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Register a new userTrans-Planckian Censorship and Inflation in Grand Unified Theories
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Authors
Kai Schmitz
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The recently proposed trans-Planckian censorship conjecture (TCC) amounts to the claim that inflation models with an inflationary energy scale larger than Lambda_inf^max ~ 10^9 GeV belong to the swampland, i.e., cannot be embedded into a consistent theory of quantum gravity. In this paper, we point out that this constraint can be readily satisfied in D-term hybrid inflation (DHI), which is a well-motivated inflation scenario in the context of supersymmetric grand unification. In DHI, the amplitude of the primordial scalar power spectrum originates from a Fayet-Iliopoulos term of the order of the unification scale, sqrt{xi} ~ 10^16 GeV. At the same time, the TCC results in an upper bound on the corresponding gauge coupling constant of g_max ~ 10^-14. We are able to show that this constraint translates into an upper bound on the gravitino mass of m_3/2^max ~ 10 MeV, which opens the possibility that dark matter is accounted for by thermally produced gravitinos, if the reheating temperature is close to T_reh ~ 100 TeV. Interestingly enough, a somewhat similar gravitino mass range has recently been derived in a model that aims at explaining dark energy in terms of axion quintessence and resolving the Hubble tension by means of decaying gravitino dark matter.
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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.
We explore the bound of the trans-Planckian censorship conjecture on an inflation model with multiple stages. We show that if the first inflationary stage is responsible for the primordial perturbations in the cosmic microwave background window, the $e$-folding number of each subsequent stage will be bounded by the energy scale of the first stage. This seems to imply that the lifetime of the current era of accelerated expansion (regarded as one of the multiple inflationary stages) might be a probe for distinguishing inflation from its alternatives. We also present a multistage inflation model in a landscape consisting of anti-de Sitter vacua separated by potential barriers.
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.
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