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.

France

Denis Werth

Spain

Lucas Pinol

Sébastien Renaux-Petel

Cosmological Flow of Primordial Correlators

Using the recently developed cosmological bootstrap method, we compute the exact analytical solution for the seed integral appearing in cosmological correlators with double massive scalar exchanges. The result is explicit, valid in any kinematic configuration, and free from spurious divergences. It is applicable to any number of fields’ species with any masses. With an appropriate choice of variables, the results contain only single-layer summations. We also propose simple approximate formulas valid in different limits, enabling direct and instantaneous evaluation. Supported by exact numerical results using CosmoFlow, we explore the phenomenology of double massive exchange diagrams. Contrary to single-exchange diagrams with ubiquitous Lorentz-covariant interactions, the size of the cubic coupling constant can be large while respecting perturbativity bounds. Because of this property, the primordial bispectrum from double-exchange diagrams can be as large as, coincidentally, current observational constraints. In addition to being sizable on equilateral configurations, we show that the primordial bispectrum exhibits a large cosmological collider signal in the squeezed limit, making the double massive exchanges interesting channels for the detection of massive primordial fields. We propose to decisively disentangle double-exchange channels from single-exchange ones with cosmological observations by exploiting the phase information of the cosmological collider signal, the inflationary flavor oscillations from multiple fields’ species exchanges and the double soft limit in the primordial trispectrum.

South Korea

Shuntaro Aoki

Japan

Fumiya Sano

Masahide Yamaguchi

Yuhang Zhu

Cosmological correlators with double massive exchanges: bootstrap equation and phenomenology

The in-in formalism provides a way to systematically organize the calculation of primordial correlation functions. Although its theoretical foundations are now firmly settled, the treatment of total time derivative interactions, incorrectly trivialized as “boundary terms”, has been the subject of intense discussions and conceptual mistakes. In this work, we demystify the use of total time derivatives — as well as terms proportional to the linear equations of motion — and show that they can lead to artificially large contributions cancelling at different orders of the in-in operator formalism. We discuss the treatment of total time derivative interactions in the Lagrangian path integral formulation of the in-in perturbation theory, and we showcase the importance of interaction terms proportional to linear equations of motion. We then provide a new route to the calculation of primordial correlation functions, which avoids the generation of total time derivatives, by working directly at the level of the full Hamiltonian in terms of phase-space variables. Instead of integrating by parts, we perform canonical transformations to simplify interactions. We explain how to retrieve correlation functions of the initial phase-space variables from the knowledge of the ones after canonical transformations. As an important first application, we find the explicit sizes of Hamiltonian cubic interactions in single-field inflation with canonical kinetic terms and for any background evolution, straight in terms of the primordial curvature perturbation and its canonical conjugate momentum, as well as the corresponding ones in the tensor sector, and the ones mixing scalars and tensors. We also briefly comment on quartic interactions. Our results are important for performing complete calculations of exchange diagrams in inflation, such as the (scalar and tensor) exchange trispectrum and the one-loop power spectrum. Being already written in a form amenable to characterize quantum properties of primordial fluctuations, they also promise to shed light on the non-linear dynamics of quantum states during inflation.

United States

Matteo Braglia

No time to derive: unraveling total time derivatives in in-in perturbation theory

We make use of Borel resummation to extract the exact time dependence from the divergent series found in the context of stochastic inflation. Correlation functions of self-interacting scalar fields in de Sitter spacetime are known to develop secular IR divergences via loops, and the first terms of the divergent series have been consistently computed both with standard techniques for curved spacetime quantum field theory and within the framework of stochastic inflation. We show that Borel resummation can be used to interpret the divergent series and to correctly infer the time evolution of the correlation functions. In practice, we adopt a method called Borel-Padé resummation where we approximate the Borel transformation by a Padé approximant. We also discuss the singularity structures of Borel transformations and mention possible applications to cosmology.

Masazumi Honda

Ryusuke Jinno

Koki Tokeshi

Borel resummation of secular divergences in stochastic inflation

Inflationary scenarios motivated by high-energy physics generically contain a plethora of degrees of freedom beyond the primordial curvature perturbation. The latter interacts in a simple way with what we name “inflationary flavor eigenstates,” which differ, in general, from freely propagating “mass eigenstates.” We show that the mixing between these misaligned states results in new striking behaviors in the squeezed limit of the curvature perturbation three-point function, depending not only on the mass spectrum but also on the “mixing angles” of the theory. These results bring about a new perspective on the cosmological collider program: contrary to a widespread belief, the primordial signal needs not be dominated by the lightest extra degree of freedom. Instead, we show that it may display either modulated oscillations, a broken power law, or a transition from oscillations to a power law, thus offering a detailed cosmic spectroscopy of the particle content of inflation.

Inflationary flavor oscillations and the cosmic spectroscopy

Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit here by studying the primordial bispectrum in a general two-field model. Our main result is the complete cubic action for inflationary fluctuations written in comoving gauge, i.e. in terms of the curvature perturbation and the entropic mode. Although full expressions for the cubic action have already been derived in terms of fields fluctuations in the flat gauge, their applicability is mostly restricted to numerical evaluations. Our form of the action is instead amenable to several analytical approximations, as our calculation in terms of the directly observable quantity makes manifest the scaling of every operator in terms of the slow-roll parameters, what is essentially a generalization of Maldacena’s single-field result to non-canonical two-field models. As an important application we derive the single-field effective field theory that is valid when the entropic mode is heavy and may be integrated out, underlining the observable effects that derive from a curved field space.

Sebastian Garcia-Saenz

Revisiting non-Gaussianity in multifield inflation with curved field space

Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly nongeodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble scales, and to their exponential amplification. Supported by first-principles numerical computations, and by the analytical insight provided by the effective field theory of inflation, we show that the bispectrum is enhanced in flattened configurations, and we argue that an analogous result holds for all higher-order correlation functions. These “hyper-non-Gaussianities” thus provide powerful model-independent constraints on nonstandard inflationary attractors motivated by the search for ultraviolet completions of inflation.