arXiv subjects

M. Laine

Publications and source records attributed to M. Laine.

At least 19 recordsLinked to original sources

arXiv2026

Matching second-order classical and 1-loop quantum tensor power spectra in de Sitter spacetime

Large corrections to the inflationary tensor power spectrum have been speculated to emerge either as second-order scalar-induced classical effects, or as 1-loop quantum corrections. These two sources are not independent of each other. Choosing the example of a massless minimally coupled scalar field, we show how the full 1-loop result can be divided into its classical and vacuum parts. Working first in dimensional regularization, we show that the classical part is IR divergent, with IR referring to small comoving momenta that have an influence for a very long time. In the full 1-loop quantum result, these divergences cancel. Introducing then a momentum cutoff that permits for a numerical evaluation of the classical contribution, we show that the IR sensitivity manifests itself as a cubic divergence. We suggest a procedure of "non-perturbative renormalization" for extracting physical information not affected by the divergence. If this can be implemented in realistic systems, it could consolidate numerical studies of inflationary scalar-induced gravitational waves.

hep-ph↗

arXiv2026

Classical equipartition dynamics between axions and non-Abelian gauge fields

Motivated by axion-like inflation and its warm embedding within the Standard Model, we study the early stages of the energy transfer between an axion condensate and an SU(2) gauge ensemble, by employing non-linear classical real-time lattice simulations. The discretized equations of motion are worked out, elaborating on Gauss constraints. A numerical solution is implemented on the CosmoLattice platform. Adopting a quadratic potential, and omitting universe expansion, we establish initial exponential growth of the low-momentum gauge modes; damping of axion oscillations after some delay; and subsequent energy equipartition between axion and gauge ensembles. A clear difference between the SU(2) and U(1) dynamics is observed, likely associated with non-Abelian self-interactions. We elaborate on what this implies for the possible thermalization of the SU(2) ensemble.

hep-ph↗

arXiv2026

Energy and momentum dependence of the soft-axion interaction rate

Axions coupled to thermal non-Abelian gauge fields may have cosmological significance. As the heat bath defines a frame, its influence depends separately on energy and momentum. A light-like momentum ($k \approx \omega$) is relevant for the axion contribution to the effective number of light neutrinos, $\Delta N^{ }_\mathrm{eff}$, whereas a vanishing momentum ($k=0$) plays a role for warm natural inflation or ultralight dark matter, and has been employed in lattice estimates (both classical and quantum-statistical) of the strong sphaleron rate. Focussing on soft energies ($\alpha_\mathrm{s}^{ }T \ll \omega \ll \pi T$), we carry out an HTL computation to show how the domains $k=0$ and $k \approx \omega$ interpolate to each other. We then compare with lattice data at $k=0$, and connect our analysis to NLO computations at $k \approx \omega \ge \pi T$. Assembling the current best input, we re-investigate light QCD axion decoupling dynamics at $T \ge 200$ MeV, showing that efficient interactions in the ultrasoft domain increase $\Delta N^{ }_\mathrm{eff}$ from $\sim 0.03$ to $\sim 0.04$ at $f^{ }_a = 4\times 10^8_{ }$ GeV.

hep-ph↗

arXiv2025

General SIGW source for reheating dynamics

Working in an arbitrary gauge, we derive the source term for scalar-induced gravitational waves (SIGW) valid during a general reheating epoch. The dominant energy component is allowed to transition smoothly from an inflaton field to a set of fluids, possibly via a period of matter domination. Gauge invariance is verified up to second order.

