Paolo Creminelli

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 .

Primordial gravitational waves, after they enter the horizon and decay away, leave a residual displacement in test particles: a memory, in analogy with gravitational waves generated by astrophysical sources. The late-time distance between test particles is related to the one at early times by [ ]. Therefore, the deformation of an initial spherical shell does not depend on the cosmological evolution, but only on the primordial value [ ] of the gravitational wave. The memory is thus related to the adiabatic tensor mode that maps the unperturbed FLRW geometries at early and late times; this is analogous to the relation between memory in Minkowski spacetime and the BMS group. The primordial memory is also connected to the consistency relations of cosmological correlators, as the flat-space memory is related to the soft theorems for gravitational wave emission. We comment on the signature of the effect on the CMB B-modes and on the large-scale structure. There is also a primordial memory effect that is subleading in the spatial gradients of the wave: it is encoded in the rotation of free-falling gyroscopes. To the memory of Valery A. Rubakov. Contribution to the special issue of the International Journal of Modern Physics A.

A bstract: We study the constraints imposed on the electromagnetic response of general media by microcausality (commutators of local fields vanish outside the light cone) and positivity of the imaginary parts (the medium can only absorb energy from the external field). The equations of motion for the average electromagnetic field in a medium — the macroscopic Maxwell equations — can be derived from the in-in effective action and the effect of the medium is encoded in the electric and magnetic permeabilities ε ( ω , | k |) and μ ( ω , | k |). Microcausality implies analyticity of the retarded Green’s functions when the imaginary part of the 4-vector ( ω , k ) lies in forward light cone. With appropriate assumptions about the behavior of the medium at high frequencies one derives dispersion relations, originally studied by Leontovich. In the case of dielectrics these relations, combined with the positivity of the imaginary parts, imply bounds on the low-energy values of the response, ε (0, 0) and μ (0, 0). In particular the quantities ε (0, 0) – 1 and ε (0, 0) – 1/ μ (0, 0) are constrained to be positive and equal to integrals over the imaginary parts of the response. We discuss various improvements of these bounds in the case of non-relativistic media and with additional assumptions about the UV behavior.

We study the S-matrix of Goldstones in the renormalizable theory of a U(1) complex scalar at finite charge, i.e. in a state that breaks Lorentz invariance. The theory is weakly coupled so that this S-matrix exists at all energies. Unlike the Lorentz invariant case, the resulting S-matrix is not analytic in the exchanged (complexified) four-momentum. The non-analyticities stem from the LSZ reduction formula, as a consequence of the energy-dependent mixing between the radial and Goldstone modes.

We study the statistics of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential (resonant non-Gaussianity). We do so by deriving the wavefunction Ψ[ζ( x )] non-perturbatively in ζ, but at first order in the amplitude of the oscillations. The expression of the wavefunction of the universe (WFU) is explicit and does not require solving partial differential equations. One finds qualitative deviations from perturbation theory for |ζ| ≳ α ⁻², where α ≫ 1 is the number of oscillations per Hubble time. Notably, the WFU exhibits distinct behaviours for negative and positive values of ζ (troughs and peaks respectively). While corrections for ζ < 0 remain relatively small, of the order of the oscillation amplitude, positive ζ yields substantial effects, growing exponentially as e ^πα/2 in the limit of large ζ. This indicates that even minute oscillations give large effects on the tail of the distribution.

We derive positivity bounds on EFT coefficients in theories where boosts are spontaneously broken. We employ the analytic properties of the retarded Green’s function of conserved currents (or of the stress-energy tensor) and assume the theory becomes conformal in the UV. The method is general and applicable to both cosmology and condensed matter systems. As a concrete example, we look at the EFT of conformal superfluids which describes the universal low-energy dynamics of CFT’s at large chemical potential and we derive inequalities on the coefficients of the operators, in three dimensions, at NLO and NNLO.