Updated on 2022/03/23

Organization
Institute for Advanced Research Designated assistant professor
Graduate School of Science Designated assistant professor
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### Degree 1

1. 博士（理学） （ 2017.3   東京大学 ）

### Research Interests 4

1. Early Universe

2. Inflation

3. Primordial Black Hole

4. Gravitational wave

### Research Areas 1

1. Natural Science / Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics

### Research History 6

1. Nagoya University   Institute for Advanced Research   Designated assistant professor

2021.4

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Country：Japan

2. Daido University   Lecturer (part-time)

2019.4 - 2021.3

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Country：Japan

Notes：Classical mechanics 1, 2

3. Nagoya University   Cosmology group   JSPS Fellow PD

2018.4 - 2021.3

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Country：Japan

4. Institute d'Astrophysique de Paris   Dr. Sébastien Renaux-Petel's Group   PD researcher

2017.4 - 2018.3

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Country：France

5. The University of Tokyo   Kavli IPMU, ICRR   JSPS Fellow DC2

2015.4 - 2017.3

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Country：Japan

6. The University of Tokyo   Kavli IPMU, ICRR   ALPS Fellow

2012.10 - 2017.3

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Country：Japan

### Education 3

1. The University of Tokyo   Graduate School of Science

2014.4 - 2017.3

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Country： Japan

Notes： Ph.D.

2. The University of Tokyo   Graduate School of Science

2012.4 - 2014.3

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Country： Japan

Notes： M.Sc. in Physics

3. The University of Tokyo   Faculty of Science   Department of Physics

2008.4 - 2012.3

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Country： Japan

### Professional Memberships 1

1. The Physical Society of Japan

2013.6

### Awards 3

1. Outstanding Presentation Award Gold Prize

2020.11   Online JGRG workshop 2020   Manifestly covariant theory of stochastic inflation

2. EPL's Highlights 2020

Conformal inflation in the metric-affine geometry

Yusuke Mikura, Yuichiro Tada, Shuichiro Yokoyama

3. 2019-20 Highlights of Classical and Quantum Gravity

Inflationary stochastic anomalies

Lucas Pinol, Sébastien Renaux-Petel, Yuichiro Tada

### Papers 27

Journal of Cosmology and Astroparticle Physics   Vol. 2022 ( 02 ) page： 021 - 021   2022.2

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Language：Japanese   Publisher：{IOP} Publishing

<jats:title>Abstract</jats:title>
<jats:p>We present a generic framework to compute the one-point
statistics of cosmological perturbations, when coarse-grained at an
arbitrary scale <jats:italic>R</jats:italic>, in the presence of quantum diffusion. Making
use of the stochastic-δ <jats:italic>N</jats:italic> formalism, we show how it can be
related to the statistics of the amount of expansion realised until
the scale <jats:italic>R</jats:italic> 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.</jats:p>

2. Naoya Kitajima, Yuichiro Tada, Shuichiro Yokoyama, Chul-Moon Yoo

Journal of Cosmology and Astroparticle Physics   Vol. 2021 ( 10 ) page： 053 - 053   2021.10

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing

In this paper, 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 $f_\mathrm{NL}=5/2$, 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.

3. Suyama T., Tada Y., Yamaguchi M.

Progress of Theoretical and Experimental Physics   Vol. 2021 ( 7 )   2021.7

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Language：Japanese   Publisher：Progress of Theoretical and Experimental Physics

We revisit squeezed-limit non-Gaussianity in single-field non-attractor inflation models from the viewpoint of the cosmological soft theorem. In single-field attractor models, an inflaton's trajectories with different initial conditions effectively converge into a single trajectory in the phase space, and hence there is only one clock degree of freedom (DoF) in the scalar part. Its long-wavelength perturbations can be absorbed into the local coordinate renormalization and lead to the so-called consistency relation between n- and (n+1)-point functions. On the other hand, if the inflaton dynamics deviates from the attractor behavior, its long-wavelength perturbations cannot necessarily be absorbed and the consistency relation is expected not to hold any longer. In this work, we derive a formula for the squeezed bispectrum including the explicit correction to the consistency relation, as a proof of its violation in the non-attractor cases. First one must recall that non-attractor inflation needs to be followed by attractor inflation in a realistic case. Then, even if a specific non-attractor phase is effectively governed by a single DoF of phase space (represented by the exact ultra-slow-roll limit) and followed by a single-DoF attractor phase, its transition phase necessarily involves two DoF in dynamics and hence its long-wavelength perturbations cannot be absorbed into the local coordinate renormalization. Thus, it can affect local physics, even taking account of the so-called local observer effect, as shown by the fact that the bispectrum in the squeezed limit can go beyond the consistency relation. More concretely, the observed squeezed bispectrum does not vanish in general for long-wavelength perturbations exiting the horizon during a non-attractor phase.

