2024

Joint workshop on General Relativity and Cosmology
Dive into the Cosmic Abyss: Echoes from Primordial Black Hole
Y. Tada
7th March 2024 @ Sunshine Shirako
invited talk

YITP long-term workshop "Gravity and Cosmology 2024"
Cancellation of quantum corrections on the soft curvature perturbations ▼
We study the cancellation of quantum corrections on the superhorizon curvature perturbations from subhorizon physics beyond the single-clock inflation from the viewpoint of the cosmological soft theorem. As an example, we focus on the transient ultra-slow-roll inflation scenario and compute the one-loop quantum corrections to the power spectrum of curvature perturbations taking into account nontrivial surface terms in the action. We find that Maldacena’s consistency relation is satisfied and guarantees the cancellation of contributions from the short-scale modes. As a corollary, primordial black hole production in single-field inflation scenarios is not excluded by perturbativity breakdown even for the sharp transition case in contrast to some recent claims in the literature. I may also comment on the relation between the tadpole diagram in the in-in formalism and the shift of the elapsed time in the stochastic-δN formalism as well as the application to the tensor perturbations.
Y. Tada, T. Terada, J. Tokuda
29th January 2024 @ YITP
oral, refereed

2023

The 32nd Texas Symposium on Relativistic Astrophysics
The present and future of primordial black holes as dark matter
Y. Tada
12th December 2023 @ Everbright International Hotel (Shanghai)
invited talk

KASHIWA DARK MATTER SYMPOSIUM 2023
The present and future of primordial black holes as dark matter
Y. Tada
5th December 2023 @ Kashiwa Library Media Hall
invited talk

JGRG 32
Cancellation of quantum corrections on the soft curvature perturbations ▼
We study the cancellation of quantum corrections on the superhorizon curvature perturbations from subhorizon physics beyond the single-clock inflation from the viewpoint of the cosmological soft theorem. As an example, we focus on the transient ultra-slow-roll inflation scenario and compute the one-loop quantum corrections to the power spectrum of curvature perturbations taking into account nontrivial surface terms in the action. We find that Maldacena’s consistency relation is satisfied and guarantees the cancellation of contributions from the short-scale modes. As a corollary, primordial black hole production in single-field inflation scenarios is not excluded by perturbativity breakdown even for the sharp transition case in contrast to some recent claims in the literature. I may also comment on the relation between the tadpole diagram in the in-in formalism and the shift of the elapsed time in the stochastic-δN formalism as well as the application to the tensor perturbations.
Y. Tada, T. Terada, J. Tokuda
27th September 2023 @ Nagoya U.
oral, refereed

COSMO'23
Squeezed bispectrum and one-loop corrections in transient constant-roll inflation ▼
In canonical single-field inflation, the production of primordial black holes (PBH) requires a transient violation of the slow-roll condition. The transient ultra slow-roll inflation is an example of such scenarios, and more generally, one can consider the transient constant-roll inflation. We investigate the squeezed bispectrum in the transient constant-roll inflation and find that Maldacena's consistency relation holds for a sufficiently long-wavelength mode, whereas it is violated for modes around the peak scale for the non-attractor case. We also demonstrate how the one-loop corrections are modified compared to the case of the transient ultra slow-roll inflation, focusing on representative one-loop terms originating from a time derivative of the second slow-roll parameter in the cubic action. We find that the perturbativity requirement on those terms does not rule out the production of PBH from the transient constant-roll inflation. Therefore, it is a simple counterexample of the recently claimed no-go theorem of PBH production from single-field inflation.
H. Motohashi, Y. Tada, T. Terada, J. Tokuda
15th September 2023 @ IFT
oral, refereed

YITP International Molecule-type Workshop "Revisiting cosmological non-linearities in the era of precision surveys"
Stochastic approach to the inflationary universe ▼
The stochastic formalism known as an effective theory of superHubble coarse-grained fields is a powerful tool for a non-perturbative analysis of the inflationary universe. It views the coarse-grained inflaton field as a stochastic Brownian motion and its random behaviour leaves an imprint for the later universe as the primordial curvature perturbation. In this talk, I will first review the basic derivation of the stochastic formalism and then describe in detail the so-called stochastic-deltaN approach to calculate the curvature perturbation in the stochastic formalism. I will formulate the power spectrum and the probability density function of the coarse-grained curvature perturbation and show its numerical implementation. As practical examples, the hybrid-inflation and flat-inflection models are discussed, related to the recent hot topic: primordial black holes. I may mention its further application to gauge field production in axion inflation beyond the dynamics of the scalar inflaton fields, and also the lattice simulation in the stochastic formalism as a full numerical computation scheme.
Y. Tada
27th July 2023 @ YITP
oral, invited

