arXiv subjects

Gerasimos Rigopoulos

Publications and source records attributed to Gerasimos Rigopoulos.

At least 19 recordsLinked to original sources

arXiv2025

Dynamical Dipolar Condensate Finite Temperature Stochastic Gross--Pitaevskii--Boltzmann Model

We formulate a generalized self-consistent stochastic quantum kinetic theory for finite-temperature ultracold Bose gases interacting via a generic long-range interaction, applicable to a broad range of systems, by means of Keldysh non-equilibrium field theory: such model is explicitly cast in the context of dipolar atomic gases, and is also shown to encompass established stochastic and kinetic treatments for ultracold atomic gases with local interactions as special cases. The condensate and low-lying modes are collectively described by a stochastic Gross-Pitaevskii equation with two collisional terms and their corresponding stochastic noise terms, with thermal particles dynamically modelled through a self-consistently coupled Quantum Boltzmann equation and dipolar interactions included by means of a coupled Poisson-like equation. Additional use of Bogoliubov-de Gennes analysis generating the Lee-Huang-Yang correction term relevant in the $T=0$ quantum-fluctuation-dominated regime, allows us to postulate the extension of such model offering a plausible scheme for interpolating between quantum-dominated and thermal-dominated fluctuation regimes, the consistency of which remains to be tested against experimental observations.

cond-mat.quant-gas↗

arXiv2025

Inflaton perturbations through an Ultra-Slow Roll transition and Hamilton-Jacobi attractors

We examine the behaviour of the gauge invariant scalar field perturbations in an analytic inflationary model that transitions from slow-roll to an ultra-slow-roll (USR) phase. We find that the numerical solution of the Mukhanov-Sasaki equation is well described by Hamilton-Jacobi (HJ) theory, as long as the appropriate branches of the Hamilton-Jacobi solutions are invoked: Modes that exit the horizon during the slow-roll phase evolve into the USR as described by the first HJ branch, up to a subdominant $\mathcal{O}(k^2/H^2)$ correction to the Hamilton-Jacobi prediction for their final amplitude that we compute, indicating the influence of neglected gradient terms. Modes that exit during the USR phase are described by a separate HJ branch once they become sufficiently superhorizon, obtained by the shift $\left(\epsilon_1,\epsilon_2\right) \simeq \left(0,-6+\Delta \right) \rightarrow \left(\tilde{\epsilon}_1,\tilde{\epsilon}_2\right)\simeq (0,-\Delta)$ and corresponding to a slow-roll solution (very close to de Sitter) supported by the same potential. This transition is similar to the conveyor belt concept put forward in our previous work [1] and suggests that the limit $\epsilon_2\rightarrow -6$ is unphysical as an asymptotic value for the background/long wavelength solution. We further discuss implications for the validity of the stochastic equations arising from the Hamilton-Jacobi formulation. Our work suggests that if Hamilton-Jacobi attractors are appropriately used, they can successfully describe the dynamics of long wavelength inflationary inhomogeneities for potentials with USR regions.

gr-qc↗

arXiv2025

Fuzzy dark matter halos with repulsive self-interactions: coherent soliton and halo vortex network with moderate self-coupling

We examine the impact of moderate repulsive self-interactions on fuzzy dark matter halos generated by merging smaller Gaussian density concentrations. We study the size of the core and the granules, the spatial dependence of the field's coherence, the turbulent vortex tangle and the oscillation frequency of the central soliton, covering the range from quantum-pressure-dominated to self-interaction-dominated stabilisation of the solitonic core. For the probed self-coupling strengths $g$ and with a fixed initial configuration, mergers with increasing $g$ result in cores with increased size and a reduced central density, oscillating with decreased frequency, in accordance with expectations from the study of isolated Self-interacting Fuzzy Dark Matter (SFDM) solitons. By contrast, the characteristic granule size and typical inter-vortex distances in the surrounding halo are only mildly affected, growing much less relative to the core. The total length of the vortex network, although less robust, shows no signs of decay over our simulation timescales. The generated halos therefore develop central self-interaction-dominated cores, but with the outer halos still supported by quantum-pressure and classical kinetic energy in equipartition as in the non-interacting case. Furthermore, measures of coherence of the field clearly separate the condensed core, identified via the Penrose-Onsager (largest eigenvalue) mode of the entire classical field, from the surrounding quasi-coherent halo. Unlike the $g=0$ case, we observe a relative increase of incoherent fluctuations coexisting with the coherent mode at the centre of the halo with increasing $g$, a phenomenon also observed in laboratory condensates at non-zero temperature.

