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Non-Standard Cosmological Models and the trans-Planckian Censorship Conjecture

The trans-Planckian censorship conjecture (TCC) puts an upper bound on the life-time of de Sitter spacetimes. It has immediate consequences for inflationary cosmology. In the standard paradigm, the universe has experienced a single stage of inflation and follows a thermal history. Then, the TCC puts an upper bound on the Hubble parameter during inflation $H_{\rm inf}$ around $0.1$ GeV. Consequently, it implies a severe fine-tuning in initial condition for inflation and non-detection of primordial gravitational waves. In this note, we study non-standard cosmological paradigms with non-thermal history and/or multiple stages of inflations. It is motivated by string theory compactifications and axiverse scenarios in which the modulus/axion fields are effective in the early universe. In early matter domination the TCC bound on $H_{\rm inf}$ can be raised up to 3 orders of magnitude. In multiple inflationary scenarios the upper bound on the observable inflation can be raised up $10^{14}$ GeV to touch the Planck 2018 bound.