New Horizons in Primordial Black Hole Physics
Statistics of coarse-grained cosmological fields in stochastic inflation ▼
We present a generic framework to compute the one-point statistics of cosmological perturbations, when coarse-grained at an arbitrary scale 𝑅, in the presence of quantum diffusion. Making use of the stochastic-𝛿𝑁 formalism, we show how it can be related to the statistics of the amount of expansion realised until the scale 𝑅 crosses out the Hubble radius. This leads us to explicit formulae for the probability density function (PDF) of the curvature perturbation, the comoving density contrast, and the compaction function. We then apply our formalism to the calculation of the mass distribution of primordial black holes produced in a single-field model containing a “quantum well” (i.e. an exactly flat region in the potential). We confirm that the PDFs feature heavy, exponential tails, with an additional cubic suppression in the case of the curvature perturbation. The large-mass end of the mass distribution is shown to be mostly driven by stochastic-contamination effects, which produce black holes more massive than those naively expected. This work bridges the final gap between the stochastic-inflation formalism and the calculation of the mass distribution of astrophysical objects such as primordial black holes and opens up various prospects that we finally discuss.
Y. Tada and V. Vennin
19th June 2023 @ Naples
oral, refereed

i-LINK workshop on observational cosmology
Revisiting the formation of massive primordial black holes in hybrid inflation
Y. Tada and M. Yamada
7th June 2023 @ Nagoya
oral, refereed

Domestic Molecule-type Workshop "Non-linear Nature of Cosmological Perturbations and its Observational Consequences"
On the soft theorem in the transient ultra-slow or constant roll inflation
H. Motohashi and Y. Tada
28th March 2023 @ YITP
oral, invited

19th Rencontres du Vietnam "Theory meeting experiments: particle astrophysics and cosmology"
Inflation theory — D'où venons-nous? Que sommes-nous? Où allons-nous? —
Y. Tada
8th January 2023 @ ICISE
oral, invited

2022

TSQS 2022
Stochastic approach to cosmic inflation ▼
Cosmic inflation, the accelerated expansion phase of the universe in advance of the hot big-bang universe, is now considered as the standard paradigm of the modern cosmology. Not only does it realize a globally homogeneous and isotropic universe, but it can also generate fine density perturbations from the quantum zero-point fluctuation as a source of current cosmic structures like stars or galaxies. In the ordinary approach, the predicted fluctuation in each inflation model is calculated with use of the perturbative quantum field theory (QFT) in the curved spacetime. However, it cannot be applied for large fluctuations which can cause for example the so-called primordial black hole, one candidate of dark matter. Instead of the standard perturbative QFT, the effective theory of the coarse-grained field called stochastic formalism is also known as another powerful tool. In the accelerated expansion spacetime, the coarse-grained effective theory reads a classical (non-quantum), stochastic process (i.e., Brownian motion) and thus even large fluctuations can be treated directly. Since we have developed how to calculate fluctuations in a form conserved even after the end of inflation, many aspects of this approach have been investigated. I will introduce these recent developments in the talk.
Y. Tada
8th November 2022 @ The University of Tokyo
poster, refereed

JGRG31
Hybrid metric-Palatini Higgs inflation ▼
We propose an extension of the Higgs inflation to the hybrid metric-Palatini gravity, where we introduce non-minimal couplings between Higgs and both the metric-type Ricci scalar and the Palatini-type one. We find that slow-roll inflation can be realized in the large-field regime, giving the observationally favored predictions on the scalar spectral index, and the tensor-to-scalar ratio can take an arbitrary value depending on the non-minimal coupling parameters, the metric-one r ~ 10^-3 being the maximum. The UV cutoff as a low-energy EFT of this model is suppressed by the large non-minimal couplings between Higgs and Ricci scalars, but it can be lifted higher than the dynamical scale by introducing a new scalar degree of freedom, which is equivalent to embedding the curved scalar field space into a higher dimensional flat space. We however find that the Plack-scale UV-completion is realized only in the metric limit.
M. He, Y. Mikura, and Y. Tada
25th October 2022 @ The University of Tokyo
oral, refereed

FY2021 学術変革領域研究「ダークマター」シンポジウム
Primordial black holes and induced gravitational waves in light of the non-Gaussian tail ▼
The primordial black hole (PBH) is one of the candidate of dark matters if their masses are as small as asteroids. PBHs are likely to be accompanied by sizable stochastic gravitational waves (GWs) induced by the large primordial density perturbations which caused PBHs. As such GWs are expected detectable by future space-based GW telescopes such as LISA, it is important to precisely relate the GW power spectrum with the PBH mass function, which can be done by refining their prediction formulations from the common primordial density perturbations. Meanwhile, recently it has been pointed out that the inflaton's ultra-slow-roll dynamics, which is a promising mechanism to amplify the primordial perturbations, can significantly change the probability of large perturbations due to the so-called non-Gaussian (NG) tail and affect the PBH abundance prediction. In our works, we update the so-called peak theory for the PBH prediction in order to deal with the NG tail. We also discuss the effect of the NG tail on the induced GWs.
K. T. Abe, A. Escrivà, N. Kitajima, R. Inui, Y. Tada, S. Yokoyama, C. M. Yoo
30th March 2022 @ Kavli IPMU (online)
oral, invited

