Trans-Planckian Censorship and Inflationary Cosmology (1909.11106v3)

Abstract: We study the implications of the recently proposed Trans-Planckian Censorship Conjecture (TCC) for early universe cosmology and in particular inflationary cosmology. The TCC leads to the conclusion that if we want inflationary cosmology to provide a successful scenario for cosmological structure formation, the energy scale of inflation has to be lower than $10^9$ GeV. Demanding the correct amplitude of the cosmological perturbations then forces the generalized slow-roll parameter $\epsilon$ of the model to be very small ($<10^{-31}$). This leads to the prediction of a negligible amplitude of primordial gravitational waves. For slow-roll inflation models, it also leads to severe fine tuning of initial conditions.

Implications of the Trans-Planckian Censorship Conjecture for Inflationary Cosmology

The paper "Trans-Planckian Censorship and Inflationary Cosmology" examines the complexities introduced by the Trans-Planckian Censorship Conjecture (TCC) in the context of early universe cosmology, especially inflationary cosmology. The authors explore the hypothesis that according to TCC, no cosmological modes with wavelengths smaller than the Planck length should exit the Hubble horizon, as consistent quantum gravity theories would render such scenarios impossible.

Key Insights and Constraints

One of the central arguments is that the TCC imposes strict bounds on inflationary models. Particularly, it requires the generalized slow-roll parameter $\epsilon$ to be exceedingly small, less than $10^{-31}$, which results in negligible amplitudes for primordial gravitational waves. Furthermore, inflation models aligning with TCC necessitate substantial fine-tuning of initial conditions without modes assuming trans-Planckian scales, thus rendering conventional slow-roll models problematic.

Considering cosmological observations, the paper emphasizes that while the standard Big Bang cosmology doesn't manifest scenarios where modes exit the Hubble horizon, alternative early universe models, like Inflation and String Gas Cosmology, encounter TCC constraints during their expansion phases. The paper further analyzes how TCC affects the energy scales during inflationary phases, proposing that these scales should remain significantly below the Planck scale to be consistent with TCC parameters.

Numerical Results and Predictions

A vital outcome from the analysis is the energy scale restriction, suggesting that the inflation energy scale $V^{1/4}$ should be less than $6 \times 10^8\, \text{GeV}$ or $3 \times 10^{-10} M_{\text{pl}}$. This conclusion stands independent of assumptions about quantum fluctuations serving as seeds for cosmic structures but leads to the implication that tensor-to-scalar ratios must be below $10^{-30}$.

Theoretical Implications and Future Directions

Given these constraints, the paper infers that any detection of primordial gravitational waves on cosmological scales would challenge the inflationary paradigm consistent with TCC and suggest alternative mechanisms for their generation. This opens pathways for examining models like String Gas Cosmology that predict non-negligible primordial gravitational wave amplitudes.

Application to Slow-Roll Inflation

The application of TCC to slow-roll inflation reveals additional constraints. The derived limit of $\Delta \phi < 10^{-13} M_{\text{pl}}$ underlines the difficulty inflation models face due to the precision required in the initial conditions, largely because slow-roll trajectories are not attractors in initial condition space under TCC constraints.

Conclusion

In conclusion, the Trans-Planckian Censorship Conjecture has profound implications for inflationary cosmology, driving the narrative towards exploring models that naturally evade trans-Planckian issues, potentially reshaping the understanding of early universe dynamics. The paper challenges researchers to rethink the initial conditions and energy scales, compelling them to consider alternative cosmological scenarios that harmonize theoretical predictions with observational data while adhering to quantum gravity principles.