gr-qc↗

arXiv2025

Fast and Flexible Neutrino Decoupling Part I: The Standard Model

Cosmological determinations of the number of relativistic neutrino species, $N^{ }_{\rm eff}$, are becoming increasingly accurate, and further improvements are expected both from CMB and BBN data. Given this context, we update the evaluation of $N^{ }_{\rm eff}$ and the current entropy density via the momentum-averaged approach. This allows for a numerically fast description of neutrino decoupling, easily portable to an array of new physics scenarios. We revisit all aspects of this approach, including collision terms with full electron mass dependence, finite temperature QED corrections to the equation of state, neutrino oscillations, and the modelling of neutrino ensembles with effective chemical potentials. For integrated observables, our results differ by less than $0.04\%$ from the solution of the momentum-dependent evolution equation. We outline how to extend the approach to BSM settings, and will highlight its power in Part II. To facilitate the practical implementation, we release a Mathematica and Python code within nudec_BSM_v2, easily linkable to BBN codes.

hep-ph↗

arXiv2025

Evolution of coupled scalar perturbations through smooth reheating. II. Thermal fluctuation regime

Curvature perturbations with short wavelengths exit the Hubble horizon when the universe may contain a thermal plasma in addition to an inflaton field that drives its expansion. We solve the corresponding fluctuation-dissipation dynamics at linear order, building upon a previously established set of gauge-invariant evolution equations. The properties of the noise autocorrelator are constrained via a matching of equilibrium correlators to quantum-statistical physics deep inside the Hubble horizon. The curvature power spectrum is determined numerically, without slow-roll approximations or assumptions about the equilibration of the inflaton field. As applications, we scrutinize two issues from recent literature: the model dependence of the thermally modified power spectrum as a function of freeze-out parameters, and the viability of embedding warm inflation within the Standard Model (we offer support for the latter proposal). The role of pre-horizon-exit acoustic oscillations is illustrated.

hep-ph↗

arXiv2025

Entropy production at electroweak bubble walls from scalar field fluctuations

The real-time dynamics of an electroweak phase transition involves large time and distance scales, the domain of hydrodynamics. However, the matching conditions of ideal hydrodynamics across a bubble wall do not fix the fluid profile completely, with the remaining degree of freedom parametrizable through entropy production. Within a framework of Langevin dynamics, viewed as an effective description valid between the hydrodynamic ($k \sim g^4_{ } T/\pi^3_{ }$) and soft momentum scales ($k \sim gT$), we determine the entropy production originating from scalar field fluctuations. The entropy discontinuity is shown to remain non-vanishing when the friction coefficient is sent to zero, in apparent violation of the ``local thermal equilibrium'' (LTE) framework. To confirm the finding, we identify its origin within Boltzmann equations, as being part of the $1\to 1$ force associated with the ``ballistic'' regime. The result implies that LTE-based upper bounds on the wall velocity cannot be saturated.

hep-ph↗

arXiv2025

Computing singlet scalar freeze-out with plasmon and plasmino states

The final-state particles from cosmological dark matter co-annihilation are expected to equilibrate. As dictated by Hard Thermal Loop resummation, the spectrum of equilibrated quasiparticles is richer than in vacuum, with a massless gauge field possessing three independent polarization states (``plasmons''), and a massless fermion developing a novel branch (``plasmino''). Furthermore, once the Higgs phenomenon sets in, vacuum and thermal mass corrections interfere. We collect together the corresponding poles and residues for the Standard Model around its crossover temperature. Choosing its singlet scalar extension for illustration, we subsequently demonstrate, both numerically and via power counting, and in accordance with general theoretical expectations, how in the freeze-out of TeV-scale dark matter, these effects remain well hidden in the inclusive annihilation cross section. In particular, the dominant (longitudinal) gauge channel is shown to be practically temperature-independent. Cosmological constraints on TeV-scale singlet scalars are reconfirmed.

hep-ph↗

arXiv2024

$\nu\bar\nu$ production, annihilation, and scattering at MeV temperatures and NLO accuracy