astro-ph.CO↗

arXiv2025

Virialized Profiles and Oscillations of Self-interacting Fuzzy Dark Matter Solitons

We investigate the effect of self-interactions on the shape and oscillations of the solitonic core profile of condensed fuzzy dark matter systems without the backdrop of a halo, revealing universal features in terms of an appropriately scaled interaction strength characterizing the crossover between the weakly- and strongly-interacting regimes. Our semi-analytical results are further confirmed by spherically symmetric simulations of the Gross-Pitaevskii-Poisson equations. Inverting our obtained relations, we highlight a degeneracy that could significantly affect constraints on the boson mass in the presence of repulsive boson self-interactions and propose the simultaneous extraction of static and dynamical solitonic features as a way to uniquely constrain both the boson mass and self-interactions.

astro-ph.CO↗

arXiv2025

Dynamical reconstruction of SPARC galactic halos within self-interacting fuzzy dark matter

Fuzzy Dark Matter with non-zero quartic self-interaction (SFDM) is shown to be a viable model for simultaneously fitting 17 dark-matter-dominated galaxies from the SPARC database with a single $(m,g)$ point in the space of boson masses and self-coupling constants: $\log_{10}\left(m \,[\mathrm{eV}/c^2] \right) = \log_{10}(1.98)-22^{+0.8}_{-0.6}$ and $\log_{10}\left(g \, [\mathrm{eV \, m}^3/kg] \right) = \log_{10}(9.08)-10^{+0.4}_{-1.2}$. This is based on the combination of an appropriately constructed static super-Gaussian profile for the inner galactic core (`soliton') region, and a Navarro-Frenk-White profile for the surrounding halo region. The explicit identification of a non-zero interaction strength may resolve issues of inconsistent constraints in non-interacting FDM. Our identification of these parameters enables the explicit {\em dynamical} reconstruction of potential host halos for such galaxies through numerical solution of the SFDM equations; we outline a {proof-of-principle procedure via merger simulations} for two galaxies (UGCA444, UGC07866), and show that this yields viable rotation curves over a dynamical period of ${\cal O}(1) \, Gyr$.

astro-ph.CO↗

arXiv2024

Unified description of corpuscular and fuzzy bosonic dark matter II: Dissipation and stochastic forces

We extend our previous work (Proukakis {\em et al.}, Phys.~Rev.~D~108,~083513 (2023)) on the dynamics of bosonic, non-relativistic and self-interacting dark matter that simultaneously contains both a ``fuzzy'' low-momentum component and one with higher momenta that may be well approximated as a collection of distinct particles and described by a corresponding phase-space distribution. Starting from the non-relativistic Schwinger-Keldysh action and working beyond leading-order in the Keldysh basis fields, encoding stochastic fluctuations of the slow modes and all fluctuations of the fast modes, we obtain stochastic self-consistently coupled Gross-Pitaevskii, collisional Boltzmann kinetic and Poisson equations. Our final set of equations, which feature various collisional (dissipative and scattering) contributions and two corresponding independent stochastic force terms, are consistent with generalized fluctuation-dissipation type relations in the limit of thermal equilibrium between the particles.

astro-ph.CO↗

arXiv2024

Hybrid model of condensate and particle Dark Matter: linear perturbations in the hydrodynamic limit

