Abstract: In this work we provide the missing link between two approaches aimed at characterizing the effect of long perturbation modes in Inflation. We consider the “Inflationary Fossils'” approach, that characterizes the power-spectrum of the inflaton field in presence of other long and non dynamical “fossil” fields, and a technique that computes, beyond perturbation theory, the power-spectrum of a scalar field in presence of a “large” fluctuation of a second field.

We clarify a few points on the applicability of the non-perturbative technique. We prove in six distinct cases, one involving a violation of the consistency conditions, that the non-perturbative approach, once expanded to first order in the coupling, matches the perturbative result following the Fossils’ approach. 

We believe that this non-perturbative technique extends to all orders the Fossils’ approach, resumming infinitely many diagrams of standard in-in perturbation theory.

Abstract: Effective field theories (EFTs) provide a systematic framework to parametrise unknown ultraviolet (UV) physics. In de Sitter space, the long-wavelength dynamics of light scalar fields is naturally described by stochastic inflation, which can be viewed as an EFT obtained after integrating out subhorizon modes. This framework highlights that qualitatively new behaviour arises when the EFT cutoff lies below the Hubble scale H. In this talk, we investigate two complementary ways of constructing and understanding EFTs in this regime.
First, we derive an EFT by integrating out heavy fields in a UV-complete theory, obtaining an effective lambdaphi^4description in de Sitter space with a cutoff set by the heavy mass scale. We perform a complete analytic matching to two explicit UV completions, including both tree-level and loop contributions. When the cutoff lies well above H, the EFT admits a unitary description, with exponentially suppressed corrections. When the cutoff is lowered below H, the effective dynamics becomes intrinsically non-unitary: the system evolves into a mixed state and exhibits diffusive behaviour, in close analogy with stochastic inflation.
Second, we construct an EFT directly by integrating out high-energy modes using a time-dependent cutoff, without reference to a specific UV completion. We show that the resulting effective dynamics reproduces the same physical predictions as the UV-matched theory. Together, these results provide a unified picture of EFTs for light fields in de Sitter space, interpolating between unitary and stochastic descriptions.

Abstract: Unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix is one of the cornerstones of the Standard Model.  The unitarity constraint that involves the top-row matrix elements, $|V_{ud}|^2+|V_{us}|^2+|V_{ub}|^2=1$ is particularly important because all elements are measured very precisely permitting a test at the 0.01% level. At this accuracy, $V_{ub}sim10^{-3}$ is irrelevant, and the unitarity constraint reduces to the two-flavor Cabibbo unitarity pattern with a single Cabibbo angle $theta_C$ and $V_{ud}=costheta_C$ and $V_{us}$. At present, a mild deficit is observed, $|V_{ud}|^2+|V_{us}|^2=0.9985(7)$. As such, this deficit may suggest some new physics, but to make this claim, all Standard Model ingredients must be firmly under control. I review these ingredients across theory and experiment and review the most recent developments.