2021

JGRG30
Probability density functions of coarse-grained curvature and density perturbations in stochastic inflation ▼
The primordial black hole (PBH) has been attracting attentions more and more. It is caused by the order-unity primordial perturbation and thus its formation rate is evaluated by the probability density function (PDF) of such a large perturbation, where the ordinary perturbative calculation is expected to break down. In fact, the stochastic formalism, a non-perturbative approach to inflation, implies an even qualitative difference in the PDF behavior: the PDF at large value decays only exponentially contrary to the Gaussian suppression even in the case where the non-Gaussianity is small enough around the origin. In order for the PBH mass function, the PDF of the perturbation coarse-grained on an arbitrary scale corresponding to the mass of interest. In this work, we formulate a non-perturbative algorithm for the PDF of the coarse-grained curvature/density perturbation, making use of the stochastic formalism. Y. Tada and V. Vennin
9th December 2021 @ Waseda U. (online)
oral, refereed

The KEK-PH + KEK-Cosmo joint workshop on "Primordial Black Holes"
Primordial black holes in peak theory with a non-Gaussian tail ▼
In this work, we update the peak theory for the estimation of the primordial black hole (PBH) abundance, particularly by implementing the critical behavior in the estimation of the PBH mass and employing the averaged compaction function for the PBH formation criterion to relax the profile dependence. We apply our peak theory to a specific non-Gaussian feature called the exponential tail, which is characteristic in ultra slow-roll models of inflation. With this type of non-Gaussianity, the probability of a large perturbation is not suppressed by the Gaussian factor but decays only exponentially, so the PBH abundance is expected to be much enhanced. Not only do we confirm this enhancement even compared to the case of the corresponding nonlinearity parameter fNL=5/2, but also we find that the resultant PBH mass spectrum has a characteristic maximal mass which is not seen in the simple Press--Schechter approach. N. Kitajima, Y. Tada, S. Yokoyama and C. M. Yoo
19th October 2021 @ KEK (online)
oral, refereed

COSMO'21
Probability density functions of coarse-grained curvature and density perturbations in stochastic inflation ▼
The primordial black hole (PBH) has been attracting attentions more and more. It is caused by the order-unity primordial perturbation and thus its formation rate is evaluated by the probability density function (PDF) of such a large perturbation, where the ordinary perturbative calculation is expected to break down. In fact, the stochastic formalism, a non-perturbative approach to inflation, implies an even qualitative difference in the PDF behavior: the PDF at large value decays only exponentially contrary to the Gaussian suppression even in the case where the non-Gaussianity is small enough around the origin. In order for the PBH mass function, the PDF of the perturbation coarse-grained on an arbitrary scale corresponding to the mass of interest. In this work, we formulate a non-perturbative algorithm for the PDF of the coarse-grained curvature/density perturbation, making use of the stochastic formalism.
Y. Tada and V. Vennin
2–6th August 2021 @ The University of Illinois (online)
poster, refereed

2021 NRF-JSPS Workshop in particle physics, cosmology, and gravitation
Primordial black holes in peak theory with a non-Gaussian tail
N. Kitajima, Y. Tada, S. Yokoyama, and C-M. Yoo
21st July 2021 @ Alpensia Resort, Pyeongchang, Korea / online
oral, invited

2020

Online JGRG Workshop 2020
Manifestly covariant theory of stochastic inflation ▼
The stochastic approach to inflation can non-perturbatively treat the superhorizon fluctuations as the classical random noise to go beyond the standard perturbative QFT approach. I first review how this approach enables us to calculate the observable curvature perturbations in a non-perturbative way and how it can be implemented in a numerical program. I then describe the covariance of the stochastic theory and the discretization scheme of the stochastic noise, which are important both theoretically and practically. Mathematically the stochastic noise can be discretized in an arbitrary manner, but we reveal the physically motivated discretization, which ensures the covariance of the stochastic theory on the inflatons' target manifold.
L. Pinol, S. Renaux-Petel, and Y. Tada
25th November 2020 @ online
poster, refereed
Outstanding Presentation Award Gold Prize

PBH & Stochastic inflation workshop
StocDeltaN: numerical approach to inflation in combination of the stochastic and delta N formalism ▼
The stochastic approach to inflation enables us to treat the superhorizon perturbations in a non-perturbative way. Though it deals only with the inflatons’ perturbations in itself, fluctuations in the duration of inflation can be connected with the observable curvature perturbations from the viewpoint of the delta N formalism. In 2015, Vennin and Starobinsky revealed the adjoint Fokker-Planck equation for the probability density function of such time fluctuations. We with Renaux-Petel are now developing a C++ package to automatically solve this adjoint FP eq. and enable a full stochastic analysis for arbitrary models of inflation. I’ll introduce this ongoing project with several examples.
S. Renaux-Petel, Y. Tada, and V. Vennin
10th November 2020 @ online
oral, invited

The 14th International Conference on Gravitation, Astrophysics and Cosmology (ICGAC14)
Manifestly covariant theory of stochastic inflation ▼
The stochastic approach to inflation can non-perturbatively treat the superhorizon fluctuations as the classical random noise to go beyond the standard perturbative QFT approach. I first review how this approach enables us to calculate the observable curvature perturbations in a non-perturbative way and how it can be implemented in a numerical program. I then describe the covariance of the stochastic theory and the discretization scheme of the stochastic noise, which are important both theoretically and practically. Mathematically the stochastic noise can be discretized in an arbitrary manner, but we reveal the physically motivated discretization, which ensures the covariance of the stochastic theory on the inflatons' target manifold.
L. Pinol, S. Renaux-Petel, Y. Tada, and V. Vennin
20th August 2020 @ National Central University, Taiwan (online)
oral, refereed

