Towards Systematic Evaluation of de Sitter Correlators via Generalized Integration-By-Parts Relations

We generalize Integration-By-Parts (IBP) and differential equations methods to de Sitter correlators related to inflation. While massive correlators in de Sitter spacetime are usually regarded as highly intricate, we find they have remarkably hidden concise structures from the perspective of IBP. We find the factorization of the IBP relations of each vertex integral family corresponding to $\mathrm{d} \tau_i$ integration. Furthermore, with a smart construction of master integrals, the universal formulas for iterative reduction and $\mathrm{d} \log$-form differential equations of arbitrary vertex integral family are presented and proved. These formulas dominate all tree-level de Sitter correlators and play a kernel role at the loop-level as well.