- The entropy correction of high mass fields (e.g. string states) can be neglected for \( \Lambda \ll M_{\text{Pl}}^4 \).
Relevant Empirical Support
1. CMB Observations: Planck Limits on \( r \) and \( n_s \)
- Planck 2018 provides strict limits on inflation parameters:
- Tensor-to-scalar ratio: \( r_{0.002} < 0.056 \) (95% CL)
- Spectral index: \( n_s = 0.9649 \pm 0.0042 \)
- Relevance to Model:
- The predictions of the string theory based model (\( r \sim 0.003 \)) are **consistent** with the Planck limit.
- The observed \( n_s \) corresponds to slow-roll inflation in ramp potentials (e.g. KKLT, Starobinsky).
- Unexplained Anomaly:
- Low-\( \ell \) deficit in CMB spectrum may be related to extra-dimensional inflation phase (can be further tested with LiteBIRD).