We analyse perturbations of self-interacting, scalar field dark matter that contains modes both in a coherent condensate state and an incoherent particle-like state. Starting from the coupled equations for the condensate, the particles' phase space distribution and their mutual gravitational potential, first derived from first principles in earlier work by the authors, we derive a hydrodynamic limit of two coupled fluids and study their linearized density perturbations in an expanding universe, also including particle pressure under an assumption for an equation of state consistent with the dynamical equations. We find that away from the condensate-only or particle-only limits, and for certain ranges of the parameters, such self-interacting mixtures can significantly enhance the density power spectrum above the standard linear $Λ$CDM value at localised wavenumbers, even pushing structure formation into the non-linear regime earlier than expected in $Λ$CDM for these scales. We also note that such mixtures can lead to degeneracies between models with different boson masses and self-coupling strengths, in particular between self-coupled models and non-coupled Fuzzy Dark Matter made up of heavier bosons. These findings open up the possibility of a richer phenomenology in scalar field dark matter models and could further inform efforts to place observational limits on their parameters.

astro-ph.CO↗

arXiv2023

Unified description of corpuscular and fuzzy bosonic dark matter

We derive from first principles equations for bosonic, non-relativistic and self-interacting dark matter which can include both a condensed, low momentum "fuzzy" component and one with higher momenta that may be approximated as a collection of particles. The resulting coupled equations consist of a modified Gross-Pitaevskii equation describing the condensate and a kinetic equation describing the higher momentum modes, the "particles", along with the Poisson equation for the gravitational potential sourced by the density of both components. Our derivation utilizes the Schwinger-Keldysh path integral formalism and applies a semi-classical approximation which can also accommodate collisional terms amongst the particles and between the particles and the condensate to second order in the self-coupling strength. The equations can therefore describe both CDM and Fuzzy Dark Matter in a unified way, allowing for the coexistence of both phases and the inclusion of quartic self-interactions.

astro-ph.CO↗

arXiv2023

Coherent and incoherent structures in fuzzy dark matter halos

We show that fuzzy dark matter halos exhibit spatial differentiation in the degree of coherence of the field configuration, ranging from completely coherent in the central solitonic core to incoherent outside it, with a crossover region in between the two phases. The solitonic core is indeed a pure condensate which overlaps almost perfectly with the Penrose-Onsager mode corresponding to the largest eigenvalue of the one-particle density matrix. The virialized outer halo surrounding the core exhibits no clear coherence as a whole upon radial and temporal averaging. However, when viewed locally and for short times, it can be described as a collection of quasi-condensate lumps exhibiting locally suppressed fluctuations which can be identified with the structures commonly referred to as granules. Phase coherence across the entire halo is inhibited by a dynamically evolving tangled web of vortices separating the localized quasi-condensate regions. Moreover, the dimensionless phase-space density in the outer halo drops significantly below its value at the core. We further examine the dynamics of this spatial structure and find that the oscillations of the core can be accurately described by two time-dependent parameters respectively characterizing the size of the core, $r_c(t)$, and the crossover region, $r_t(t)$. For the halos produced in our merger simulations this feature is reflected in the (anti-)correlated oscillation of the peak value of the field configuration's power-spectrum. The turbulent vortex tangle of the virialized halo appears to reach a quasi-equilibrium state over probed timescales, with the incompressible component of the kinetic energy exhibiting a characteristic $k^{-3}$ tail in its spectrum, indicative of a $ρ\sim r^2$ density profile around the quantum vortex cores. Comparison of the peak wavenumbers in the corresponding power-spectra shows that the inter-vortex...

astro-ph.CO↗

arXiv2023

Computing First-Passage Times with the Functional Renormalisation Group

We use Functional Renormalisation Group (FRG) techniques to analyse the behaviour of a spectator field, $σ$, during inflation that obeys an overdamped Langevin equation. We briefly review how a derivative expansion of the FRG can be used to obtain Effective Equations of Motion (EEOM) for the one- and two-point function and derive the EEOM for the three-point function. We show how to compute quantities like the amplitude of the power spectrum and the spectral tilt from the FRG. We do this explicitly for a potential with multiple barriers and show that in general many different potentials will give identical predictions for the spectral tilt suggesting that observations are agnostic to localised features in the potential. Finally we use the EEOM to compute first-passage time (FPT) quantities for the spectator field. The EEOM for the one- and two-point function are enough to accurately predict the average time taken $\left\langle \mathcal{N}\right\rangle$ to travel between two field values with a barrier in between and the variation in that time $δ\mathcal{N}^2$. It can also accurately resolve the full PDF for time taken $ρ(\mathcal{N})$, predicting the correct exponential tail. This suggests that an extension of this analysis to the inflaton can correctly capture the exponential tail that is expected in models producing Primordial Black Holes.

