arXiv subjects

Arttu Rajantie

Publications and source records attributed to Arttu Rajantie.

At least 19 recordsLinked to original sources

arXiv2026

Gravitational waves from super-Hubble bubbles

We consider a cosmological first-order phase transition in which bubbles of true vacuum nucleate during inflation but do not collide and percolate until the Universe has entered the radiation-dominated era. If the collisions take place soon after the end of inflation, the size of these bubbles can be significantly greater than the Hubble length. This has two important consequences for the gravitational waves produced by the bubble collisions: First, as the peak frequency is determined by the comoving bubble radius, it can be well below the MHz frequencies typical for bubble collisions at the end of inflation. Second, when comparing collisions beginning at the same time, the amplitude of the gravitational waves is greatly enhanced relative to Hubble-sized and smaller bubbles. Together, these two effects mean that gravitational waves produced by super-Hubble bubbles soon after the end of inflation can be within the observable frequency and amplitude ranges of LIGO and NANOGrav, as well as LISA and other future gravitational wave experiments. We demonstrate this with a simple illustrative model.

astro-ph.CO↗

arXiv2026

Asymptotic limits of constrained instantons

We revisit the topic of false vacuum decay in field theory. We focus on a toy model of a real massive scalar field with an unstable quartic potential. This model has a false vacuum, and decay out of the false vacuum can be described via the method of constrained instantons, which work by introducing a constraint on the path integral. We identify and develop three different asymptotic limits which enable analytic construction of approximate {constrained} solutions. The first, in which the constrained solution is small compared to the inverse mass of the scalar field, is an application of the perturbative methods of Affleck, although we re-derive the main results and identify several terms which were previously neglected. Second, for very large constrained solutions we adapt the thin-wall approximation of Coleman. However, we find that the large instanton limit does not always exist. In this case we identify another useful limit, in which the Lagrange multiplier used to implement the constraint is large. In this limit, the solution's scaling with the parameters may be found via dimensional analysis and an exact solution is obtained with a single numerical computation.

hep-th↗

arXiv2026

Scalar field effective potentials in de Sitter spacetime

We investigate two different definitions of a scalar field effective potential in quantum field theory in de Sitter spacetime: the standard textbook definition, and the constraint effective potential proposed by O'Raifeartaigh et al. in 1986. While these definitions are equivalent in Minkowski spacetime, they differ significantly in de Sitter. We demonstrate this by computing them both explicitly at one-loop order in perturbation theory. It is well known that the perturbative expansion of the standard effective potential fails converge for light fields. In contrast, the constraint effective potential does not suffer from this infrared problem, and it can therefore be computed using perturbation theory. We discuss the physical interpretation of the two effective potentials. In particular, we provide evidence supporting an earlier conjecture that the constraint effective potential is the correct one to use in the stochastic Starobinsky-Yokoyama theory.

hep-th↗

arXiv2026

Constrained instantons in scalar field theories

Instantons, localised saddle points of the action, play an important role in describing non-perturbative aspects of quantum field theories, for example vacuum decay or violation of conservation laws associated with anomalous symmetries. However, there are theories in which no saddle point exists. In this paper, we revisit the idea of constrained instantons, proposed initially by Affleck in 1981, and develop it into a complete method for computing the vacuum decay rate in such cases. We apply this approach to the massive scalar field theory with a negative quartic self-interaction using two different constraints. We solve the field equations numerically and find a two-branch structure, with two distinct solutions for each value of the constraint. By counting the negative modes, we identify one branch of solutions as the constrained instantons and the other as the minima of the action subject to the constraint. We discuss their significance for the computation of the vacuum decay rate.

hep-th↗

arXiv2025

Curvature perturbations from vacuum transition during inflation

We demonstrate that in the presence of a light scalar spectator field, vacuum transitions taking place during inflation can produce large, potentially detectable non-Gaussian signatures in the primordial curvature perturbation. Such transitions are common in theories with multiple scalar fields when the potential has several minima. Our computation proceeds by numerically finding the instanton solution that describes quantum tunnelling between vacuum states in a de Sitter background, calculating its dependence on the spectator field and, thereby, its effect on the expansion of space. For a scenario with Higgs inflation, we obtain the non-Gaussianity parameter $f_\mathrm{NL} \sim O(10)$ and study its parameter dependence.

astro-ph.CO↗

arXiv2024

Magnetic monopoles -- theory overview

I give a theoretical overview of magnetic monopoles, focusing on the physical perspective of monopoles as hypothetical particles rather than as mathematical objects. I argue that monopoles are exceptionally interesting hypothetical particles and discuss the prospects of addressing the question of their existence, and possibly producing them, in particle physics experiments.

