Abstract
The recently proposed trans-Planckian censorship conjecture (TCC) seems to require that the energy scale of inflation is significantly lower than the Planck scale $(H_\text{inf}<10^{-20} \Mpl)$. This, in turn, implies that the tensor-to-scalar ratio for inflation is negligibly small, \textit{independent} of assumptions of slow-roll or even of having a single scalar field, thus ruling out inflation if primordial tensor modes are ever observed. After demonstrating the robustness and generality of these bounds, we show that having an excited initial state for cosmological perturbations seems to be a way out of this problem for models of inflation.
Highlights
One of the crowning glories of inflation [1,2,3,4,5,6] lies in its ability to explain the origin of small inhomogeneities, which seed the large scale structure of our universe, as quantum vacuum fluctuations [7,8]
As is well known [9,10], these quantum fluctuations which oscillate within the Hubble horizon, become classical and freeze on exiting it during inflation, and eventually reenter the horizon at late times to seed the anisotropies in the cosmic microwave background radiation [11,12] and the large scale structure [13] which we observe today
Inflation, as a lowenergy effective field theory (EFT), would fail if macroscopic perturbations can be traced backed to modes which are smaller than the Planck length at early times
Summary
One of the crowning glories of inflation [1,2,3,4,5,6] lies in its ability to explain the origin of small inhomogeneities, which seed the large scale structure of our universe, as quantum vacuum fluctuations [7,8]. Since the TCC prohibits this for trans-Planckian modes, one gets an upper bound on the duration of such accelerated phases so that a Planck length mode never exits the Hubble horizon If inflation started off at some finite time and is not past infinite, the preinflationary dynamics naturally points toward a NBD state for the fluctuations, e.g., from a previous radiation-dominated era [46], a phase of anisotropic expansion [47,48], a nonattractor solution [49], tunneling from a false vacuum [50], the effects of having a high-energy cutoff [14,51,52,53,54,55], multifield dynamics [56] or a specific quantum gravity proposal [57]. This, in turn, naturally leads us toward a NBD state for inflation and we show how assuming such a state might be able to evade the constraints given in [28]
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