Sébastien Renaux-Petel

A bstract: In this work, we build a novel frequency-momentum space for ( d + 1)-dimensional de Sitter (dS) correlators from first principles. This construction follows directly from the decomposition into unitary irreducible representations (UIRs) of the spacetime isometry group SO(1, d + 1). While the spatial momentum space is given by the standard d -dimensional Fourier transform, the frequency space arises from diagonalising the quadratic Casimir operator, leading to the ( d + 1)-dimensional Kontorovich-Lebedev-Fourier (KLF) transform. We show that square-integrable functions decompose only along the principal series, whereas more general functions can receive discrete contributions from other UIRs. Applying this framework to the bulk CFT two-point function reproduces its Källén-Lehmann representation. Using the path integral formulation, we derive the Feynman rules for in-in perturbation theory in KLF space, leading to the introduction of KLF-space correlators, which are simply related to late-time correlation functions through a reduction formula. Furthermore, the KLF-space formulation sheds light on the simple mathematical structure of perturbative computations. In particular, the propagators take the form of simple rational functions, and tree-level diagrams can be written as spectral integrals over known meromorphic functions, as demonstrated in the example of the single-exchange four-point function. At the loop level, we show, through the example of the self-energy correction to the scalar propagator, that the group-theoretical nature of the construction allows the momentum integral to be recast as an orthogonality relation among SO(1, d + 1) Clebsch-Gordan coefficients.

Scalar-induced gravitational waves (SIGWs) provide a powerful probe of inflationary dynamics on scales far smaller than those accessible to the cosmic microwave background and large-scale structure. In scenarios with a transient ultraslow-roll phase, the curvature power spectrum can be strongly enhanced on small scales, potentially generating an observable stochastic GW background. In this regime, scalar dynamics during inflation can become nonlinear, challenging the validity of standard perturbative predictions. Existing semianalytical calculations of SIGWs rely on the linear evolution of inflation fluctuations. In this work, we compute SIGWs from USR inflation using lattice simulations. We evolve the inflaton field nonlinearly during inflation and extract the curvature perturbation nonperturbatively, then simulate its postreheating horizon reentry by evolving the Newtonian potential linearly while retaining the full non-Gaussian structure of the initial conditions for the primordial fluctuations in the tensor source. For moderate non-Gaussianity, the semianalytical prediction captures the correct order of magnitude of the GW signal but receives important corrections. When inflationary non-Gaussianities are large, it can fail dramatically in both amplitude and spectral shape, independently of the overall size of the tensor power spectrum. Our results show that reliable predictions of SIGWs in such scenarios require nonperturbative control of the inflationary scalar dynamics. The code used for this work is available here.

We investigate a qualitatively new regime of inflationary models with small and rapid oscillations in the potential — resonant non-Gaussianity. In contrast to the standard scenario, where most of the observable information is encoded in the power spectrum, in this regime the oscillatory signal predominantly appears in higher-order correlation functions with large n . This behavior emerges when the oscillation frequency ω exceeds the naive cutoff of the theory, 4 π f . However, as noted by Hook and Rattazzi [1], the actual cutoff is somewhat higher — though only logarithmically — when the amplitude of the oscillations is small. We identify a phenomenologically relevant window in which n -point functions with 3 ≲ n ≲ 9 are potentially observable. In this regime, the signal exhibits 350–1000 oscillations per decade in k .

We study loop corrections in the effective field theory of inflation with imaginary speed of sound, which has been shown to provide an effective description of multi-field inflationary models characterized by strongly non-geodesic motion and heavy entropic perturbations. We focus on the one-loop corrections to the scalar and tensor power spectra, taking into account all relevant vertices at leading order in derivatives and in slow-roll. We find a power-law dependence of the scalar two-point function on the scale that defines the range of validity of the effective theory, analogous to the enhancement observed in tree-level correlation functions. Even more dramatic, the relative correction to the tensor spectrum is exponentially enhanced, albeit also suppressed in the slow-roll limit. In spite of these large effects, our results show that this class of models can satisfy the requirement of perturbative control and a consistent loop expansion within a range of parameters of phenomenological interest. On the other hand, models predicting large values of the power spectrum on small scales are found to be under strong tension. As a technical bonus, we carefully explain the prescription for the regularization and manipulation of loop integrals in this set-up, where one has a non-trivial domain of integration for time and momentum integrals owing to the regime of validity of the effective field theory. This procedure is general enough to be of potential applicability in other contexts.

