arXiv subjects

Yuichiro Tada

Publications and source records attributed to Yuichiro Tada.

At least 19 recordsLinked to original sources

arXiv2026

Calculating the squeezed bispectrum in stochastic inflation by Monte Carlo simulation

The bispectrum of cosmological perturbations is an important probe of inflation and the underlying particle physics. However, calculating it becomes challenging in inflation models where inflaton dynamics is dominated by quantum diffusion rather than slow-roll, especially in the multi-field case. In this paper, employing the stochastic-$\delta \mathcal{N}$ formalism, we propose a Monte Carlo-based method to calculate the bispectrum in the squeezed limit, as an extension of the method for the power spectrum that we previously proposed. Our method involves generating paths of inflatons' time evolution that branch only several times, avoiding nested path generation, which incurs a prohibitive computational cost. As numerical demonstrations, we apply the proposed method to single- and double-field chaotic inflation for validation, and to hybrid inflation with mild waterfall, for which, to the best of our knowledge, the bispectrum is calculated for the first time in this work.

astro-ph.CO↗

arXiv2026

Constant-Roll Inflation: Analytical Formulae for Power Spectrum and Implications for Induced Gravitational Waves

Constant-roll inflation provides a simple and analytically tractable framework for describing transient departures from slow roll, including non-attractor phases that can enhance the primordial curvature perturbation on small scales. In this work, we investigate the curvature power spectrum generated in a slow-roll--constant-roll--slow-roll scenario, focusing on the positions and amplitudes of the two characteristic peaks associated with the two transitions. We show that, in the parameter range where both peaks are well separated and sufficiently pronounced, the underlying constant-roll parameters can be reconstructed from the peak positions and amplitudes without performing a brute-force parameter scan. In addition, we construct a smoothed analytic approximation to the power spectrum, designed for efficient estimates of scalar-induced gravitational waves and related phenomenological applications.

astro-ph.CO↗

arXiv2026

Domain-wall Quintessence

We investigate a dark energy model driven by a planar domain-wall-like structure with a thickness comparable to, or larger than, the current Hubble radius, focusing on its intrinsic anisotropy and observational viability. Near the centre of the domain wall (DW), the spacetime is anisotropic, with distinct expansion rates parallel and perpendicular to the wall. This anisotropic structure induces direction-dependent cosmic expansion and modifies photon geodesics from cosmological sources, leaving characteristic signatures in cosmological observables. We confront the model with recent observational data. We first compute the anisotropic Cosmic Microwave Background (CMB) temperature multipoles generated by the DW and impose constraints from the Planck 2018 measurements. These constraints severely limit the allowed DW abundance, requiring the DW energy density to be less than $\mathcal{O}(10^{-5})$ of the current critical density in order to suppress the quadrupole contributions. We then perform a Markov Chain Monte Carlo (MCMC) analysis using Type Ia supernova (SNe Ia) data, including the Pantheon+ SH0ES and DESY5 samples, to compare the DW scenario with the standard $\Lambda$CDM model. We find that although the DW naturally realises anisotropic accelerated expansion, the combined constraints from the CMB and SNe Ia favour the $\Lambda$CDM limit, in which the DW contribution is negligible, and the universe is effectively isotropic. Our results demonstrate that a Hubble-scale domain wall is tightly constrained by current observations and can only play a subdominant role in the late-time cosmic acceleration.

astro-ph.CO↗

arXiv2026

Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta{N}$ formalism

Understanding when inflationary perturbations become genuinely nonlinear near the horizon crossing requires methods that go beyond both linear perturbation theory and the gradient expansion. In this work, we introduce a nonlinear lattice framework for single-field inflation based on a shear-free, locally Friedmann-Lema\^itre-Robertson-Walker geometry. This approach captures inhomogeneous local expansion rates, curvature contributions to the local Friedmann equation, and proper-volume weighting at a fraction of the computational cost of full numerical relativity. We construct fully nonlinear $\delta N$ observables on uniform-density slices, together with other practical time-dependent estimators for the curvature perturbations. After validating the framework in a standard slow-roll regime, we apply it to Starobinsky's linear-potential model featuring an intermittent ultra-slow-roll (USR) phase and a sharp potential transition. During this non-attractor USR regime, the lattice captures the separation of curvature perturbation estimators, the growth and subsequent stabilisation of non-Gaussianity, and a transient weakening of the shear-free approximation when the inflaton velocity becomes very small. Our framework provides a practical intermediate approach between rigid background lattice simulations and full numerical relativity, offering a nonlinear bridge between lattice methods, the $\delta N$ formalism, and the stochastic inflation formalism as perturbations transition beyond the linear regime.