Interaction rates of neutrinos and antineutrinos within a QED plasma determine the dynamics of their decoupling in the early universe. We show how to define the relevant double-differential production, annihilation, and scattering rates at NLO. Integrating over these rates with specific weights, other quantities from the literature can be obtained, such as energy transfer rates, or a neutrino interaction rate. In the limit of massless electrons, we show that NLO corrections to the energy transfer rates are as small as those that enter the previously determined neutrino interaction rate, and only have a small influence on the neutrino decoupling parameter, $N_{\rm eff}\,$. For comparison, the influence of a finite electron mass is quantified at LO. Finally we provide a tabulation and fast interpolation routine for all double-differential rates, in order to allow for their use in non-approximate kinetic equations, which may further reduce the systematic uncertainties of the Standard Model prediction for $N_{\rm eff}\,$.

hep-ph↗

arXiv2024

Evolution of coupled scalar perturbations through smooth reheating. I. Dissipative regime

If the inflaton is a heavy scalar field, it may equilibrate slower than some other degrees of freedom, e.g. non-Abelian gauge bosons. In this case, perturbations in the inflaton field and in a thermal plasma coexist from a given moment onwards. We derive a gauge-invariant set of three coupled equations governing the time evolution of such a system. Despite singular coefficients, a reliable numerical solution can be obtained for a long time period, starting from phase oscillations inside the Hubble horizon, and extending until acoustic oscillations in a radiation-dominated universe. Benchmarks are illustrated from a "weak regime", where perturbations have a quantum-mechanical origin but get dissipated by interactions with the plasma. Among applications of our formalism could be inhomogeneity-induced nucleations in post-inflationary phase transitions, and the production of scalar-induced gravitational waves.

hep-ph↗

arXiv2024

QED corrections to the thermal neutrino interaction rate

Motivated by precision computations of neutrino decoupling at MeV temperatures, we show how QED corrections to the thermal neutrino interaction rate can be related to the electron-positron spectral function as well as an effective $\barννγ$ vertex. The spectral function is needed both in a timelike and in a spacelike domain, and for both of its physical polarization states (transverse and longitudinal with respect to spatial momentum). Incorporating an NLO evaluation of this spectral function, an estimate of the $\barννγ$ vertex, and HTL resummation of scatterings mediated by soft Bose-enhanced $t$-channel photons, we compute the interaction rate as a function of the neutrino momentum and flavour. Effects on the $ -(0...2)\%$ level are found, noticeably smaller than a previous estimate of a related quantity.

hep-ph↗

arXiv2024

Baryonic thermal screening mass at NLO

We determine the resummed 1-loop correction to a baryonic thermal screening mass. The calculation is carried out in the framework of a dimensionally reduced effective theory, where quarks are heavy fields due to their non-zero Matsubara frequencies. The correction due to interactions is computed at O($g^2_{ }$) in the coupling constant. In order to solve a 3-body Schr\"odinger equation, we exploit a two-dimensional generalization of the hyperspherical harmonics method. At electroweak scale temperatures, the NLO correction represents a $\sim 4.6 \%$ increase of the free-theory value $3\pi T$ of the screening mass.

hep-ph↗

arXiv2024

Double-graviton production from Standard Model plasma

The thermal plasma filling the early universe generated a stochastic gravitational wave background that peaks in the microwave frequency range today. If the graviton production rate is expressed as a series in a fine-structure constant, $α$, and the temperature over the Planck mass, $T^2_{ } / m_{\rm pl}^2$, then the lowest-order contributions come from single ($\sim αT^2_{ }/m_{\rm pl}^2$) and double ($\sim T^4_{ }/m_{\rm pl}^4$) graviton production via $2\to 2$ scatterings. We show that in the Standard Model, single-graviton production dominates if the maximal temperature is smaller than $4\times 10^{18}_{ }$ GeV. This justifies previous calculations which relied solely on single-graviton production. We mention Beyond the Standard Model scenarios in which the single and double-graviton contributions could be of comparable magnitudes. Finally, we elaborate on what these results imply for the range of applicability of General Relativity as an effective theory.