astro-ph.CO↗

arXiv2022

Coarse-graining in time with the Functional Renormalisation Group: Relaxation in Brownian Motion

We apply the functional Renormalisation Group (fRG) to study relaxation in a stochastic process governed by an overdamped Langevin equation with one degree of freedom, exploiting the connection with supersymmetric quantum mechanics in imaginary time. After reviewing the functional integral formulation of the system and its underlying symmetries, including the resulting Ward-Takahashi identities for arbitrary initial conditions, we compute the effective action $Γ$ from the fRG, approximated in terms of the leading and subleading terms in the gradient expansion: the Local Potential Approximation and Wavefunction Renormalisation respectively. This is achieved by coarse-graining the thermal fluctuations in time resulting in e.g. an effective potential incorporating fluctuations at all timescales. We then use the resulting effective equations of motion to describe the decay of the covariance, and the relaxation of the average position and variance towards their equilibrium values at different temperatures. We use as examples a simple polynomial potential, an unequal Lennard-Jones type potential and a more complex potential with multiple trapping wells and barriers. We find that these are all handled well, with the accuracy of the approximations improving as the relaxation's spectral representation shifts to lower eigenvalues, in line with expectations about the validity of the gradient expansion. The spectral representation's range also correlates with temperature, leading to the conclusion that the gradient expansion works better for higher temperatures than lower ones. This work demonstrates the ability of the fRG to expedite the computation of statistical objects in otherwise long-timescale simulations, acting as a first step to more complicated systems.

cond-mat.stat-mech↗

arXiv2021

Inflation is always semi-classical: Diffusion domination overproduces Primordial Black Holes

We use the Hamilton-Jacobi (H-J) formulation of stochastic inflation to describe the evolution of the inflaton during a period of Ultra-Slow Roll (USR), taking into account the field's velocity and its gravitational backreaction. We demonstrate how this formalism allows one to modify existing slow-roll (SR) formulae to be fully valid outside of the SR regime. We then compute the mass fraction, $β$, of Primordial Black Holes (PBHs) formed by a plateau in the inflationary potential. By fully accounting for the inflaton velocity as it enters the plateau, we find that PBHs are generically overproduced before the inflaton's velocity reaches zero, ruling out a period of free diffusion or even stochastic noise domination on the inflaton dynamics. We also examine a local inflection point and similarly conclude that PBHs are overproduced before entering a quantum diffusion dominated regime. We therefore surmise that the evolution of the inflaton is always predominantly classical with diffusion effects always subdominant. Both the plateau and the inflection point are characterized by a very sharp transition between the under- and over-production regimes. This can be seen either as severe fine-tunning on the inflationary production of PBHs, or as a very strong link between the fraction $β$ and the shape of the potential and the plateau's extent.

astro-ph.CO↗

arXiv2021

$Δ\mathcal{N}$ and the stochastic conveyor belt of Ultra Slow-Roll

We analyse field fluctuations during an Ultra Slow-Roll phase in the stochastic picture of inflation and the resulting non-Gaussian curvature perturbation, fully including the gravitational backreaction of the field's velocity. By working to leading order in a gradient expansion, we first demonstrate that consistency with the momentum constraint of General Relativity prevents the field velocity from having a stochastic source, reflecting the existence of a single scalar dynamical degree of freedom on long wavelengths. We then focus on a completely level potential surface, $V=V_0$, extending from a specified exit point $ϕ_{\rm e}$, where slow roll resumes or inflation ends, to $ϕ\rightarrow +\infty$. We compute the probability distribution in the number of e-folds $\mathcal{N}$ required to reach $ϕ_{\rm e}$ which allows for the computation of the curvature perturbation. We find that, if the field's initial velocity is high enough, all points eventually exit through $ϕ_{\rm e}$ and a finite curvature perturbation is generated. On the contrary, if the initial velocity is low, some points enter an eternally inflating regime despite the existence of $ϕ_{\rm e}$. In that case the probability distribution for $\mathcal{N}$, although normalizable, does not possess finite moments, leading to a divergent curvature perturbation.