gr-qc↗

arXiv2026

STOchastic LAttice Simulation of hybrid inflation

We investigate the spatial profile of the curvature perturbation generated in multi-waterfall hybrid inflation models, which are known to produce various topological defects. Using the lattice simulation code STOchastic LAttice Simulation, based on the stochastic formalism of inflation, we analyse six cases by varying the number of waterfall fields $n$ and the functional form of the inflaton potential (``Quadratic'' and ``Cubic'' cases). Our statistical analysis shows that the probability density functions (PDFs) and power spectra are broadly consistent with the so-called stochastic-$\delta N$ algorithm. The ``Cubic'' case also exhibits a characteristic upper bound in the PDF, as discovered in our previous work, that suppresses \acl{PBH} formation while potentially affecting halo formation. Furthermore, we employ the Euler characteristic as a topological diagnostic tool to identify the structures of the waterfall fields as well as the curvature perturbation. We find that the topological defects, such as domain walls ($n=1$), cosmic strings ($n=2$), and monopoles ($n=3$), are reconnected during inflation into finer structures by the stochastic noise, making their correlation lengths much smaller than the Hubble scale at the critical point of the waterfall phase transition counterintuitively. The Euler characteristic also implies global structures of the curvature perturbation for $n=1$, though we do not conclude if they are due to the domain wall, because neither the strings ($n=2$) nor monopoles ($n=3$) leave such structures. The global structures of the curvature perturbation will provide a novel probe for the physics of the early universe.

astro-ph.CO↗

arXiv2026

Quintessence with tachyonic resonance and late-time cosmic-microwave-background and gravitational-wave signals

Combinations of recent cosmological observations, including Dark Energy Spectroscopic Instrument (DESI), show hints of a dynamical nature for dark energy. While the data suggest the possibility of the phantom crossing, it is worth thoroughly exploring quintessence models. Given that phenomenological parametrisations of the equation-of-state parameter $w(a)$ with a sharp transitional feature fit the data well, we study the realisation of such models in quintessence. In the late Universe, the quintessence field begins to oscillate abruptly, changing the behaviour of $w$. Naturally, such a model entails tachyonic instability, and particle production modifies $w$. We perform numerical lattice simulations to study the time dependence of $w$. In addition, the violent particle production produces significant density perturbations and the stochastic gravitational-wave background, whose characteristic scale depends on the mass scale of the quintessence around the minimum of the potential. We discuss the observability of these late-time cosmological signals through cosmic microwave background, quasar astrometry, pulsar timing arrays, and other observational probes.

astro-ph.CO↗

arXiv2025

Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting

The stochastic-$\delta \mathcal{N}$ formalism is widely used to study inflation models in which the quantum diffusion of inflatons dominates the background dynamics, leading to interesting phenomena such as the production of primordial black holes. Among numerical approaches to calculate the curvature perturbation spectrum $\mathcal{P}_\zeta(k)$ in this formalism, the Monte Carlo simulation-based approach has been proposed as a promising choice, especially in multifield cases. In this approach, we generate many paths of inflatons from the initial points to the end of inflation, obtain statistics of $\delta N$ from the paths, and then estimate $\mathcal{P}_\zeta(k)$. However, this method involves a nested Monte Carlo simulation, which requires generating many branch paths from each trunk path at the point corresponding to the scale $k$ of interest, resulting in a high computational cost. In this paper, we propose a new Monte Carlo-based approach that utilizes least squares fitting, introducing two novel features for reducing computational cost. First, we devise a simple estimator of a key statistic $\langle \delta\mathcal{N}_{\mathbf{X}}^2\rangle$, the variance of $\delta \mathcal{N}$ conditioned on the branching point, to avoid nesting path generation. Second, via least squares fitting of a parametric function to the sampled values of the estimator, we obtain not just an estimate of $\mathcal{P}_\zeta(k)$ for a single value of $k$ but an approximating function of $\mathcal{P}_\zeta(k)$ over a range of $k$ of interest. We also conduct numerical demonstrations for concrete inflation models, which show the usefulness of our method.

astro-ph.CO↗

arXiv2025

Stochastic-tail of the curvature perturbation in hybrid inflation

The exponential-tail behaviours of the probability density function (PDF) of the primordial curvature perturbation are confirmed in the mild-waterfall variants of hybrid inflation with the use of the stochastic formalism of inflation. On top of these tails, effective upper bounds on the curvature perturbation are also observed, corresponding to the exact hilltop trajectory during the waterfall phase. We find that in the model where the leading and higher-order terms in the expansion of the inflaton potential around the critical point are fine-tuned to balance, this upper bound can be significantly reduced, even smaller than the primordial black hole (PBH) threshold, as a novel perturbation-reduction mechanism than the one proposed by Tada and Yamada. It makes PBH formation much difficult compared to the Gaussian or exponential-tail approximation. We also introduce Johnson's $S_U$-distribution as a useful fitting function for the PDF, which reveals a nonlinear mapping between the Gaussian field and the curvature perturbation.

