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We study the analytic structure of in-in correlation functions in a deSitter background. The aim of this study is to probe the initial conditions for inflation through the features of correlation functions of the field fluctuations, and understand precisely how an in-in correlator responds to particles in the initial state. We emphasize that the choice of vacuua and the corresponding particle interpretation for these fluctuations is flexible, and we clarify the role of this choice at the level of calculations and their diagrammatic interpretation. We consider several possibilities aside from the standard Bunch Davies vacuum prescription for the initial state, and trace the change in pole structure as one begins adding excitations; starting from just a single particle, to highly excited states and special cases such as a coherent state. We illustrate - with the example of coherent states - the subtleties in concluding a Bunch Davies initial state from the absence of physical poles in the bispectrum, which is interesting in light of some recent literature. Initial states with a finite number of excitations are plagued with disconnected diagrams isolated in phase space, and we highlight their implications on the observation of these signals, and how the situation changes as one begins to excite more and more particles. We also comment about the implications of various initial conditions on the squeezed limit of the bispectrum. These new pole structures are a direct consequence of mixing of positive and negative frequency modes which is a characteristic of curved spacetimes; in particular, we see in detail how particles in an initial state replicate mode mixing structures. This study aims to clarify the missing details that link quantum and classical initial conditions, and sharpen our understanding of in-in correlators in inflation., Comment: 46 pages, typos corrected, sections have been slightly rearranged, no changes in the main results

A major task in phenomenology today is constraining the parameter space of SMEFT and constructing models of fundamental physics that the SM derives from. To this effect, we report an exhaustive list of sum rules for 4-fermion operators of dimension 6, connecting low energy Wilson coefficients to cross-sections in the UV. Unlike their dimension 8 counterparts which are amenable to a positivity bound, the discussion here is more involved due to the weaker convergence and indefinite signs of the dispersion integrals. We illustrate this by providing examples with weakly coupled UV completions leading to opposite signs of the Wilson coefficients for both convergent and non-convergent dispersion integrals. We further decompose dispersion integrals under weak isospin and color groups which lead to a tighter relation between IR measurements and UV models. These sum rules can become an effective tool for constructing consistent UV completions for SMEFT following the prospective measurement of these Wilson coefficients., Comment: 24 pages