Cosmological correlators offer a remarkable window into the high-energy physics governing Universe's earliest moments, with the tantalising prospect of discovering new particles. However, extracting new physics from these observables requires both precise theoretical predictions of inflationary theories and accurate, analytical templates suitable for data analysis throughout parameter and kinematic spaces. In this paper, we extend the current analytical results by computing the most general boost-breaking seed correlator mediated by the tree-level exchange of a massive spinning particle. We derive the result using two complementary approaches, bootstrapping from boundary differential equations, and direct spectral integration. Both representations are packaged as a single partially resummed series that converges in all physical kinematics. Computing this correlator marks a milestone for carving out the space of all boost-breaking correlators, and therefore completes the tree-level catalogue. We then introduce a general procedure to obtain accurate approximations for cosmological collider signals based on the saddle-point method. This approach allows for a clear physical intuition of various signals hidden in correlators, as the bulk physics is made manifest through the location of these saddles in the complex time plane, which depend on the external kinematics. Evaluating the time integrals at these saddles yields results given as elementary functions that remain valid beyond soft limits and provide intuitive control over both the signal shape and amplitude. We demonstrate the power of this method in both de Sitter-invariant and boost-breaking scenarios, and uncover novel refined waveform and strength dependence for oscillatory signals from massive fields. We provide a complete cosmological collider shape template capturing all boost-breaking effects for upcoming cosmological surveys.

Many early universe scenarios predict an enhancement of scalar perturbations at scales currently unconstrained by cosmological probes. These perturbations source gravitational waves (GWs) at second order in perturbation theory, leading to a scalar-induced gravitational wave (SIGW) background. The LISA detector, sensitive to mHz GWs, will be able to constrain curvature perturbations in a new window corresponding to scales k ∈ [10¹⁰, 10¹⁴] Mpc^-1, difficult to probe otherwise. In this work, we forecast the capabilities of LISA to constrain the source of SIGWs using different approaches: i) agnostic, where the spectrum of curvature perturbations is binned in frequency space; ii) template-based, modeling the curvature power spectrum based on motivated classes of models; iii) ab initio, starting from first-principles model of inflation featuring an ultra-slow roll phase. We compare the strengths and weaknesses of each approach. We also discuss the impact on the SIGW spectrum of non-standard thermal histories affecting the kernels of SIGW emission and non-Gaussianity in the statistics of the curvature perturbations. Finally, we propose simple tests to assess whether the signal is compatible with the SIGW hypothesis. The pipeline used is built into the SIGWAY code.

The time evolution of primordial fluctuations conceals a wealth of insights into the high-energy physics at play during the earliest moments of our Universe, which is ultimately encoded in late-time spatial correlation functions. However, the conventional procedure to compute them is technically challenging, and a complete dictionary mapping the landscape of inflationary theories and the corresponding observable signatures is not yet available. In this paper, we develop a framework to compute tree-level cosmological correlators based on following their time evolution from their origin as quantum zero-point fluctuations to the end of inflation. From first principles, the structure of the bulk time evolution imposes a set of universal differential equations in time satisfied by equal-time correlators. We automatise the process of systematically solving these equations. This allows us to accurately capture all physical effects and obtain exact results in theories formulated at the level of inflationary fluctuations that include any number of degrees of freedom with arbitrary dispersion relations and masses, coupled through any time-dependent interactions. We then illustrate the power of this formalism by exploring the phenomenology of cosmological correlators emerging from the interaction with a massive scalar field. After an extensive analysis of the quadratic theory and classifying perturbativity bounds, we study both the size and the shape dependence of non-Gaussianities in the entire parameter space, including the strong mixing regime. We present novel characteristics of cosmological collider signals in (would be) single-, double-, and triple-exchange three-point correlators. In the presence of primordial features, after subtracting gauge artefacts unavoidably generated by a breaking of scale-invariance, we show that soft limits of cosmological correlators offer a new possibility to probe the inflationary landscape. Finally, we provide templates to search for in future cosmological surveys.

Various scenarios of cosmic inflation enhance the amplitude of the stochastic gravitational wave background (SGWB) at frequencies detectable by the LISA detector. We develop tools for a template-based analysis of the SGWB and introduce a template databank to describe well-motivated signals from inflation, prototype their template-based searches, and forecast their reconstruction with LISA. Specifically, we classify seven templates based on their signal frequency shape, and we identify representative fundamental physics models leading to them. By running a template-based analysis, we forecast the accuracy with which LISA can reconstruct the template parameters of representative benchmark signals, with and without galactic and extragalactic foregrounds. We identify the parameter regions that can be probed by LISA within each template. Finally, we investigate how our signal reconstructions shed light on fundamental physics models of inflation: we discuss their impact for measurements of e.g., the couplings of inflationary axions to gauge fields; the graviton mass during inflation; the fluctuation seeds of primordial black holes; the consequences of excited states during inflation, and the presence of small-scale spectral features.