astro-ph.CO↗

arXiv2025

Dip and non-linearity in the curvature perturbation from inflation with a transient non-slow-roll stage

We consider models of inflation that contain a transient non-slow-roll stage and investigate the conditions under which a dip appears in the power spectrum of the curvature perturbation. Using the $\delta N$ formalism, we derive a general relation between the comoving curvature perturbation ${\cal{R}}$ and the scalar field perturbation $\delta\varphi$ and its velocity perturbation $\delta\pi$. Compared with the result obtained in linear perturbation theory, it turns out that properly taking account of the $\delta\pi$ contribution is essential to reproduce the dip in the power spectrum. Namely, the curvature perturbation is proportional to a specific linear combination of $\delta\varphi$ and $\delta\pi$ at the linear order. We also investigate the non-linearity at the dip scale and find that models with a bump or an upward step exhibit much larger non-linearity than ultra-slow-roll and Starobinsky's linear potential models. Finally, we demonstrate the importance of non-linearity by computing the probability density functions (PDFs) for the above-mentioned models and show that highly asymmetric PDFs are realised for models with a bump or a step.

astro-ph.CO↗

arXiv2024

Primordial black holes and induced gravitational waves from logarithmic non-Gaussianity

We investigate the formation of primordial black hole (PBH) based on numerical relativity simulations and peak theory as well as the corresponding scalar induced gravitational wave (SIGW) signals in the presence of \emph{logarithmic non-Gaussianities} which has recently been confirmed in a wide class of inflation models. Through numerical calculations, we find certain parameter spaces of the critical thresholds for the type A PBH formation and reveal a maximum critical threshold value. We also find that there is a region where no PBH is produced from type II fluctuations contrary to a previous study. We then confirm that SIGW signals originated from the logarithmic non-Gaussianity are detectable in the Laser Interferometer Space Antenna if PBHs account for whole dark matter. Finally, we discuss the SIGW interpretation of the nHz stochastic gravitational wave background reported by the recent pulsar timing array observations. We find that PBH overproduction is a serious problem for most of the parameter space, while this tension might still be alleviated in the non-perturbative regime.

astro-ph.CO↗

arXiv2024

Towards a classification of UV completable Higgs inflation in metric-affine gravity

Towards a classification of UV completable Higgs inflation in the framework of parity-even metric-affine gravity, we investigate the particle spectrum of a deformed theory in the large-$N$ limit. In a simple Higgs inflation model in metric-affine gravity, it is known that its UV cutoff is much smaller than the Planck scale. While it calls for UV completion, a concrete example has not yet been found, even with the large-$N$ limit known as a successful technique to complete an original Higgs inflation defined on the Riemannian geometry. This motivates us to study how small deformation of the simple Higgs inflation affects the emergence and properties of dynamical fields particularly in the large-$N$ limit. As a UV theory has to be free of ghosts or tachyons at least around Minkowski space, we perform the parameter search and find the healthy parameter region where a new heavy particle can propagate without these pathologies.

hep-th↗

arXiv2024

Improved quantum algorithm for calculating eigenvalues of differential operators and its application to estimating the decay rate of the perturbation distribution tail in stochastic inflation

Quantum algorithms for scientific computing and their applications have been studied actively. In this paper, we propose a quantum algorithm for estimating the first eigenvalue of a differential operator $\mathcal{L}$ on $\mathbb{R}^d$ and its application to cosmic inflation theory. A common approach for this eigenvalue problem involves applying the finite-difference discretization to $\mathcal{L}$ and computing the eigenvalues of the resulting matrix, but this method suffers from the curse of dimensionality, namely the exponential complexity with respect to $d$. Our first contribution is the development of a new quantum algorithm for this task, leveraging recent quantum singular value transformation-based methods. Given a trial function that overlaps well with the eigenfunction, our method runs with query complexity scaling as $\widetilde{O}(d^3/\epsilon^2)$ with $d$ and estimation accuracy $\epsilon$, which is polynomial in $d$ and shows an improvement over existing quantum algorithms. Then, we consider the application of our method to a problem in a theoretical framework for cosmic inflation known as stochastic inflation, specifically calculating the eigenvalue of the adjoint Fokker--Planck operator, which is related to the decay rate of the tail of the probability distribution for the primordial density perturbation. We numerically see that in some cases, simple trial functions overlap well with the first eigenfunction, indicating our method is promising for this problem.

