De sitter'de küme ayrışımının tekrar ele alınması

We investigate cluster decomposition in four-dimensional de Sitter space using two complementary approaches. First, we analyze equal-time two-point correlation functions at late times for scalar fields categorized by their unitary irreducible representations under the de Sitter group. The principal and complementary series exhibit power-law decay with spatial separation, while the discrete series shows a logarithmic divergence. Although this divergent behavior might initially appear to result from zero modes, further analysis shows that zero modes must be removed across all representation categories. The failure of cluster decomposition is therefore a distinct feature of the discrete series. In the second approach, we study the statistical distribution of distances between coarse-grained field configurations. We perform a saddle point analysis of the Laplace integral that defines the distribution, but leave the full evaluation to future work.