Scalar two-point functions at the late-time boundary of de Sitter

Understand

We calculate two-point functions of scalar fields of mass $m$ and their conjugate momenta at the late-time boundary of de Sitter with Bunch-Davies boundary conditions, in general $d+1$ spacetime dimensions.

• We perform the calculation using the wavefunction picture and using canonical quantization.
• With the latter one clearly sees how the late-time field and conjugate momentum operators are linear combinations of the normalized late-time operators $\alphaN$ and $\betaN$ that correspond to unitary irreducible representations of the de Sitter group with well-defined inner products.
• The two-point functions resulting from these two different methods are equal and we find that both the autocorrelations of $\alphaN$ and $\betaN$ and their cross correlations contribute to the late-time field and conjugate momentum two-point functions.