Note: The values \( q_i \) and \( n_i \) must satisfy flux quantization conditions:
\[\frac{1}{(2\pi)^2 \alpha'} \int_{\Sigma_i} G_{(3)} = n_i \in \mathbb{Z}, \quad \alpha' = \frac{1}{2\pi M_{\text{Pl}}^2}.\]
A3. Full Derivation: de Sitter Entropy
The de Sitter entropy (\( S_{\text{dS}} \)) for a bubble with is given by:
1. Basic Formula:
\[S_{\text{dS}} = \frac{\text{Area Horizon}}{4G} = \frac{3\pi M_{\text{Pl}}^2}{\Lambda},\]
where is the horizon radius \( R_H = \sqrt{3/\Lambda} \).
2. String Theory Correction:
Untuk kompaktifikasi dengan volume \( \mathcal{V} \sim l_s^6 \) (\( l_s = \sqrt{\alpha'} \)):
\[S_{\text{dS}} = \frac{2\pi^2 \mathcal{V} M_{\text{Pl}}^2}{\Lambda} + \mathcal{O}(g_s),\]
where \( g_s \) is the coupling string.
