arXiv subjects

Jean Alexandre

Publications and source records attributed to Jean Alexandre.

At least 19 recordsLinked to original sources

arXiv2026

Wilsonian Cosmology: de Sitter (in)Stability

We develop a (Wilsonian) functional-renormalisation-group framework for scalar cosmology in which quantum fluctuations of a scalar field are coarse-grained on cosmological spacelike hypersurfaces. Integrating out quantum fluctuations with wavelengths smaller than the Hubble radius $H(t)^{-1}$, we obtain an effective scalar potential $U(\phi(t),H(t))$ that evolves in time. We derive a non-perturbative flow equation for this potential, together with the coupled set of (modified) Friedmann equations. We then apply this formalism to the simplest possible case of a de Sitter vacuum when the scalar field is at rest, in two situations which satisfy exactly our flow equation: $(i)$ A flat potential, for which we find that the only pure de Sitter solution is unstable and corresponds to a saddle point. $(ii)$ A quadratic potential with curvature $m^2>0$, for which we find that the presence of the mass term stabilises the system. The latter case leads to a de Sitter attractor either at the Hubble scale when the mass is larger than the Hubble scale at initial time, or by introducing a new attractor located at $H=m$ in the case the mass is smaller, which may be particularly relevant to the phenomenological study of dark energy and inflation theories.

hep-th↗

arXiv2026

Magnetic-monopole resummation justifies perturbatively calculated collider production cross sections

A one-loop resummation scheme, inspired by Dyson-Schwinger (DS) formalism of strongly coupled quantum field theories, is applied to spin-1/2 magnetic monopoles (MMs), in the context of an effective field theory (EFT), invariant under the gauge group U(1)_em x U(1)', where U(1)' is a dual strongly coupled Abelian interaction, associated with a "dark photon". The latter leads to a MM appearing as a limiting case of a "dyon", with a tiny "electric charge", compensated by a huge wave-function renormalization of the MM, thereby leading to a finite renormalized MM-photon coupling. An ultra-violet fixed point structure is found in the resummed theory, which is purely non-perturbative due to different boundary conditions of the resummation equations, compared to the weak coupling (perturbative) case. The renormalized coupling of the MM to the electromagnetic photon in the fixed-point theory is identified with the magnetic charge, compatible with the Dirac quantization condition. This provides for the first time a formal justification of the use of tree-level Drell-Yan and photon-fusion MM production processes in collider searches, and of the corresponding cross sections and MM mass bounds thereof. The latter provide a means to constrain the resummed-EFT parameters experimentally. The DS resummation applies here primarily to elementary MMs. However, this approach may also be applied to the last stage (collapse) of the formation of composite MM pairs at colliders, in case they behave as quantum excitations, with their core radius comparable to the Compton wavelength, thereby avoiding the extreme suppression of their production.

hep-ph↗

arXiv2025

Mass and entropy of asymptotically flat eternal quantum black holes in 2D

Semi-classical dilaton gravity in (1+1)-dimensions remains one of the only arenas where quantum black holes can be exactly constructed, fully accounting for backreaction due to quantum matter. Here we provide a comprehensive analysis of the mass and thermodynamic properties of static asymptotically flat quantum black holes both analytically and numerically. First, we analytically investigate eternal quantum black hole solutions to a one-parameter family of analytically solvable models interpolating between Russo-Susskind-Thorlacius and Bose, Parker, and Peleg gravities. Examining these models in a semi-classically allowed parameter space, we find naked singularities may exist for quantum fields in the Boulware state. Using a quasi-local formalism, where we confine the black hole to a finite sized cavity, we derive the conserved energy and analyze the system's thermal behavior. Specifically, we show the semi-classical Wald entropy precisely equals the generalized entropy, accounting for both gravitational and fine grained matter entropies, and we find a range where the quantum black holes are thermally stable. Finally, we numerically construct eternal black hole solutions to semi-classical Callan-Giddings-Harvey-Strominger gravity and find their thermal behavior is qualitatively different from their analytic counterparts. In the process, we develop an analytic expansion of the solutions and find it accurately approximates the full numerical solutions in the semi-classical limit.

gr-qc↗

arXiv2025

Exact Renormalisation Group Evolution of the Inflation Dynamics: Reconciling $\alpha$-Attractors with ACT

We present a non-perturbative framework for the dynamics of slow-roll inflation that consistently incorporates quantum corrections, based on an alternative functional renormalisation group (RG) approach. We derive the coupled Friedmann-RG flow equations governing the joint evolution of spacetime, the inflaton field, and its effective potential. Applying this formalism to $\alpha$-attractor E-models, we find that the RG flow induces a dynamical destabilisation of the inflationary trajectory, leading to a premature termination of slow roll. Remarkably, the resulting predictions bring $\alpha$-attractors into full agreement with the latest ACT data without introducing new physics beyond a consistent quantum-corrected treatment of the inflaton dynamics.

