arXiv subjects

Nathan Belrhali

Publications and source records attributed to Nathan Belrhali.

7 recordsLinked to original sources

arXiv2026

Analytical Cosmological Collider at Strong Mixing in Laplace Space

Primordial non-Gaussianities are at their largest when the curvature perturbation is coupled to a massive field by a mixing too strong to be treated perturbatively. We show that this regime, naturally reached in multifield inflation, is solved analytically by the Laplace-space representation we recently introduced, in which every mode becomes a superposition of plane waves weighted by a single kernel. The bispectrum then follows as a rapidly convergent series of elementary functions, in perfect agreement with independent numerical results. We find that the cosmological collider signal at strong mixing is larger than widely believed, with only half of the usual Boltzmann suppression. Its amplitude further grows with the number of time derivatives of the curvature perturbation in the interaction, singling out the most promising observational targets.

hep-th↗

arXiv2026

Cosmological Correlators in KLF and the Double-Exchange

In this work, we present the procedure to find series representations of tree-level cosmological correlators using the Kontorovich-Lebedev-Fourier (KLF) space formalism. This framework allows us to trade the in-in nested time integrals for frequency integrals over rational propagators and vertex functions, which encode interactions among quantum fields on a de Sitter background. Because these functions are the key objects to understand in order to perform a diagrammatic computation, we derive their relevant analytic properties by using both their integral representation and series representation in terms of Lauricella functions. For a vertex involving any number of fields, we obtain the location of singularities, the corresponding residues and the large-frequency asymptotic behaviour. Gathering these properties at each frequency integration allows us to compute a tree-level correlator directly, without relying on the differential equations it satisfies. To illustrate this procedure, we provide a complete treatment of the double-exchange diagram. The computation naturally distinguishes the different physical contributions, whether to the background or to the cosmological collider signal. The newly derived result is expressed at most in terms of a double series over hypergeometric functions, which simplifies the analytical expression of the correlator.

hep-th↗

arXiv2026

Laplace Space for Cosmological Correlators

Deep inside the horizon, every cosmological mode oscillates as a flat-space plane wave. A Laplace transform turns this fact into a general method: it resolves each curved-space mode into a superposition of plane waves dressed by a kernel that encodes the spacetime geometry, field content and dynamics, collapsing the time integrals onto flat-space ones. This provides simple diagrammatic rules that turn cosmological correlator diagrams into their flat-space counterparts integrated against Laplace-space kernels. On the paradigmatic massive single exchange, this integral representation makes the energy singularities manifest and evaluates in closed form as a single, rapidly convergent series valid throughout the kinematic domain, with no patching of separate expansions. The Laplace approach sheds conceptual and computational light on cosmological correlators in virtually any theory of the early universe.

hep-th↗

arXiv2026

Massive Cosmological Correlators from Flat Space: a Laplace-Space Approach

We develop a new approach to cosmological correlators, built on a simple physical fact: deep inside the Hubble radius every mode oscillates as a flat-space plane wave, the curvature of spacetime making itself felt only as the mode is stretched towards the horizon. A Laplace transform turns this observation into a computational tool, resolving each curved-space mode function into a continuous superposition of plane waves labelled by a dual variable and dressed by a kernel that encodes the spacetime geometry, field content and dynamics. Every time integral then reduces to an elementary flat-space one, yielding simple diagrammatic rules for cosmological correlators. We illustrate the construction on the massive single-exchange correlator. The Laplace representation makes its total- and partial-energy singularities transparent ''from flat space'', and yields a single closed-form, rapidly convergent series valid throughout the entire kinematic domain. Although developed for conformally coupled fields exchanging massive scalars in de Sitter, the approach carries over essentially unchanged to virtually all situations of interest in primordial cosmology.

hep-th↗

arXiv2026

De Sitter Momentum Space

We construct a natural and nonperturbative momentum space for quantum field theory on $(d+1)$-dimensional de Sitter (dS) spacetime in the Poincaré slicing, adapted to early Universe cosmology. In particular, we identify the dS frequency as the unitary-representation label of the dS isometry group $\mathrm{SO}(1, d+1)$. By diagonalizing the quadratic Casimir together with spatial translations, we provide a harmonic expansion of operators in what we call the Kontorovitch-Lebedev-Fourier (KLF) space. This momentum space shares many structural properties with its Minkowski counterpart, for instance: equations of motion reduce to algebraic equations, and the quadratic dynamics provides a simple propagator analogous to flat space. We reformulate the perturbative computation of in-in correlators in KLF momentum space, showing from first principles how time integrals turn into frequency-space integrals over meromorphic functions. We show how our construction streamlines computations, naturally accommodates the contributions from principal and complementary series in the Källén-Lehmann spectral decomposition of composite operators, and leads to a group-theoretical method to evaluate loop momentum integrals.

hep-th↗

arXiv2026

Kontorovich-Lebedev-Fourier Space for de Sitter Correlators

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 $\mathrm{SO}(1,d+1)$. 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 $\mathrm{SO}(1,d+1)$ Clebsch-Gordan coefficients.

hep-th↗

arXiv2024

Beam focusing and consequences for Doppler Backscattering measurements

The phenomenon of beam focusing of microwaves in a plasma near a turning-point caustic is discussed in the context of the analytical solution to the Gaussian beam-tracing equations in the 2D linear-layer problem. The location of maximum beam focusing and the beam width at that location are studied in terms of the beam initial conditions. The analytic solution is used to study the effect of this focusing on Doppler backscattering (DBS). We find that the filter function that characterises the scattering intensity contributions along the beam path through the plasma is inversely proportional to the beam width, predicting enhanced scattering contributions from the beam focusing region. We show that the DBS signal enhancement for small incident angles between the beam path and the density gradient is due to beam focusing and not due to forward scattering. The analytic beam model is used to predict the measurement of the $k_y$ density-fluctuation wavenumber power spectrum via DBS, showing that the spectral exponent of the turbulent, intermediate-to-high $k_y$ density-fluctuation spectrum might be quantitatively measurable via DBS, but not the spectral peak corresponding to the driving scale of the turbulent cascade.

physics.plasm-ph↗