quant-ph↗

arXiv2024

Constant roll and non-Gaussian tail in light of logarithmic duality

The curvature perturbation in a model of constant-roll (CR) inflation is interpreted in view of the logarithmic duality discovered in Ref. [1] according to the $\delta N$ formalism. We confirm that the critical value $\beta:=\ddot{\varphi}/(H\dot{\varphi})=-3/2$ determining whether the CR condition is stable or not is understood as the point at which the dual solutions, i.e., the attractor and non-attractor solutions of the field equation, are interchanged. For the attractor-solution domination, the curvature perturbation in the CR model is given by a simple logarithmic mapping of a Gaussian random field, which can realise both the exponential tail (i.e., the single exponential decay) and the Gumbel-distribution-like tail (i.e., the double exponential decay) of the probability density function, depending on the value of $\beta$. Such a tail behaviour is important for, e.g., the estimation of the primordial black hole abundance.

astro-ph.CO↗

arXiv2024

STOLAS: STOchastic LAttice Simulation of cosmic inflation

We develop a C++ package of the STOchastic LAttice Simulation (STOLAS) of cosmic inflation. It performs the numerical lattice simulation in the application of the stochastic-$\delta N$ formalism. STOLAS can directly compute the three-dimensional map of the observable curvature perturbation without estimating its statistical properties. In its application to two toy models of inflation, chaotic inflation and Starobinsky's linear-potential inflation, we confirm that STOLAS is well-consistent with the standard perturbation theory. Furthermore, by introducing the importance sampling technique, we have success in numerically sampling the current abundance of primordial black holes in a non-perturbative way. The package is available at https://github.com/STOchasticLAtticeSimulation/STOLAS_dist.

astro-ph.CO↗

arXiv2024

Multifield Stochastic Dynamics in GUT Hybrid Inflation and Gravitational Wave Signatures of GUT Higgs Representation

We revisit the hybrid inflation model within the framework of the Grand Unified Theory (GUT), focusing on cases where the waterfall phase transition extends over several e-foldings to dilute monopoles. Considering the stochastic effects of quantum fluctuations, we demonstrate that the waterfall fields (i.e., GUT Higgs) maintain a nonzero vacuum expectation value around the waterfall phase transition. By accurately accounting for the number of degrees of freedom of the GUT Higgs field, we establish that these fluctuations can produce observable gravitational waves without leading to an overproduction of primordial black holes. The amplitude of these gravitational waves is inversely proportional to the degrees of freedom of the waterfall fields, thereby providing a unique method to probe the representation of the GUT Higgs.

hep-ph↗

arXiv2024

The LISA forecast on a smooth crossover beyond the Standard Model through the scalar-induced gravitational waves

Supposing the Laser Interferometer Space Antenna (LISA) gravitational wave (GW) detector, we exhibit the detectability of a hypothetical smooth crossover in the early universe beyond the Standard Model of particle physics through the scalar-induced gravitational wave (SIGW) in terms of the Fisher forecast. A crossover at $\sim100\,\mathrm{TeV}$ can leave a signal on the GW spectrum in the $\sim\mathrm{mHz}$ frequency range, the sweet spot of the LISA sensitivity. These possibilities are also interesting in the primordial black hole (PBH) context as the associated PBH mass $\sim10^{22}\,\mathrm{g}$ lies at the window to explain the whole dark matter. We found that the properties of the crossover can be well determined if the power spectrum of primordial scalar perturbations are as large as $\sim5\times10^{-4}$ on the corresponding scale $\sim10^{12}\,\mathrm{Mpc^{-1}}$.

astro-ph.CO↗

arXiv2024

Quintessential interpretation of the evolving dark energy in light of DESI

The recent result of Dark Energy Spectroscopic Instrument (DESI) in combination with other cosmological data shows evidence of the evolving dark energy parameterized by $w_0w_a$CDM model. We interpret this result in terms of a quintessential scalar field and demonstrate that it can explain the DESI result even though it becomes eventually phantom in the past. Relaxing the assumption on the functional form of the equation-of-state parameter $w=w(a)$, we also discuss a more realistic quintessential model. The implications of the DESI result for Swampland conjectures, cosmic birefringence, and the fate of the Universe are discussed as well.

astro-ph.CO↗

arXiv2023

Prospects of detection of subsolar mass primordial black hole and white dwarf binary mergers

The subsolar mass primordial black hole (PBH) attracts attention as robust evidence of its primordial origin against the astrophysical black hole. Not only with themselves, PBHs can also form binaries with ordinary astrophysical objects, catching them by gravitational wave (GW) bremsstrahlung. We discuss the detectability of the inspiral GWs from binaries consisting of a PBH and a white dwarf (WD) by using space-borne gravitational wave interferometers like DECIGO. The conservative assessment shows the expected event number in three years by DECIGO is $\mathcal{O}(10^{-6})$ for $M_\mathrm{PBH} \sim 0.1M_\odot$. Possible enhancement mechanisms of WD-PBH binary formation may amplify this event rate. We discuss how large enhancement associated with WDs is required to detect WD-PBH merger events without violating the existing constraints on the PBH-PBH merger by the ground-based detector.

gr-qc↗