Abstract
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 left|V^{prime}right|ge frac{2}{sqrt{left(d-1right)left(d-2right)}}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.
Highlights
The dS Swampland conjecture, the Trans-Planckian Censorship Conjecture (TCC) forbids long-lived meta-stable dS spaces, but it does allow sufficiently short-lived ones
TCC is stronger than the dS Swampland conjecture but it is weaker for small field ranges
Other attempts at coming up with a dS conjecture motivated by more basic aspects of quantum gravity includes [3, 8] where quantum breaking of dS is suggested as the main principle leading to c being proportional to V instead of being a constant and [7] where the postulate of lack of existence of eternal inflation1 has led to c being proportional to V 1/2
Summary
In a quantum gravitational theory, we do not believe that the notion of spacetime as a continuum would make sense at distance scales smaller than Planck length. In such a theory we can have expansions in the background, which raises the question of what happens to these scales becoming larger than Planck length. As is known in the context of inflationary models, when sub-Planckian quantum fluctuations become larger than the Hubble horizon 1/H, they can become classical and freeze. This would lead to the classical observation of a sub-Planckian quantum mode, which is a bit strange! We would like to propose an alternative viewpoint: that such questions should never arise in a consistent quantum gravitational theory! That no trajectory of a consistent quantum theory of gravity should lead to a classical blow-up of the sub-Planckian modes to become larger than the Hubble horizon 1/H and that all the QFT’s that do lead to this scenario belong to the Swampland
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