The 3rd KMI School：Machine Learning in Particle and Astrophysics
StocDeltaN: numerical approach to inflation beyond the perturbation theory in the stochastic formalism ▼
The important role of inflation in the early universe is to generate the primordial perturbation as a source of current cosmic structures from the quantum zero-point fluctuation. The driving field, inflaton, gets fluctuated on the horizon scale and therefore each horizon patch behaves like as the Brownian motion, known as the stochastic formalism. The conserved perturbation inherited by the later universe is not the inflaton perturbation itself but the duration fluctuation of inflation. Therefore the problem is reduced to the probability distribution of the first passage time in a diffusion system. In principle, there is no need of the perturbative expansion in this approach, compared to the standard QFT calculation. We provide a C++ package "StocDeltaN", which automatically solve such a diffusion system and calculate the power spectrum of the primordial perturbation. It is applicable to general multi-scalar models beyond the slow-roll approximation.
S. Renaux-Petel, Y. Tada, and V. Vennin
6th March 2020 @ Nagoya U.
poster, refereed
POSTPONED

2019

Focus Week on Primordial Black Holes
Primordial black hole tower: Dark matter, earth-mass, and LIGO black holes ▼
We investigate a possibility of primordial black hole (PBH) formation with a hierarchical mass spectrum in multiple phases of inflation. As an example, we find that one can simultaneously realize a mass spectrum that has recently attracted a lot of attention: stellar-mass PBHs (~O(10)M_\odot) as a possible source of binary black holes detected by LIGO/Virgo collaboration, asteroid-mass (~O(10^-12)M_\odot) as a main component of dark matter, and earth-mass (~O(10^-5)M_\odot) as a source of ultrashort-timescale events in Optical Gravitational Lensing Experiment microlensing data. The recent refined de Sitter swampland conjecture may support such a multiphase inflationary scenario with hierarchical mass PBHs as a transition signal of each inflationary phase.
Y. Tada and S. Yokoyama
6th December 2019 @ KavliIPMU
oral, refereed

JGRG29
Stochastic inflation with an extremely large number of e-folds ▼
We propose a class of single-field, slow-roll inflation models in which a typical number of e-folds can be extremely large. The key point is to introduce a very shallow local minimum near the top of the potential in a hilltop inflation model. In particular, a typical number of e-folds is enhanced if classical behavior dominates around the local minimum such that the inflaton probability distribution is drifted to the local minimum as a whole. After the inflaton escapes from the local minimum due to the stochastic dynamics, the ordinary slow-roll inflation follows and it can generate the primordial density perturbation consistent with observation. Interestingly, our scenario inherits the advantages of the old and new inflation: the typical e-folds can be extremely large as in the old inflation, and slow-roll inflation naturally follows after the stochastic regime as in the new inflation. In our numerical example, the typical number of e-folds can be as large as 10^10^8, which is large enough for various light scalars such the QCD axion to reach the Bunch-Davies distribution.
N. Kitajima, Y. Tada, and F. Takahashi
27th November 2019 @ Kobe U.
oral, refereed

Theoretical aspects of non-Gaussianity from modern perspectives
Stochastic approach to non-Gaussianity
Y. Tada and V. Vennin
19th November 2019 @ YITP
oral, refereed

GWPAW 2019
Primordial black hole tower: Dark matter, earth-mass, and LIGO black holes
Y. Tada and S. Yokoyama
16th October 2019 @ Sanjo Kaikan, The University of Tokyo
oral, refereed

COSMO19
Primordial black hole tower: Dark matter, earth-mass, and LIGO black holes ▼
We investigate a possibility of primordial black hole (PBH) formation with a hierarchical mass spectrum in multiple phases of inflation. As an example, we find that one can simultaneously realize a mass spectrum which has recently attracted a lot of attention, stellar-mass PBHs ($\sim\mathcal{O}(10)M_\odot$) as a possible source of binary black holes detected by LIGO/VIRGO collaboration, asteroid-mass ($\sim\mathcal{O}(10^{-12})M_\odot$) as a main component of dark matter, and earth-mass ($\sim\mathcal{O}(10^{-15})M_\odot$) as a source of ultrashort-timescale events in OGLE microlensing data. The recent refined swampland conjecture may support these multi-phase inflationary scenario with hierarchical mass PBHs as a transition signal of each inflationary phase.
Y. Tada and S. Yokoyama
4th September 2019 @ RWTH Aachen U.
poster, refereed

15th Rencontres du Vietnam "COSMOLOGY"
Primordial black hole tower: Dark matter, earth-mass, and LIGO black holes ▼
As proposed by Hawking and Carr more than four decades ago, black holes can be formed even during the early radiation-dominated era in advance of the ordinary star formation, called “primordial black hole (PBH)”. The possible mass of PBHs covers very wide range, and the extremely light one (~10^-12 M_\odot) attracts attention as a candidate of the main component of dark matters. qMoreover recent LIGO/VIRGO’s gravitational wave detections have revealed the ubiquitous existence of slightly massive and less spinning BHs, which also can be explained by the primordial ones. I first briefly review such astrophysical motivations of PBHs and current constraints on those. Then I show that PBHs can be easily realized if inflation is not a single continuous phase but can be divided into multiple phases. Interestingly recently proposed “dS conjecture” in the context of string theory may also support such a multi-phase inflation scenario.
Y. Tada and S. Yokoyama
16th August 2019 @ ICISE
oral, invited

