arXiv subjects

Paolo Creminelli

Publications and source records attributed to Paolo Creminelli.

At least 19 recordsLinked to original sources

arXiv2026

On the Asymptotic Causal Structure in Gravitational EFTs

It is usually assumed that a healthy EFT should not allow superluminal propagation. In the presence of gravity, however, the notion of superluminality becomes subtle, since there is no invariant way to compare with an underlying Minkowski light cone. One can instead resort to an asymptotic criterion: whether the EFT can induce signal propagation faster than what allowed by the asymptotic structure of spacetime. In this work we study the asymptotic causal structure of gravitational EFTs by analysing signal propagation in black-hole backgrounds in the presence of higher-derivative operators. We show that in spacetime dimensions D>4 the effective light cones can lead to genuine asymptotic superluminality, which can be used to constrain the regime of validity of the EFT. By contrast, in D=4 the asymptotic causal structure is universally identical to that of Schwarzschild: prompt null curves remain insensitive to higher-derivative corrections and no asymptotic time advance is possible. We first study the representative operator $R_{\mu\nu\rho\sigma}F^{\mu\nu}F^{\rho\sigma}$, then show that this conclusion is true for any EFT, as it relies only on the asymptotic behaviour of the metric. Finally, we discuss two ways to define superluminality in D=4 spacetimes: introducing a covariant cut-off by putting the theory in an asymptotically-AdS background, or imposing a hard cut-off by working at finite distance.

hep-th↗

arXiv2025

Analyticity and positivity of Green's functions without Lorentz

We study the properties imposed by microcausality and positivity on the retarded two-point Green's function in a theory with spontaneous breaking of Lorentz invariance. We assume invariance under time and spatial translations, so that the Green's function $G$ depends on $\omega$ and $\vec k$. We discuss that in Fourier space microcausality is equivalent to the analyticity of $G$ when $\Im (\omega,\vec k)$ lies in the forward light-cone, supplemented by bounds on the growth of $G$ as one approaches the boundaries of this domain. Microcausality also implies that the imaginary part of $G$ (its spectral density) cannot have compact support for real $(\omega,\vec k)$. Using analyticity, we write multi-variable dispersion relations and show that the spectral density must satisfy a family of integral constraints. Analogous constraints can be applied to the fluctuations of the system, via the fluctuation-dissipation theorem. A stable physical system, which can only absorb energy from external sources, satisfies $\omega \cdot \Im G(\omega,\vec k) \ge 0$ for real $(\omega,\vec k)$. We show that this positivity property can be extended to the complex domain: $\Im [\omega\, G(\omega,\vec k)] >0$ in the domain of analyticity guaranteed by microcausality. Functions with this property belong to the Herglotz-Nevanlinna class. This allows to prove the analyticity of the permittivities $\epsilon(\omega,k)$ and $\mu^{-1}(\omega,k)$ that appear in Maxwell equations in a medium. We verify the above properties in several examples where Lorentz invariance is broken by a background field, e.g. non-zero chemical potential, or non-zero temperature. We study subtracted dispersion relations when the assumption $G \to 0$ at infinity must be relaxed.

hep-th↗

arXiv2025

Large $n$-point Functions in Resonant Inflation

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 $\omega$ exceeds the naive cutoff of the theory, $4\pi f$. However, as noted by Hook and Rattazzi [2306.12489], 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 $3 \lesssim n \lesssim 9$ are potentially observable. In this regime, the signal exhibits 350-1000 oscillations per decade in $k$.

astro-ph.CO↗

arXiv2024

Non-analyticity of the $S$-matrix with spontaneously broken Lorentz invariance

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.

hep-th↗

arXiv2024

The Memory of Primordial Gravitational Waves

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 $\xi^i_{\rm late} = \frac{a_{\rm late}}{a_{\rm early}} (\delta^i_j -\frac12 \bar h^i_j)\xi^j_{\rm early}$. Therefore, the deformation of an initial spherical shell does not depend on the cosmological evolution, but only on the primordial value $\bar h^i_{j}$ 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.

gr-qc↗

arXiv2024

Positivity bounds on electromagnetic properties of media

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 $\varepsilon(ω,|\boldsymbol{k}|)$ and $μ(ω,|\boldsymbol{k}|)$. Microcausality implies analyticity of the retarded Green's functions when the imaginary part of the $4$-vector $(ω,\boldsymbol{k})$ 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, $\varepsilon(0,0)$ and $μ(0,0)$. In particular the quantities $\varepsilon(0,0)-1$ and $\varepsilon(0,0) - 1/μ(0,0)$ 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.

hep-th↗

arXiv2024

Non-perturbative Wavefunction of the Universe in Inflation with (Resonant) Features