4. Katsuya T. Abe, Yuichiro Tada, Ikumi Ueda

Journal of Cosmology and Astroparticle Physics   Vol. 2021 ( 6 ) page： 048 - 048   2021.6

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing

The standard model of particle physics is known to be intriguingly successful. However their rich phenomena represented by the phase transitions (PTs) have not been completely understood yet, including the possibility of the existence of unknown dark sectors. In this Letter, we investigate the measurement of the equation of state parameter $w$ and the sound speed $c_{\rm s}$ of the PT plasma with use of the gravitational waves (GWs) of the universe. Though the propagation of GW is insensitive to $c_{\rm s}$ in itself, the sound speed value affects the dynamics of primordial density (or scalar curvature) perturbations and the induced GW by their horizon reentry can then be an indirect probe both $w$ and $c_{\rm s}$. We numerically reveal the concrete spectrum of the predicted induced GW with two simple examples of the scalar perturbation spectrum: the monochromatic and scale-invariant spectra. In the monochromatic case, we see that the resonant amplification and cancellation scales of the induced GW depend on the $c_{\rm s}$ va lues at different time respectively. The scale-invariant case gives a more realistic spectrum and its specific shape will be compared with observations. In particular, the QCD phase transition corresponds with the frequency range of the pulsar timing array (PTA) observations. If the amplitude of primordial scalar power is in the range of $10^{-4}\lesssim A_\zeta\lesssim10^{-2}$, the induced GW is consistent with current observational constraints and detectable in the future observation in Square Kilometer Array. Futhermore the recent possible detection of stochastic GWs by NANOGrav 12.5 yr analysis~[1 ] can be explained by the induced GW if $A_\zeta\sim\sqrt{7}\times10^{-3}$.

5. Mikura Y., Tada Y., Yokoyama S.

Physical Review D   Vol. 103 ( 10 )   2021.5

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Language：Japanese   Publisher：Physical Review D

We motivate a minimal realization of slow-roll k-inflation by incorporating the local conformal symmetry and the broken global SO(1,1) symmetry in the metric-affine geometry. With use of the metric-affine geometry where both the metric and the affine connection are treated as independent variables, the local conformal symmetry can be preserved in each term of the Lagrangian and thus higher derivatives of scalar fields can be easily added in a conformally invariant way. Predictions of this minimal slow-roll k-inflation, ns∼0.96, r∼0.005, and cs∼0.03, are not only consistent with current observational data but also have a prospect to be tested by forthcoming observations.

6. Lucas Pinol, Sébastien Renaux-Petel, Yuichiro Tada

Journal of Cosmology and Astroparticle Physics   Vol. 2021 ( 4 ) page： 048 - 048   2021.4

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing

Stochastic inflation is an effective theory describing the super-Hubble, coarse-grained, scalar fields driving inflation, by a set of Langevin equations. We previously highlighted the difficulty of deriving a theory of stochastic inflation that is invariant under field redefinitions, and the link with the ambiguity of discretisation schemes defining stochastic differential equations. In this paper, we solve the issue of these "inflationary stochastic anomalies" by using the Stratonovich discretisation satisfying general covariance, and identifying that the quantum nature of the fluctuating fields entails the existence of a preferred frame defining independent stochastic noises. Moreover, we derive physically equivalent It\^o-Langevin equations that are manifestly covariant and well suited for numerical computations. These equations are formulated in the general context of multifield inflation with curved field space, taking into account the coupling to gravity as well as the full phase space in the Hamiltonian language, but this resolution is also relevant in simpler single-field setups. We also develop a path-integral derivation of these equations, which solves conceptual issues of the heuristic approach made at the level of the classical equations of motion, and allows in principle to compute corrections to the stochastic formalism. Using the Schwinger-Keldysh formalism, we integrate out small-scale fluctuations, derive the influence action that describes their effects on the coarse-grained fields, and show how the resulting coarse-grained effective Hamiltonian action can be interpreted to derive Langevin equations with manifestly real noises. Although the corresponding dynamics is not rigorously Markovian, we show the covariant, phase-space Fokker-Planck equation for the Probability Density Function of fields and momenta when the Markovian approximation is relevant [... ]

7. Y. Mikura, Y. Tada, S. Yokoyama

EPL (Europhysics Letters)   Vol. 132 ( 3 ) page： 39001 - 39001   2020.11

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing

Systematic understanding for classes of inflationary models is investigated from the viewpoint of the local conformal symmetry and the slightly broken global symmetry in the framework of the metric-affine geometry. In the metric-affine geometry, which is a generalisation of the Riemannian one adopted in the ordinary General Relativity, the affine connection is an independent variable of the metric rather than given e.g. by the Levi-Civita connection as its function. Thanks to this independency, the metric-affine geometry can preserve the local conformal symmetry in each term of the Lagrangian contrary to the Riemannian geometry, and then the local conformal invariance can be compatible with much more kinds of global symmetries. As simple examples, we consider the two-scalar models with the broken $\mathrm{SO}(1,1)$ or $\mathrm{O}(2)$, leading to the well-known $\alpha$-attractor or natural inflation, respectively. The inflaton can be understood as their pseudo Nambu-Goldstone boson.