3-day workshop: INFLATION AND GEOMETRY
Stochastic formalism and curvature perturbation ▼
In the stochastic formalism, perturbations on inflaton fields are absorbed into the background dynamics as Brownian noise, enabling the analysis beyond the perturbation theory. In this talk, I briefly review the so-called stochastic-deltaN approach, which combines the stochastic and deltaN formalisms to calculate the observable curvature perturbations in a non-perturbative way. This approach can be described by the recursive set of partial differential equations, and therefore it can be numerically implemented as I will introduce. I also mention the extension this formalism to the non-trivial field space cases.
T. Fujita, L. Pinol, S. Renaux-Petel, Y. Tada, J. Tokuda, and V. Vennin
13th June 2019 @ IAP
oral, invited

2-day mini-workshop: Axion Cosmology
PBH tower in multi-phase inflation ▼
Primordial black holes (PBH) have been attracting attentions again in response to the LIGO's first direct detection of gravitational waves (GW) from the merger of slightly more massive BHs $\sim\mathcal{O}(10)\,M_\odot$ than ordinary ones. Also much lighter PBH $\sim\mathcal{O}(10^{20})\,\mathrm{g}$ can comprise all dark matters (DM) and therefore the interesting mass ranges of PBH are separated. On the other hand, the recent swampland conjecture suggests that the string theory might disfavor even the quasi-stable dS spacetime, implying multiple phases of inflation. In this talk, we investigate the PBH formation with multiple masses in such a multi-phase inflation model beyond the slow-roll approximation on the second derivative of the inflatons' potential. We also discuss the secondary GW induced by large density perturbations causing PBH.
Y. Tada and S. Yokoyama
15th May 2019 @ YITP
oral, refereed

Future Perspective in Cosmology and Gravity
PBH tower in multi-phase inflation ▼
Primordial black holes (PBH) have been attracting attentions again in response to the LIGO's first direct detection of gravitational waves (GW) from the merger of slightly more massive BHs $\sim\mathcal{O}(10)\,M_\odot$ than ordinary ones. Also much lighter PBH $\sim\mathcal{O}(10^{20})\,\mathrm{g}$ can comprise all dark matters (DM) and therefore the interesting mass ranges of PBH are separated. On the other hand, the recent swampland conjecture suggests that the string theory might disfavor even the quasi-stable dS spacetime, implying multiple phases of inflation. In this talk, we investigate the PBH formation with multiple masses in such a multi-phase inflation model beyond the slow-roll approximation on the second derivative of the inflatons' potential. We also discuss the secondary GW induced by large density perturbations causing PBH.
Y. Tada and S. Yokoyama
3rd April 2019 @ Nagoya U.
oral, refereed

Accelerating Universe in the Dark
PBH tower in multi-phase inflation ▼
Primordial black holes (PBH) have been attracting attentions again in response to the LIGO's first direct detection of gravitational waves (GW) from the merger of slightly more massive BHs $\sim\mathcal{O}(10)\,M_\odot$ than ordinary ones. Also much lighter PBH $\sim\mathcal{O}(10^{20})\,\mathrm{g}$ can comprise all dark matters (DM) and therefore the interesting mass ranges of PBH are separated. On the other hand, the recent swampland conjecture suggests that the string theory might disfavor even the quasi-stable dS spacetime, implying multiple phases of inflation. In this talk, we investigate the PBH formation with multiple masses in such a multi-phase inflation model beyond the slow-roll approximation on the second derivative of the inflatons' potential. We also discuss the secondary GW induced by large density perturbations causing PBH.
Y. Tada and S. Yokoyama
7th March 2019 @ Kyoto U.
oral, refereed

FAPESP-JSPS Workshop on dark energy, dark matter, and galaxies
Aspects of primordial black hole as dark matter
K. Inomata, M. Kawasaki, A. Kusenko, K. Mukaida, Y. Tada, T. T. Yanagida, and S. Yokoyama
19th February 2019 @ U. of Sao Paulo
oral, refereed
Young Representative Speaker

2018

JGRG28
Stochastic formalism and curvature perturbations ▼
After briefly reviewing our recent works about the stochastic formalism extended to general multi-field cases, we show several results of our new numerical code. Combining the stochastic and delta N formalism, it can automatically calculate the statistics of e-folding numbers in the phase space for general inflationary models and then obtain the power spectrum of the curvature perturbations.
T. Fujita, L. Pinol, S. Renaux-Petel, Y. Tada, and J. Tokuda
8th November 2018 @ Rikkyo U.
oral, refereed