hep-ph↗

arXiv2024

Curvature perturbations from preheating with scale dependence

We extend the formalism to calculate non-Gaussianity of primordial curvature perturbations produced by preheating in the presence of a light scalar field. The calculation is carried out in the separate universe approximation using the non-perturbative delta N formalism and lattice field theory simulations. Initial conditions for simulations are drawn from a statistical ensemble determined by modes that left the horizon during inflation, with the time-dependence of Hubble rate during inflation taken into account. Our results show that cosmic variance, i.e., the contribution from modes with wavelength longer than the size of the observable universe today, plays a key role in determining the dominant contribution. We illustrate our formalism by applying it to an observationally-viable preheating model motivated by non-minimal coupling to gravity, and study its full parameter dependence.

astro-ph.CO↗

arXiv2024

Stochastic parameters for scalar fields in de Sitter spacetime

The stochastic effective theory approach, often called stochastic inflation, is widely used in cosmology to describe scalar field dynamics during inflation. The existing formulations are, however, more qualitative than quantitative because the connection to the underlying quantum field theory (QFT) has not been properly established. A concrete sign of this is that the QFT parameters depend on the renormalisation scale, and therefore the relation between the QFT and stochastic theory must have explicit scale dependence that cancels it. In this paper we achieve that by determining the parameters of the second-order stochastic effective theory of light scalar fields in de Sitter to linear order in the self-coupling constant $λ$. This is done by computing equal-time two-point correlators to one-loop order both in QFT using dimensional regularisation and the $\overline{\rm MS}$ renormalisation scheme and the equal-time four-point correlator to leading order in both theories, and demanding that the results obtained in the two theories agree. With these parameters, the effective theory is valid when $m\lesssim H$ and $λ^2\ll m^4/H^4$, and therefore it is applicable in cases where neither perturbation theory nor any previously proposed stochastic effective theories are.

gr-qc↗

arXiv2022

Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime

We introduce a second-order stochastic effective theory for light scalar fields in de Sitter spacetime, extending the validity of the stochastic approach beyond the massless limit and demonstrating how it can be used to compute long-distance correlation functions non-perturbatively. The parameters of the second-order stochastic theory are determined from quantum field theory through a perturbative calculation, which is valid if the self-interaction parameter $λ$ satisfies $λ\ll m^2/H^2$, where $m$ is the scalar and $H$ is the Hubble rate. Therefore it allows stronger self-interactions than conventional perturbation theory, which is limited to $λ\ll m^4/H^4$ by infrared divergences. We demonstrate the applicability of the second-order stochastic theory by comparing its results with perturbative quantum field theory and overdamped stochastic calculations, and discuss the prospects of improving its accuracy with a full one-loop calculation of its parameters.

gr-qc↗

arXiv2022

The effective Higgs potential and vacuum decay in Starobinsky inflation

Based on the current experimental data, the Standard Model predicts that the current vacuum state of the Universe is metastable, leading to a non-zero rate of vacuum decay through nucleation of bubbles of true vacuum. Our existence implies that there cannot have been any such bubble nucleation events anywhere in our whole past lightcone. We consider a minimal scenario of the Standard Model together with Starobinsky inflation, using three-loop renormalization group improved Higgs effective potential with one-loop curvature corrections. We show that the survival of the vacuum state through inflation places a lower bound $ξ\gtrsim 0.1$ on the non-minimal Higgs curvature coupling, the last unknown parameter of the Standard Model. This bound is significantly stronger than in single field inflation models with no Higgs-inflaton coupling. It is also sensitive to the details of the dynamics at the end of inflation, and therefore it can be improved with a more detailed study of that period.

astro-ph.CO↗

arXiv2022

Phase transitions in de Sitter: The stochastic formalism

The stochastic spectral expansion method offers a simple framework for calculations in de Sitter spacetimes. We show how to extend its reach to metastable vacuum states, both in the case when the potential is bounded from below, and when it is unbounded from below and therefore no stable vacuum state exists. In both cases, the decay rate of the metastable vacuum is given by the lowest non-zero eigenvalue associated to the Fokker-Planck equation. We show how the corresponding eigenfunction determines the field probability distribution which can be used to compute correlation functions and other observables in the metastable vacuum state.

gr-qc↗

arXiv2022

Phase Transitions in de Sitter: Quantum Corrections

We investigate the decay rate of a false vacuum state in de Sitter space at high Hubble rates, using two methods: the Hawking-Moss instanton method which is fully quantum mechanical but relies on the saddle-point approximation, and the Starobinsky-Yokoyama stochastic approach which is non-perturbative but does not include quantum effects. We use the flux-over-population method to compute the Hawking-Moss decay rate at one-loop order, and demonstrate that in its domain of validity, it is reproduced by the stochastic calculation using the one-loop constraint effective potential. This suggests that the stochastic approach together with the constraint effective potential can be used to accurately describe vacuum decay beyond the saddle-point approximation.

