Pre-inflation and trans-Planckian censorship
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. Article .
November 2020 Vol. 63 No. 11: 110411 https://doi.org/10.1007/s11433-020-1573-5
Pre-inflation and trans-Planckian censorship Yong Cai1* , and YunSong Piao1,2* 1 School
of Physics, University of Chinese Academy of Sciences, Beijing 100049, China; of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
2 Institute
Received March 26, 2020; accepted April 28, 2020; published online August 11, 2020
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. inflation, primordial perturbation, trans-Planckian censorship conjecture PACS number(s): Citation:
98.80.-k, 98.80.Cq, 04.50.Kd
Y. Cai, and Y. S. Piao, Pre-inflation and trans-Planckian censorship, Sci. https://doi.org/10.1007/s11433-020-1573-5
1 Introduction Inflation [1-4] is the standard paradigm of the early universe. It predicted the nearly Gaussian and scale-invariant primordial perturbations, which are consistent with the observations of cosmic microwave background (CMB) anisotropies [5, 6]. However, inflation is not the final story of the early universe, since it is past-incomplete, as shown in refs. [7, 8]. Usually, the initial state of the inflationary perturbations is set as the Bunch-Davis (BD) vacuum [9], which is the lowestenergy state of de Sitter spacetime. However, due to the pastincompleteness of inflation [8], initially, the background and fluctuations of spacetime will be inevitably involved in the cosmological singularity, where the length scale is smaller than the Planck scale or the cutoff scale of the effective field theory (EFT). This is the so-called “trans-Planckian” problem of inflation [10, 11]. In this situation, inflation does not
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Astron. 63, 110411 (2020),
automatically pick out the BD state as the initial state of perturbation modes1) . Recently, Bedroya and Vafa [18] proposed the transPlanckian censorship conjecture (TCC), which states that “a field theory consistent with a quantum theory of gravity does not lead to a cosmological expansion where any perturbation with length scale greater than the Hubble radius trace back to trans-Planckian scales at an earlier time”, see also its application to inflation models [19]. Actually, since inflation is past-incomplete, the inflationary perturbations inevitably originated from the subPlanckian scale fluctuations. It is well-known that the BD
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