was generated by amplification of quantum fluctuations during inflation. We also present a class of inflationary models which both satisfy the above limit for the scale of inflation and are in perfect agreement with observational data.
In this paper, we propose a new Swampland condition, the Trans-Planckian Censorship Conjecture (TCC), based on the idea that in a consistent quantum theory of gravity sub-Planckian quantum fluctuations should remain quantum and never become larger than the Hubble horizon and freeze in an expanding universe. Applied to the case of scalar fields, it leads to conditions that are similar to the refined dS Swampland conjecture. For large field ranges, TCC is stronger than the dS Swampland conjecture but it is weaker for small field ranges. In particular for asymptotic regions of field space, TCC leads to a bound $|V|geq {2over sqrt{(d-1)(d-2)}}V$, which is consistent with all known cases in string theory. Like the dS Swampland conjecture, the TCC forbids long-lived meta-stable dS spaces, but it does allow sufficiently short-lived ones.
We study the implications of the recently proposed Trans-Planckian Censorship Conjecture (TCC) for early universe cosmology and in particular inflationary cosmology. The TCC leads to the conclusion that if we want inflationary cosmology to provide a successful scenario for cosmological structure formation, the energy scale of inflation has to be lower than $10^9$ GeV. Demanding the correct amplitude of the cosmological perturbations then forces the generalized slow-roll parameter $epsilon$ of the model to be very small ($<10^{-31}$). This leads to the prediction of a negligible amplitude of primordial gravitational waves. For slow-roll inflation models, it also leads to severe fine tuning of initial conditions.
During an accelerated expansion of the Universe, quantum fluctuations of sub-Planckian size can be stretched outside the horizon and be regarded effectively classical. Recently, it has been conjectured that such horizon-crossing of trans-Planckian modes never happens inside theories of quantum gravity (the trans-Planckian censorship conjecture, TCC). We point out several conceptual problems of this conjecture, which is in itself formulated as a statement on the restriction of possible scenarios in a theory: by contrast a standard swampland conjecture is a restriction of possible theories in the landscape of the quantum gravity. We emphasize the concept of swampland universality, i.e. that a swampland conjecture constrains any possible scenario in a given effective field theory. In order to illustrate the problems clearly we introduce sever
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