hep-ph↗

arXiv2024

Soft contributions to the thermal Higgs width across an electroweak phase transition

We estimate the equilibration rate of a nearly homogeneous Higgs field, displaced from its ground state during the onset of an electroweak phase transition. The computation is carried out with Hard Thermal Loop resummed perturbation theory, and a significant part of the result originates from Bose-enhanced $t$-channel $2\leftrightarrow 2$ scatterings. The expression is shown to be IR finite and gauge independent. Possible applications to Langevin simulations of bubble nucleation are mentioned, and we also contrast with the friction affecting bubble growth.

hep-ph↗

arXiv2024

Update on gravitational wave signals from post-inflationary phase transitions

In view of recent interest in high-frequency detectors, broad features of gravitational wave signals from phase transitions taking place soon after inflation are summarized. The influence of the matter domination era that follows the slow-roll stage is quantified in terms of two equilibration rates. Turning to the highest-frequency part of the spectrum, we show how it is constrained by the fact that the bubble distance scale must exceed the mean free path.

gr-qc↗

arXiv2023

Inflationary gravitational wave background as a tail effect

The free propagator of a massless mode in an expanding universe can be written as a sum of two terms, a lightcone and a tail part. The latter describes a subluminal (time-like) signal. We show that the inflationary gravitational wave background, influencing cosmic microwave background polarization, and routinely used for constraining inflationary models through the so-called $r$ ratio, originates exclusively from the tail part.

gr-qc↗

arXiv2023

Maximal temperature of strongly-coupled dark sectors

Taking axion inflation as an example, we estimate the maximal temperature ($T_{\rm max}^{ }$) that can be reached in the post-inflationary universe, as a function of the confinement scale of a non-Abelian dark sector ($Λ_{\rm IR}^{ }$). Below a certain threshold $Λ_{\rm IR}^{ } < Λ_{\rm 0}^{ } \sim 2\times 10^{-8}_{ } m_{\rm pl}^{ }$, the system heats up to $T_{\rm max}^{ } \sim Λ_{\rm 0}^{ } > T_{\rm c}^{ }$, and a first-order thermal phase transition takes place. On the other hand, if $Λ_{\rm IR}^{ } > Λ_{\rm 0}^{ }$, then $T_{\rm max}^{ } \sim Λ_{\rm IR}^{ } < T_{\rm c}^{ }$: very high temperatures can be reached, but there is no phase transition. If the inflaton thermalizes during heating-up (which we find to be unlikely), or if the plasma includes light degrees of freedom, then heat capacity and entropy density are larger, and $T_{\rm max}^{ }$ is lowered towards $Λ_{\rm 0}^{ }$. The heating-up dynamics generates a gravitational wave background. Its contribution to $N^{ }_{\rm eff}$ at GHz frequencies, the presence of a monotonic $\sim f_{\rm 0}^3$ shape at $(10^{-4}_{ } - 10^2_{ })\,$Hz frequencies, and the frequency domain of peaked features that may originate via first-order phase transitions, are discussed.

hep-ph↗

arXiv2023

Langevin simulation of dark matter kinetic equilibration

Recently it has been questioned, notably in the context of the scalar singlet dark matter model with $m_φ^{ }\simeq 60$ GeV, how efficiently kinetic equilibrium is maintained if freeze-out dynamics is pushed down to low temperatures by resonant effects. We outline how Langevin simulations can be employed for addressing the non-equilibrium momentum distribution of non-relativistic particles in a cosmological background. For a scalar singlet mass $m_φ^{ }\simeq 60$ GeV, these simulations suggest that kinetic equilibrium is a good approximation down to $T \sim 1$ GeV, with the deviation first manifesting itself as a red-tilted spectrum. This reduces the annihilation cross section, confirming findings from other methods that a somewhat larger ($ < 20\%$) coupling than in equilibrium is needed for obtaining the correct abundance.

hep-ph↗