gr-qc↗

arXiv2021

One-loop electromagnetic correlators of SQED in power-law inflation

We examine scalar quantum electrodynamics in power-law inflation space-time, and compute the one-loop correction to electric and magnetic field correlators at superhorizon separations. The effect at one-loop descends from the coupling of the vector to the charged scalar current which is greatly enhanced due to gravitational particle production. We conclude that non-perturbative effects must exist due to (i) secular growth, (ii) spatial running, and (iii) infrared sensitivity of the one-loop correction to the correlators. Electric and magnetic correlators exhibit a hierarchy that is due to Faraday's law and accelerated expansion, and must hold non-perturbatively.

gr-qc↗

arXiv2021

Observational constraints on Hyperinflation

We study a Hyperinflation model involving a field doublet on a hyperbolic field-space manifold and an exponential potential, providing a concise treatment of the evolution of the entropic and adiabatic perturbations around the homogeneous hyperbolic attractor solution. We find that the adiabatic spectral index narrows down the admissible values of the potential's slope to a very small region, severely restricting the state space of the allowed background solutions.

gr-qc↗

arXiv2021

Functional Renormalisation Group for Brownian Motion I: The Effective Equations of Motion

We use the functional Renormalisation Group (fRG) to describe the in and out of equilibrium dynamics of stochastic processes, governed by an overdamped Langevin equation. Exploiting the connection between Langevin dynamics and supersymmetric quantum mechanics in imaginary time, we write down renormalisation flow equations for the effective action, approximated in terms of the Local Potential Approximation and Wavefunction Renormalisation. We derive \textit{effective equations of motion} (EEOM) from the effective action (EA) $Γ$ for the average position $\left\langle x\right\rangle$, variance $\langle \left(x- \langle x \rangle\right)^2\rangle$ and covariance. The fRG flow equations outlined here provide a concrete way to compute the EA and thus solve the derived EEOM. The obtained effective potential should determine directly the exact equilibrium statistics, name the position, the variance, as well as all higher order cumulants of the equilibrium Boltzmann distribution. This first paper of a two part series is mostly concerned with setting up the necessary formalism while in part two we will numerically solve the equations derived her and assess their validity both in and out of equilibrium.

cond-mat.stat-mech↗

arXiv2020

Feynman Rules for Stochastic Inflationary Correlators

We elaborate on the functional integral describing the stochastic dynamics of a spectator field during inflation, comparing its diagrammatic expansion to that obtained directly from a perturbative solution of the corresponding Langevin equation. We state Feynman rules for computing arbitrary temporal $n$-point functions and perform some illustrative computations for a $λϕ^4$ interaction, paying attention to the role played by a functional Jacobian determinant in the path integral. We also briefly consider the case when the field contributes to the expansion rate, making the noise multiplicative, which introduces additional vertices.

gr-qc↗

arXiv2018

Functional renormalization group in stochastic inflation

We apply the functional renormalization group to Starobinsky's stochastic equation describing the local dynamics of a light scalar field in de Sitter. After elaborating on the over-damped regime of stochastic dynamics, we introduce an effective average action for the stochastic field, resulting by progressively integrating out frequencies, and study its flow equation in the local potential approximation (LPA). This effective action determines the approach to equilibrium and allows for the computation of unequal time correlators $\left\langleϕ(t)ϕ(t+Δt)\right\rangle$ for large values of $Δt$. The stochastic RG flow in the LPA can be formulated in two ways, one that preserves the stochastic supersymmetry and one that breaks it. We show that both predict a characteristic decay time very close to that determined by the dynamical mass for a massless self-interacting scalar in de Sitter $m^2\sim \sqrtλH^2$. Furthermore, the temporal supersymmetric formulation remarkably recovers the flow for the effective potential found using Quantum Field Theory methods and a smoothing over spatial wavelengths. We also discuss how the stochastic framework generically predicts an infrared mass which is a few percent smaller than the dynamical mass obtained in the LPA. Our results further support the notion that stochastic inflation captures the correct IR dynamics of light scalar fields in inflation.

gr-qc↗