hep-th↗

arXiv2025

Flavour interferometry in Reissner-Nordstrom background

We derive the phase acquired by a neutral scalar particle propagating along Reissner-Nordstrom geodesics. Considering two flavours propagating on different trajectories which intersect, we plot the interference pattern induced by gravitational lensing from the charged compact object. Although the effect of the charge is subdominant in the metric, it proves to be significant in the phase, and shifts the interference pattern, compared to the Schwarzschild case. This pattern is characterised by two oscillation lengths which, if known, would allow the determination of both eigen masses independently.

gr-qc↗

arXiv2024

Impact of resummation on the production and experimental bounds of scalar high-electric-charge objects

A one-loop Dyson-Schwinger-like resummation scheme is applied to scalar High-Electric-Charge compact Objects (HECOs), extending previous work on spin-1/2 case. The electromagnetic interactions of HECOs are considered within the framework of strongly coupled scalar Quantun Electrodynamics. The resummation amounts to determining non-trivial ultraviolet (UV) fixed points, at which the effective Lagrangian, which will lead to the pertinent predictions on the cross sections, is computed. In contrast to the fermionic HECO case, in which the fixed point structure was determined solely by the interactions of the HECOs with the photon field, in the scalar case the existence of non-trivial UV fixed points requires the presence of additional strong self interactions among the HECOs. Our resummation scheme, which is notably different from a lattice strong-coupling approach, makes the computation of the pertinent scalar-HECO-production cross sections reliable, thus allowing revisiting the mass bounds obtained from searches for such objects in current or future colliders. Our MadGraph implementation of the results leads to enhanced (up to ~30%) lower bounds on the mass of scalar HECOs, as compared to those extracted from the tree-level processes typically used in LHC collider searches by ATLAS and MoEDAL experiments.

hep-ph↗

arXiv2024

Revisiting experimental mass limits on HECOs using Dyson-Schwinger resummation

High-Electric-Charge compact Objects (HECOs) appear in several theoretical particle physics models beyond the Standard Model, and are actively searched for in current colliders, such as the Large Hadron Collider (LHC). In such searches, mass bounds of these objects have been placed, using Drell-Yan and Photon-Fusion processes at tree level so far. However, such estimates are not reliable, given that, as a result of the large values of the electric charge of the HECO, perturbative QED calculations break down. We present a Dyson-Schwinger-like resummation scheme, which allows for a large gauge coupling and thus makes the computation of the pertinent HECO-production cross sections reliable, thus allowing us to extract improved mass bounds for such objects from ATLAS and MoEDAL searches.

hep-ph↗

arXiv2024

Tunnelling and the Casimir effect on a $D$-dimensional sphere

Two fundamental signatures of Quantum Mechanics are tunnelling and the Casimir effect. We examine the ground state energetic properties of a scalar field confined on a $D$-dimensional sphere, and subjected to these two effects. We focus on $D=2$ and $D=3$, with a non-minimal coupling of a massless scalar field to curvature, which provides a radius-dependent effective mass. This scenario allows tunnelling to be more important than the Casimir effect, in a certain regime of parameters, and potential implications in Early Cosmology are discussed for the case $D=3$, which could avoid a cosmological singularity.

hep-th↗

arXiv2024

Piecewise linear potentials for false vacuum decay and negative modes

We study bounce solutions and associated negative modes in the class of piecewise linear triangular-shaped potentials that may be viewed as approximations of smooth potentials. In these simple potentials, the bounce solution and action can be obtained analytically for a general spacetime dimension $D$. The eigenequations for the fluctuations around the bounce are universal and have the form of a Schr\"odinger-like equation with delta-function potentials. This Schr\"odinger equation is solved exactly for the negative modes whose number is confirmed to be one. The latter result may justify the usefulness of such piecewise linear potentials in the study of false vacuum decay.

hep-ph↗

arXiv2024

Mapping 1+1-dimensional black hole thermodynamics to finite volume effects

Both black hole thermodynamics and finite volume effects in quantum field theory violate the null energy condition. Motivated by this, we compare thermodynamic features between two $1+1$-dimensional systems: (i) a scalar field confined to a periodic spatial interval of length $a$ and tunneling between two degenerate vacua; (ii) a dilatonic black hole at temperature $T$ in the presence of matter fields. If we identify $a\propto T^{-1}$, we find similar thermodynamic behaviour, which suggests some deeper connection arising from the presence of non-trivial boundary conditions in both systems. We then extend our results to $2+1$ and $3+1$-dimensions and, although a more complete study is necessary, the connection found in $1+1$-dimensions seems to be valid in higher dimensions too.