MOGRA 2018
Stochastic inflation in a general field space ▼
Inflationary models in non-trivial field spaces encoded by their non-canonical kinetic terms have attracted attentions recently. We have then extended the so-called stochastic formalism to such a general case. This formalism investigates the fluctuation of inflatons treating them as Brownian motions. This work highlights the involved problem of this formalism, related with the mathematical uncertainty of the definition of noise integral. Comparing the correlation functions in the stochastic formalism and quantum field theory, we clarify that this uncertainty cannot be removed but rather the smallness of this would be a new criterion of the validity for the application of this formalism. We also check that it does not affect the observable curvature perturbations so much at least in a single-field case. Practical application prescriptions of this formalism may be also mentioned.
T. Fujita, L. Pinol, S. Renaux-Petel, Y. Tada, and J. Tokuda
10th August 2018 @ Nagoya U.
oral, refereed

Fifteenth Marcel Grosmann Meeting
Stochastic inflation in a general field space ▼
Inflationary models in non-trivial field spaces encoded by their non-canonical kinetic terms have attracted attentions recently. On the other hand, the so-called stochastic formalism is known as a powerful tool to investigate a quantum diffusion effect on inflation. In this formalism, field fluctuations originating from the quantum zero-point oscillation are mimicked by classical random noise. We consistently formulate this prescription in a curved field space with use of the path integral method including metric perturbations. We also point out that this formalism has an inevitable ambiguity related with the arbitrariness of noise integral represented by the Ito or Stratonovich process. The smallness of this ambiguity is suggested to be a novel criterion of the validity of the application of this formalism.
T. Fujita, L. Pinol, S. Renaux-Petel, Y. Tada, and J. Tokuda
5th July 2018 @ University of Rome "La Sapienza"
oral, refereed

Infrared physics of gauge theories and quantum dynamics of inflation
Subtleties in stochastic formalism - Ito vs. Stratonovich ▼
The equation of motion for inflaton fields is given by the Langevin equation in the stochastic formalism. Mathematically there is an uncertainty in how to interpret the noise integral like as the Ito or Stratonovich integral in such a stochastic differential equation. From the view point of the invariance of the multi-scalar Langevin we derived under the field-space coordinate transformation, we point out that there are drawbacks both in the Ito and Stratonovich interpretations.
L. Pinol, S. Renaux-Petel, and Y. Tada
20th–21st January 2018 @ Biwako Club
oral, refereed

2017

COSMO 17
Stochastic Formalism in Curved Field Space ▼
In multi-field inflation scenarios, the scalar fields can span curved field spaces in general. Recently it was pointed out that the sufficiently large field curvature can make the entropic degrees of freedom tachyonic during inflation and alter the inflation dynamics [PRL117, 141301]. This geometrical destabilization can be applied to a large class of inflationary models. To analyze the destabilization, we formalize the stochastic approach in the general curved field space from first principles, and also show some brief applications.
L. Pinol, S. Renaux-Petel, and Y. Tada
28th August–1st September 2017 @ the Universite Paris Diderot site, Amphitheatre Buffon
oral, refereed

Gordon Research Conference & Seminars "String Theory & Cosmology"
Primordial Black Hole, Dark Matter, and Gravitational Wave ▼
The primordial black hole (PBH), which might be produced due to possible large primordial perturbations, has been recently refocused on more and more. One of the main motivations of PBH is dark matter (DM), although the latest observational constraints have almost closed the possible window, except for ~10^{-13} solar-mass PBH. Also the first direct detection of gravitational waves (GWs) by LIGO/Virgo collaboration sheds light on the possibility that the observed massive black holes might be primordial ones. In my poster, I review these situations of PBH and discuss the PBH formation in a novel double inflation model.
K. Inomata, M. Kawasaki, A. Kusenko, K. Mukaida, Y. Tada, and T. T. Yanagida
27th May–2nd June 2017 @ Renaissance Tuscany Il Ciocco, Lucca (Barga), Italy
poster, refereed

2016

The 26th Workshop on General Relativity and Gravitation in Japan (JGRG26)
Squeezed Bispectrum in the delta N Formalism without Gauge Artifact
Y. Tada and V. Vennin
24th–28th October 2016 @ Osaka City University
oral, refereed

RESCEU Summer School
PBH Dark Matter in Supergravity Inflation Models
M. Kawasaki, A. Kusenko, Y. Tada, and T. T. Yanagida
24th–28th August 2016 @ Gifu
oral, not refereed

2015

Second LeCosPA International Symposium "Everything About Gravity"
Can massive primordial black holes be produced in mild waterfall hybrid inflation?
M. Kawasaki and Y. Tada
14th–18th December 2015 @ NTU
oral, refereed

International Conference on Particle Physics and Cosmology (COSMO-15)
PRIMORDIAL BLACK HOLES AS BIASED TRACERS
Y. Tada and S. Yokoyama
7th–11th September 2015 @ Warsaw
oral, refereed

2014

International Conference on Particle Physics and Cosmology (COSMO 2014)
Non-perturbative approach for curvature perturbations in stochastic-delta N formalism
T. Fujita, M. Kawasaki, and Y. Tada
25th–29th August 2014 @ Chicago
poster, refereed

2013

KEK Theory Meeting on Particle Physics Phenomenology (KEK-PH2013 FALL)
A new algorithm for calculating the curvature perturbations in stochastic inflation
T. Fujita, M. Kawasaki, Y. Tada, and T. Takesako
30th September–3rd October 2013 @ KEK
oral, refereed