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 $Ψ[ζ(\boldsymbol{x})]$ 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| \gtrsim α^{-2}$, where $α\gg 1$ 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.

hep-th↗

arXiv2023

Dissipative Inflation via Scalar Production

We describe a new mechanism that gives rise to dissipation during cosmic inflation. In the simplest implementation, the mechanism requires the presence of a massive scalar field with a softly-broken global $U(1)$ symmetry, along with the inflaton field. Particle production in this scenario takes place on parametrically sub-horizon scales, at variance with the case of dissipation into gauge fields. Consequently, the backreaction of the produced particles on the inflationary dynamics can be treated in a \textit{local} manner, allowing us to compute their effects analytically. We determine the parametric dependence of the power spectrum which deviates from the usual slow-roll expression. Non-Gaussianities are always sizeable whenever perturbations are generated by the noise induced by dissipation: $f_{\rm NL}^{\rm eq} \gtrsim {O}(10)$.

hep-th↗

arXiv2022

Positivity bounds on effective field theories with spontaneously broken Lorentz invariance

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.

hep-th↗

arXiv2021

Beyond Perturbation Theory in Inflation

Inflationary perturbations are approximately Gaussian and deviations from Gaussianity are usually calculated using in-in perturbation theory. This method, however, fails for unlikely events on the tail of the probability distribution: in this regime non-Gaussianities are important and perturbation theory breaks down for $|ζ| \gtrsim |f_{\rm \scriptscriptstyle NL}|^{-1}$. In this paper we show that this regime is amenable to a semiclassical treatment, $\hbar \to 0$. In this limit the wavefunction of the Universe can be calculated in saddle-point, corresponding to a resummation of all the tree-level Witten diagrams. The saddle can be found by solving numerically the classical (Euclidean) non-linear equations of motion, with prescribed boundary conditions. We apply these ideas to a model with an inflaton self-interaction $\propto λ\dotζ^4$. Numerical and analytical methods show that the tail of the probability distribution of $ζ$ goes as $\exp(-λ^{-1/4}ζ^{3/2})$, with a clear non-perturbative dependence on the coupling. Our results are relevant for the calculation of the abundance of primordial black holes.

hep-th↗

arXiv2020

Hairy Black-holes in Shift-symmetric Theories

Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current $J^2$ diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since $J^2$ is not a scalar quantity, since $J^μ$ is not a diff-invariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function $G_5 \sim \log X$. In this case the shift-symmetry current is diff-invariant, but contains powers of $X$ in the denominator, so that its divergence at the horizon is again immaterial. We confirm that other hairy solutions in the presence of non-analytic Horndeski functions are pathological, featuring divergences of physical quantities as soon as one departs from time-independence and spherical symmetry. We generalise the no-hair theorem to Beyond Horndeski and DHOST theories, showing that the coupling with Gauss-Bonnet is necessary to have hair.

hep-th↗

arXiv2020

Dark-Energy Instabilities induced by Gravitational Waves

We point out that dark-energy perturbations may become unstable in the presence of a gravitational wave of sufficiently large amplitude. We study this effect for the cubic Horndeski operator (braiding), proportional to $α_{\rm B}$. The scalar that describes dark-energy fluctuations features ghost and/or gradient instabilities for gravitational-wave amplitudes that are produced by typical binary systems. Taking into account the populations of binary systems, we conclude that the instability is triggered in the whole Universe for $|α_{\rm B} |\gtrsim 10^{-2}$, i.e. when the modification of gravity is sizeable. The instability is triggered by massive black-hole binaries down to frequencies corresponding to $10^{10}$ km: the instability is thus robust, unless new physics enters on even longer wavelengths. The fate of the instability and the subsequent time-evolution of the system depend on the UV completion, so that the theory may end up in a state very different from the original one. The same kind of instability is present in beyond-Horndeski theories for $|α_{\rm H}| \gtrsim 10^{-20}$. In conclusion, the only dark-energy theories with sizeable cosmological effects that avoid these problems are $k$-essence models, with a possible conformal coupling with matter.

gr-qc↗

arXiv2020

A de Sitter no-hair theorem for 3+1d Cosmologies with isometry group forming 2-dimensional orbits

We study, using Mean Curvature Flow methods, 3+1 dimensional cosmologies with a positive cosmological constant, matter satisfying the dominant and the strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces that are the closed orbits of a symmetry group. If these surfaces have non-positive Euler characteristic (or in the case of 2-spheres, if the initial 2-spheres are large enough) and also if the initial spatial slice is expanding everywhere, then we prove that asymptotically the spacetime becomes physically indistinguishable from de Sitter space on arbitrarily large regions of spacetime. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations.

