Cosmological correlation functions are significantly more complex than their flat-space analogues, such as tree-level scattering amplitudes. While these amplitudes have simple analytic structure and clear factorisation properties, cosmological correlators often feature branch cuts and lack neat expressions. In this paper, we develop off-shell perturbative methods to study and compute cosmological correlators. We show that such approach not only makes the origin of the correlator singularity structure and factorisation manifest, but also renders practical analytical computations more tractable. Using a spectral representation of massive cosmological propagators that encodes particle production through a suitable iϵ prescription, we remove the need to ever perform nested time integrals as they only appear in a factorised form. This approach explicitly shows that complex correlators are constructed by gluing lower-point off-shell correlators, while performing the spectral integral sets the exchanged particles on shell. Notably, in the complex mass plane instead of energy, computing spectral integrals amounts to collecting towers of poles as the simple building blocks are meromorphic functions. We demonstrate this by deriving a new, simple, and partially resummed representation for the four-point function of conformally coupled scalars mediated by tree-level massive scalar exchange in de Sitter. Additionally, we establish cosmological largest-time equations that relate different channels on in-in branches via analytic continuation, analogous to crossing symmetry in flat space. These universal relations provide simple consistency checks and suggest that dispersive methods hold promise for developing cosmological recursion relations, further connecting techniques from modern scattering amplitudes to cosmology.

France

Denis Werth

Spectral representation of cosmological correlators

Correlation functions of primordial density fluctuations provide an exciting probe of the physics governing the earliest moments of our Universe. However, the standard approach to compute them is technically challenging. Theoretical predictions are therefore available only in restricted classes of theories. In this Letter, we present a complete method to systematically compute tree-level inflationary correlators. This method is based on following the time evolution of equal-time correlators and it accurately captures all physical effects in any theory. These theories are conveniently formulated at the level of inflationary fluctuations, and can feature any number of degrees of freedom with arbitrary dispersion relations and masses, coupled through any type of time-dependent interactions. We demonstrate the power of this approach by exploring the properties of the cosmological collider signal, a discovery channel for new high-energy physics, in theories with strong mixing and in the presence of features. This work lays the foundation for a universal program to assist our theoretical understanding of inflationary physics and generate theoretical data for an unbiased interpretation of upcoming cosmological observations.

Spain

Lucas Pinol

Sébastien Renaux-Petel

Cosmological Flow of Primordial Correlators

Parity violation in the early Universe holds great promise for uncovering new physics. In particular, the primordial scalar four-point correlation function is allowed to develop a parity-violating component when massive spinning particles coupled to a helical chemical potential are present during inflation. In this paper, we explore the rich physics of such a parity-violating trispectrum in the presence of a reduced speed of sound for the Goldstone boson of broken time translations. We show that this signal can be significantly large while remaining under perturbative control, offering promising observational prospects for future cosmological surveys. In the limit of a reduced sound speed, the dynamics admits an effective nonlocal description organized as a time-derivative expansion. This reveals that parity violation arises due to emergent nonlocality in the single-field effective theory. At leading order, this effective theory yields a compact trispectrum template, written in terms of elementary functions. We then conduct a comprehensive analysis of the kinematic dependence of this parity-violating trispectrum and reveal new features. In addition to the low-speed collider resonance, we find a new class of signals lying in the internal soft-limit of the correlator. This signal is characterized by an oscillatory pattern periodic in the momentum ratio, with a frequency determined by the speed of sound and the chemical potential, making it drastically distinct from the conventional cosmological collider signal.