2024

"Physics meets Mathematics" Summary Workshop
インフレーションと超準解析 — 原始ブラックホールに向けて —
多田祐一郎
2024年2月10–12日 @ 明治元年創業びわ湖畔の料理旅館 恵美寿荘
主催

2023

基研研究会 素粒子物理学の進展2023 (PPP2023)
原始ブラックホールは自然科学なのか
多田祐一郎
2023年9月1日 @ YITP
招待講演

日本物理学会春季大会
多重滝場ハイブリッドインフレーションと原始ブラックホール ▼
滝場が緩やかなハイブリッドインフレーションにおいて十分大きいスケールに大きな初期ゆらぎが作られ得るとして、重い原始ブラックホール (PBH) の実現が期待されたが、ゆらぎのスケールと振幅に単純な比例関係が成り立つことが明らかになり、重い PBH は必ず過剰生成されることが結論づけられた。一方滝場が1つではなく複数ある場合は滝場の数だけゆらぎが抑制されることが示唆されており、それにより適切な量の PBH を作る可能性は残されていた。本研究において我々はインフレーションの確率形式を用い初期ゆらぎを計算することで、確かにゆらぎが抑制されることを定量的に確認し、必要な滝場の数を明らかにする。
多田祐一郎, 山田將樹
2023年3月23日 @ オンライン
口頭, 査読なし

2022

第35回 理論懇シンポジウム
原始ブラックホール研究の近年の進展 ▼
LIGO による重力波直接観測の成功以降、原始ブラックホール (BH) はますます注目を集めており、特に小惑星程度の原始 BH は暗黒物質の候補として盛んに研究されている。原始 BH が大きな初期ゆらぎに起因したならばそのようなゆらぎは同時に背景重力波も作り、近い将来 LISA 望遠鏡で検証できる。大きなゆらぎはインフレーション機構への示唆としても重要である。近年これらの関係性が集中的に研究されており、例えば数値シミュレーションおよびピーク理論の整備により初期ゆらぎの統計性から原始 BH 量の正確な予測が可能になってきている。一方で初期ゆらぎの確率分布が非常に重い裾を持つ可能性も指摘され、それによる重力波量の変更も議論されている。本発表ではこれらの近年の状況をまとめて紹介する。
多田祐一郎
2022年12月21–23日 @ 福島
ポスター, 査読あり

第11回観測的宇宙論ワークショップ
曲率ゆらぎへの非摂動的アプローチ ▼
曲率ゆらぎのガウス分布からのずれはインフレーション機構への重要な示唆であり、近年はさらに非摂動的な確率分布の裾も注目されている。本講演ではインフレーションの確率形式等を用いた曲率ゆらぎの統計性の非摂動解析をご紹介するとともに、インフレーション宇宙の3次元格子シミュレーションを提案する。これによりN体計算等の初期条件を第一原理的に与えられれば興味深い。 多田祐一郎
2022年12月13日 @ 国立天文台
招待講演

Workshop on Gravitation & Cosmology
Recent progress on stochastic inflation
多田祐一郎
2022年11月29日 @ 富山
集中講義

日本物理学会秋季大会
アクシオンインフレーションにおける U(1) ゲージ場の確率形式 ▼
本研究では擬スカラーインフラトンと結合する U(1) ゲージ場の確率形式を定式化する。物理的電磁場に対する確率微分方程式を導き、それらの解析解を与える。また数値シミュレーションによりハッブル長で平均化された電磁場が常にその方向を変えることを見る。これらは局所的に等方性が自発的破れを起こしていることを意味するが、各ハッブル領域は独立であると見なされ大局的な統計的等方性は保存されたままである。
藤田智弘, 向田享平, 多田祐一郎
2022年9月6日 @ 岡山理科大
口頭, 査読なし

日本物理学会第77回年次大会
原始ブラックホールのピーク理論と非ガウス尾 ▼
原始ブラックホール量の見積もり法としてピーク理論を用いた統計処理が注目されているが、我々はブラックホール質量の臨界挙動とブラックホール形成判定条件としての平均化コンパクション関数を導入するようピーク理論を更新した。またこの手法を用い、近年注目されている「指数尾」と呼ばれる非ガウス性を持った初期ゆらぎに対してのブラックホール質量関数を議論する。負の非線形パラメータを持つ非ガウスゆらぎに対するブラックホール形成判定条件の数値解析にも触れる。
A. Escrivà, 北嶋直弥, 多田祐一郎, 横山修一郎, 柳哲文
2022年3月17日 @ オンライン
口頭, 査読なし

2021

日本物理学会秋季大会
粗視化曲率ゆらぎの確率密度関数 ▼
インフレーションによる曲率ゆらぎについて、パワースペクトルやバイスペクトル等の小さなゆらぎに対する統計性は摂動論から良くわかっているが、原始ブラックホール等の文脈では大きなゆらぎの統計性を正確に知る必要がある。大きなゆらぎに対しては摂動論が破綻することが予想され、したがって非摂動的手法である確率形式を応用する研究が注目されている。素朴な確率形式では曲率ゆらぎの粗視化スケールはインフレーション終了時のホライズンサイズに固定されてしまうが、実際の運用では粗視化スケールを任意に取りたい。本講演ではいくつかの例とともに、任意粗視化スケールに対する曲率ゆらぎの確率密度関数の導出法を紹介する。
多田祐一郎 and V. Vennin
2021年9月14日 @ オンライン
口頭, 査読なし