hep-th↗

arXiv2020

Asymptotic Behavior of Cosmologies with $Λ>0$ in 2+1 Dimensions

We study, using Mean Curvature Flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler characteristic and are initially expanding everywhere, then we prove that the spatial slices reach infinite volume, asymptotically converge on average to de Sitter and they become, almost everywhere, physically indistinguishable from de Sitter. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations and the formation of black holes.

hep-th↗

arXiv2019

Resonant Decay of Gravitational Waves into Dark Energy

We study the decay of gravitational waves into dark energy fluctuations $π$, taking into account the large occupation numbers. We describe dark energy using the effective field theory approach, in the context of generalized scalar-tensor theories. When the $m_3^3$ (cubic Horndeski) and $\tilde m_4^2$ (beyond Horndeski) operators are present, the gravitational wave acts as a classical background for $π$ and modifies its dynamics. In particular, $π$ fluctuations are described by a Mathieu equation and feature instability bands that grow exponentially. Focusing on the regime of small gravitational-wave amplitude, corresponding to narrow resonance, we calculate analytically the produced $π$, its energy and the change of the gravitational-wave signal. The resonance is affected by $π$ self-interactions in a way that we cannot describe analytically. This effect is very relevant for the operator $m_3^3$ and it limits the instability. In the case of the $\tilde m_4^2$ operator self-interactions can be neglected, at least in some regimes. The modification of the gravitational-wave signal is observable for $3 \times 10^{-20} \lesssim α_{\rm H} \lesssim 10^{-17}$ with a LIGO/Virgo-like interferometer and for $10^{-16} \lesssim α_{\rm H} \lesssim 10^{-10}$ with a LISA-like one.

gr-qc↗

arXiv2018

Gravitational Wave Decay into Dark Energy

We study the decay of gravitational waves into dark energy fluctuations $π$, through the processes $γ\to ππ$ and $γ\to γπ$, made possible by the spontaneous breaking of Lorentz invariance. Within the EFT of Dark Energy (or Horndeski/beyond Horndeski theories) the first process is large for the operator $\frac12 \tilde m_4^2(t) \, δg^{00}\, \left( {}^{(3)}\! R + δK_μ^νδK^μ_ν-δK^2 \right)$, so that the recent observations force $\tilde m_4 =0$ (or equivalently $α_{\rm H}=0$). This constraint, together with the requirement that gravitational waves travel at the speed of light, rules out all quartic and quintic GLPV theories. Additionally, we study how the same couplings affect the propagation of gravitons at loop order. The operator proportional to $\tilde m_4^2$ generates a calculable, non-Lorentz invariant higher-derivative correction to the graviton propagation. The modification of the dispersion relation provides a bound on $\tilde m_4^2$ comparable to the one of the decay. Conversely, operators up to cubic Horndeski do not generate sizeable higher-derivative corrections.

astro-ph.CO↗

arXiv2018

Light Particles with Spin in Inflation

The existence of light particles with spin during inflation is prohibited by the Higuchi bound. This conclusion can be evaded if one considers states with a sizeable coupling with the inflaton foliation, since this breaks the de Sitter isometries. The action for these states can be constructed within the Effective Field Theory of Inflation, or using a CCWZ procedure. Light particles with spin have prescribed couplings with soft inflaton perturbations, which are encoded in consistency relations. We study the phenomenology of light states with spin 2. These mix with the graviton changing the tensor power spectrum and can lead to sizeable tensor non-Gaussianities. They also give rise to a scalar bispectrum and trispectrum with a characteristic angle-dependent non-Gaussianity.

hep-th↗

arXiv2018

Dark Energy after GW170817 and GRB170817A

The observation of GW170817 and its electromagnetic counterpart implies that gravitational waves travel at the speed of light, with deviations smaller than a few $\times 10^{-15}$. We discuss the consequences of this experimental result for models of dark energy and modified gravity characterized by a single scalar degree of freedom. To avoid tuning, the speed of gravitational waves must be unaffected not only for our particular cosmological solution, but also for nearby solutions obtained by slightly changing the matter abundance. For this to happen the coefficients of various operators must satisfy precise relations that we discuss both in the language of the Effective Field Theory of Dark Energy and in the covariant one, for Horndeski, beyond Horndeski and degenerate higher-order theories. The simplification is dramatic: of the three functions describing quartic and quintic beyond Horndeski theories, only one remains and reduces to a standard conformal coupling to the Ricci scalar for Horndeski theories. We show that the deduced relations among operators do not introduce further tuning of the models, since they are stable under quantum corrections.

astro-ph.CO↗