hep-th↗

arXiv2024

Double-well instantons in finite volume

Assuming a toroidal space with finite volume, we derive analytically the full one-loop vacuum energy for a scalar field tunnelling between two degenerate vacua, taking into account discrete momentum. The Casimir energy is computed for an arbitrary number of dimensions using the Abel-Plana formula, while the one-loop instanton functional determinant is evaluated using the Green's functions for the fluctuation operators. The resulting energetic properties are non-trivial: both the Casimir effect and tunnelling contribute to the Null Energy Condition violation, arising from a non-extensive true vacuum energy. We discuss the relevance of this mechanism to induce a cosmic bounce, requiring no modified gravity or exotic matter.

hep-th↗

arXiv2023

False vacuum decay rates, more precisely

We develop a method for accurately calculating vacuum decay rates beyond the thin-wall regime in a pure scalar field theory at the one-loop level of the effective action. It accounts for radiative effects resulting from quantum corrections to the classical bounce, including gradient effects stemming from the inhomogeneity of the bounce background. To achieve this, it is necessary to compute not only the functional determinant of the fluctuation operator in the background of the classical bounce but also its functional derivative evaluated at the classical bounce. The former is efficiently calculated using the Gel'fand-Yaglom method. We illustrate how the latter can also be calculated with the same method, combined with a computation of various Green's functions.

hep-ph↗

arXiv2023

Resummation schemes for high-electric-charge objects leading to improved experimental mass limits

High-Electric-Charge compact Objects (HECOs) appear in several theoretical particle physics models beyond the Standard Model, and are actively searched for in current colliders, such as the Large Hadron Collider at CERN. In such searches, mass bounds of these objects have been placed, using Drell-Yan and photon-fusion processes at tree level so far. However, such mass-bound estimates are not reliable, given that, as a result of the large values of the electric charge of the HECO, perturbative Quantum Electrodynamics calculations break down. In this work, we perform a Dyson-Schwinger resummation scheme (as opposed to lattice strong-coupling approach), which makes the computation of the pertinent HECO-production cross sections reliable, thus allowing us to extract improved mass bounds for such objects from ATLAS and MoEDAL searches.

hep-ph↗

arXiv2023

Tunnelling-induced cosmic bounce in the presence of anisotropies

If we imagine rewinding the universe to early times, the scale factor shrinks and the existence of a finite spatial volume may play a role in quantum tunnelling effects in a closed universe. It has recently been shown that such finite volume effects dynamically generate an effective equation of state that could support a cosmological bounce. In this work we extend the analysis to the case in which a (homogeneous) anisotropy is present, and identify a criteria for a successful bounce in terms of the size of the closed universe and the properties of the quantum field.

gr-qc↗

arXiv2023

Oscillation probabilities for a PT-symmetric non-Hermitian two-state system

There is growing interest in viable quantum theories with PT-symmetric non-Hermitian Hamiltonians, but a formulation of transition matrix elements consistent with positivity and perturbative unitarity has so far proved elusive. This Letter provides such a formulation, which relies crucially on the ability to span the state space in such a way that the interaction and energy eigenstates are orthonormal with respect to the same positive-definite inner product. We apply this non-Hermitian approach to two-neutrino flavour oscillations, and show how it can accommodate the seesaw mechanism.

quant-ph↗

arXiv2023

Cosmic bounce and phantom-like equation of state from tunnelling

We allow a scalar field on a flat FLRW background metric to tunnel between two degenerate vacua. The resulting true vacuum state then violates the Null Energy Condition, and the corresponding homogeneous fluid induces a bounce, after which it has a phantom-like equation of state and asymptotically leads to a de Sitter phase. The mechanism presented here requires no exotic matter or modified gravity, it is purely generated by quantum fluctuations and is valid for a generic double well potential.

hep-th↗

arXiv2023

Null energy condition violation: Tunnelling versus the Casimir effect

We show that tunnelling between two degenerate minima, as allowed in a finite volume, leads to a non-extensive symmetric ground state. This results in Null Energy Condition violation for sufficiently low temperatures, when a continuous set of momenta in the box containing the field is assumed. Taking into account discrete momenta can modify this picture and is achieved via the addition of the Casimir energy to the tunnelling-induced ground state energy. Focusing on zero-temperature, these non-trivial effects are found to compete, depending on the typical length scales involved.

hep-th↗

arXiv2022

Wilsonian approach to the interaction $\phi^2(i\phi)^\varepsilon$

We study the renormalisation of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction $\phi^2(i\phi)^\varepsilon$ using the Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalisable at the one-loop level only for integer values of $\varepsilon$, a result which is not yet established within the $\varepsilon$-expansion. Particular attention is therefore paid to the two interesting cases $\varepsilon=1,2$, and the one-loop beta functions for the coupling associated with the interaction $i\phi^3$ and $-\phi^4$ are computed. It is found that the $-\phi^4$ theory has asymptotic freedom in four-dimensional spacetime. Some general properties for the Euclidean partition function and $n$-point functions are also derived.

hep-th↗