日本物理学会第76回年次大会
インフレーションの確率形式に対する共変な定式化 ▼
通常インフレーションにおけるゆらぎに対しては摂動的量子場の計算が用いられるが、インフレーションの確率形式においては超ホライズンのゆらぎを古典乱数として非摂動的に扱うことができる。発表ではまずこの確率形式がインフレーション後の初期密度ゆらぎの計算にどのように役立つかを概観し、これを実装した数値計算プログラムについて簡単に紹介する。その後インフレーション確率形式の共変な定式化について議論する。数学的に確率過程は離散化を指定しないと一意に定まらないが、我々は物理的に好ましい離散化を明らかにし、インフラトン場の多様体上で確率運動方程式が共変になるよう確率インフレーションを定式化した。
L. Pinol, S. Renaux-Petel, 多田祐一郎
2021年3月13日 @ オンライン
口頭, 査読なし

2020

日本物理学会第75回年次大会
極長ストカスティックインフレーション ▼
ヒルトップ型インフレーションに浅いポテンシャル極小点を導入することで極めて長いインフレーションを実現する可能性を議論する。極小点は十分浅く、ストカスティック効果により抜け出せ、その後観測宇宙を再現する通常のヒルトップインフレーションが続く。具体的には典型的に 10^{10^{10}} e-folds 程度のインフレーションが実現でき、例えば QCD axion が Bunch-Davies 分布に至るのに十分な長さである。
北嶋直弥, 多田祐一郎, 高橋史宜
2020年3月17日 @ 名古屋大学
口頭, 査読なし

2019

2018

第31回 理論懇シンポジウム
ストカスティックインフレーションと曲率ゆらぎ ▼
ストカスティック形式と delta N 形式を組み合わせることで インフレーションでの曲率ゆらぎを計算するストカスティック-delta N 形式が提唱されているが、 それを実装することでほぼ自動的かつインフラトンの拡散効果も取り入れて 曲率ゆらぎのパワースペクトルを求める数値計算コードを紹介する。
藤田智弘, L. Pinol, S. Renaux-Petel, 多田祐一郎, 徳田順生
2018年12月19–21日 @ 京都大
ポスター, 査読なし
CANCELLED

日本物理学会秋季大会
ストカスティックインフレーションのノイズ処方について ▼
インフレーションにおける量子拡散の効果を調べるための 強力な処方としてストカスティック形式が知られている。 この形式では場の量子ゆらぎが古典的白色雑音で近似されるが、 この雑音の積分に関する不定性に付随して、 一般の複数場模型においてストカスティック形式には不可避な曖昧さが 存在することを指摘する。 また逆説的にこの曖昧さの小ささがストカスティック形式の 適用妥当性の新しい指標になることを提唱する。
藤田智弘, L. Pinol, S. Renaux-Petel, 多田祐一郎, 徳田順生
2018年9月14日 @ 信州大
口頭, 査読なし

2017

日本物理学会秋季大会
曲がった場空間におけるストカスティック形式 ▼
スカラー場が複数存在するインフレーション模型において、 それらスカラー場は一般に曲がった場空間計量を張り得る。 この時場空間の曲率が十分に大きければ、 インフレーション中にエントロピー方向の自由度が 実効的にタキオニックになり得ることが指摘された(PRL. 117. 141301)。 我々はこの現象を解析するため、 曲がった場空間におけるストカスティック形式を作用から 第一原理に則って定式化する。
L. Pinol, S. Renaux-Petel, 多田祐一郎
2017年9月12–15日 @ 宇都宮大学
口頭, 査読なし

2016

日本物理学会秋季大会
超重力ニューインフレーションにおける原始ブラックホール形成
川崎雅裕, A. Kusenko, 多田祐一郎, 柳田勉
2016年9月 @ 宮崎大学
口頭, 査読なし

松江素粒子物理学研究会
Can massive primordial black holes be produced in mild waterfall hybrid inflation?
川崎雅裕, 多田祐一郎
2016年3月 @ 島根大学
口頭, 招待

2015

日本物理学会秋季大会
超対称ハイブリッドインフレーションでの原始ブラックホール形成
川崎雅裕, 多田祐一郎
2015年9月 @ 大阪市立大学
口頭, 査読なし

日本物理学会第70回年次大会
バイアス効果による原始ブラックホール暗黒物質への制限
多田祐一郎, 横山修一郎
2015年3月 @ 早稲田大学
口頭, 査読なし

2014

日本物理学会秋季大会
ストカスティック-δN形式による曲率ゆらぎへの非摂動的アプローチ
藤田智弘, 川崎雅裕, 多田祐一郎
2014年9月 @ 佐賀大学
口頭, 査読なし

2013

日本物理学会秋季大会
ストカスティック効果を用いたインフレーションのゆらぎの解析
藤田智弘, 川崎雅裕, 多田祐一郎, 竹迫知博
2013年9月 @ 高知大学
口頭, 査読なし