gr-qc↗

arXiv2021

Free scalar correlators in de Sitter via the stochastic approach beyond slow roll

The stochastic approach to calculating scalar correlation functions in de Sitter spacetime is extended beyond the overdamped "slow roll" approximation. We show that with the correct noise term, it reproduces the exact asymptotic long-distance behaviour of field correlators in free field theory, thereby demonstrating the viability of the technique. However, we also show that the naïve way of calculating the noise term by introducing a cut-off at the horizon does not give the correct answer unless the cut-off is chosen specifically to give the required result. We discuss the implications of this for interacting theories.

gr-qc↗

arXiv2021

Higgs-like spectator field as the origin of structure

We show that the observed primordial perturbations can be entirely sourced by a light spectator scalar field with a quartic potential, akin to the Higgs boson, provided that the field is sufficiently displaced from vacuum during inflation. The framework relies on the indirect modulation of reheating, which is implemented without any direct coupling between the spectator field and the inflaton and does not require non-renormalisable interactions. The scenario gives rise to local non-Gaussianity with $f_{\rm NL}\simeq 5$ as the typical signal. As an example model where the indirect modulation mechanism is realised for the Higgs boson, we study the Standard Model extended with right-handed neutrinos. For the Standard Model running we find, however, that the scenario analysed does not seem to produce the observed perturbation.

hep-ph↗

arXiv2021

Schwinger pair production of magnetic monopoles: momentum distribution for heavy-ion collisions

Magnetic monopoles may be produced by the dual Schwinger effect in strong magnetic fields. Today, the strongest known magnetic fields in the universe are produced fleetingly in heavy-ion collisions. We use the complex worldline instanton method to calculate the momentum distribution of magnetic monopoles produced in heavy-ion collisions, in an approximation that includes the effect of the magnetic field to all orders but neglects monopole self-interactions. The result saturates the preparation time-energy uncertainty principle, and yields a necessary ingredient for experimental monopole searches in heavy-ion collisions.

hep-ph↗

arXiv2021

Stochastic isocurvature constraints for axion dark matter with high-scale inflation

Axions are among the best motivated dark matter candidates. Their production in the early Universe by the vacuum misalignment mechanism gives rise to isocurvature perturbations, which are constrained by cosmic microwave background measurements. In this paper, we compute the axion isocurvature power spectrum using spectral expansion in the stochastic Starobinsky-Yokoyama formalism, which captures non-linear effects in the axion dynamics. In contrast to most of the existing literature, we focus on high inflationary Hubble rates of order $10^{13}~{\rm GeV}$, and demonstrate that there is a significant window in which axions can account for all or part of the dark matter abundance without violating the isocurvature bounds or tensor mode bounds. Crucially, we find that the isocurvature spectrum is dominated by non-perturbative contributions in a large part of this window. Therefore the commonly used linear approximation is not reliable in this region, making the stochastic approach essential.

astro-ph.CO↗

arXiv2021

Instanton solution for Schwinger production of 't Hooft-Polyakov monopoles

We present the results of an explicit numerical computation of a novel instanton in Georgi-Glashow SU(2) theory. The instanton is physically relevant as a mediator of Schwinger production of 't Hooft-Polyakov magnetic monopoles from strong magnetic fields. In weak fields, the pair production rate has previously been computed using the worldline approximation, which breaks down in strong fields due to the effects of finite monopole size. Using lattice field theory we have overcome this limit, including finite monopole size effects to all orders. We demonstrate that a full consideration of the internal monopole structure results in an enhancement to the pair production rate, and confirm earlier results that monopole production becomes classical at the Ambjorn-Olesen critical field strength.

hep-th↗

arXiv2021

Vacuum decay constraints on the Higgs curvature coupling from inflation

We derive lower bounds for the Higgs-curvature coupling from vacuum stability during inflation in three inflationary models: quadratic and quartic chaotic inflation, and Starobinsky-like power-law inflation. In contrast to most previous studies we take the time-dependence of the Hubble rate into account both in the geometry of our past light-cone and in the Higgs effective potential, which is approximated with three-loop renormalisation group improvement supplemented with one-loop curvature corrections. We find that in all three models, the lower bound is $ξ\gtrsim 0.051\ldots 0.066$ depending on the top quark mass. We also demonstrate that vacuum decay is most likely to happen a few $e$-foldings before the end of inflation.

astro-ph.CO↗