Trans-Planckian Censorship and single-field inflaton potential

Abstract

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 singlefield slow-roll inflation. We point out that (1) there is generically an initial condition in which the total e-folding number N 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 total small. In concrete setups, we find a stringent constraint on the inflationary energy scale, V 1/4 inf < O(10) TeV with r < O(10 −50 ), and the running parameter is bounded above as α s −4 × 10 −3 . arXiv:1910.09460v2 [hep-th] 3 Jan 2020

Swampland constraints on no-boundary quantum cosmology

“…A similar setup was considered in the context of a Swampland conjecture in ref. [94]. This is what we have in our mind implicitly, but in the actual numerical analyses, we turn off ε and just discuss to what extent the field value can be extended without violating the Swampland conjectures.…”

Trans-Planckian censorship and other swampland bothers addressed in warm inflation

“…This restricts the energy scale of a phase of inflation to be fairly low, hence placing a bound on the tensor-to-scalar ratio of r < O(10 −30 ), as shown in [16]. Even though there are models that satisfy this constraint [18][19][20][21], it has been also pointed out that the bound is less demanding for bouncing cosmologies and other pre-inflationary scenarios, basically for the same reasons that they are less sensitive to the TP problem [16,22]. Along those lines, other scenarios like a multi-stage inflation [23], excited initial states [24] or non-standard expansion histories [25,26] can also mitigate the TCC constraints.…”

Strengthening the TCC bound on inflationary cosmology

“…As we show in this note, if this is the case then the constraints on the energy scale of inflation become more severe; see also 1 The fact that the accelerated expansion of space during inflation leads to a trans-Planckian problem for fluctuations was already pointed out in [7], and see [8] for a review with references to other works on this problem. 2 Constraints which can be derived from the TCC when relaxing the condition of immediate radiation-domination after the end of inflation have been considered in [9,10], and relaxed bounds when abandoning the assumption of an almost constant value of the expansion rate have been studied in [9,11]-note that the post-inflation w = −1/3 phase in the setup of [9] has a spacetime diagram which is identical to the limiting value of power-law inflation studied in [11] when the inflationary phase has a value of w which approaches the value −1/3 from below (and in [12] in the context of warm inflation [13]), while TCC constraints on the shape of the inflaton potential in single-field slow-roll inflation are derived in [14]. In deriving the bound on r, it was assumed that the initial state of the fluctuations is the usual Minkowskilike vacuum.…”