8. Teruaki Suyama, Yuichiro Tada, Masahide Yamaguchi

Progress of Theoretical and Experimental Physics   Vol. 2020 ( 11 )   2020.11

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Oxford University Press (OUP)

<title>Abstract</title>
Non-Gaussianities of primordial perturbations in the soft limit provide important information about the light degrees of freedom during inflation. The soft modes of the curvature perturbations, unobservable for a local observer, act to rescale the spatial coordinates. We determine how the trispectrum in the collapsed limit is shifted by the rescaling due to the soft modes. We find that the form of the inequality between the $f_\mathrm{NL}$ and $\tau_\mathrm{NL}$ parameters is not affected by the rescaling, demonstrating that the role of the inequality as an indicator of the light degrees of freedom remains intact. We also comment on the local observer effect on the consistency relation for ultra-slow-roll inflation.

Physical Review D   Vol. 101 ( 10 )   2020.5

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In the context of string theory, several conjectural conditions have been proposed for low energy effective field theories not to be in swampland, the UV-incomplete class. The recent ones represented by the de Sitter and trans-Planckian censorship conjectures in particular seem to conflict with the inflation paradigm of the early universe. We first point out that scenarios where inflation is repeated several times (multi-phase inflation) can be easily compatible with these conjectures. In other words, we relax the constraint on the single inflation for the large scale perturbations to only continue at least around 10 e-folds. In this context, we then investigate if a spectator field can be a source of the almost scale-invariant primordial perturbations on the large scale. As a consequence of such an isocurvature contribution, the resultant perturbations exhibit the non-vanishing non-Gaussianity in general. Also the perturbation amplitude on smaller scales can be completely different from that on the large scale due to the multiplicity of inflationary phases. These signatures will be a smoking gun of this scenario by the future observations.

10. Naoya Kitajima, Yuichiro Tada, Fuminobu Takahashi

Physics Letters B   Vol. 800   2020.1

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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 $10^{10^{10 } }$, which is large enough for various light scalars such
the QCD axion to reach the Bunch-Davies distribution.

11. Induced gravitational waves as a probe of the sound speed during the QCD phase transition

Ueda Ikumi, Tada Yuichiro, Abe Katsuya

Meeting Abstracts of the Physical Society of Japan   Vol. 75.1 ( 0 ) page： 543 - 543   2020

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Language：Japanese   Publisher：The Physical Society of Japan

Physical Review D   Vol. 100 ( 2 )   2019.7

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society ({APS})

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 ($\sim\mathcal{O}(10^{-5})M_\odot$) 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 multi-phase inflationary scenario with hierarchical mass PBHs as a transition signal of each inflationary phase.

13. Lucas Pinol, Sébastien Renaux-Petel, Yuichiro Tada

Class. Quant. Grav.   Vol. 36 ( 7 )   2019.4

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The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical stochastic theory. It is usually formulated in terms of Langevin equations, giving rise to a Fokker-Planck equation for the probability distribution function of the fields, and possibly their momenta. The link between these two descriptions is ambiguous in general, as it depends on an implicit discretisation procedure, the two prominent ones being the It\^o and Stratonovich prescriptions. Here we show that the requirement of general covariance under field redefinitions is verified only in the latter case, however at the expense of introducing spurious `frame' dependences. This stochastic anomaly disappears when there is only one source of stochasticity, like in slow-roll single-field inflation, but manifests itself when taking into account the full phase space, or in the presence of multiple fields. Despite these difficulties, we use physical arguments to write down a covariant Fokker-Planck equation that describes the diffusion of light scalar fields in non-linear sigma models in the overdamped limit. We apply it to test scalar fields in de Sitter space and show that some statistical properties of a class of two-field models with derivative interactions can be reproduced by using a correspondence with a single-field model endowed with an effective potential. We also present explicit results in a simple extension of the single-field $\lambda \phi^4$ theory to a hyperbolic field space geometry. The difficulties we describe seem to be the stochastic counterparts of the notoriously difficult problem of maintaining general covariance in quantum theories, and the related choices of operator ordering and path-integral constructions. Our work thus opens new avenues of research at the crossroad between cosmology, statistical physics, and quantum field theory.

14. Tomohiro Fujita, Ryo Namba, Yuichiro Tada

Physics Letters B   Vol. 778   page： 17 - 21   2018.3

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}

We show that a detectable tensor-to-scalar ratio $(r\ge 10^{-3})$ on the CMB
scale can be generated even during extremely low energy inflation which
saturates the BBN bound $\rho_{\rm inf}\approx (30 {\rm MeV})^4$. The source of
the gravitational waves is not quantum fluctuations of graviton but those of
$SU(2)$ gauge fields, energetically supported by coupled axion fields. The
curvature perturbation, the backreaction effect and the validity of
perturbative treatment are carefully checked. Our result indicates that
measuring $r$ alone does not immediately fix the inflationary energy scale.

15. Inomata, Keisuke, Kawasaki, Masahiro, Mukaida, Kyohei, Tada, Yuichiro, Yanagida, Tsutomu T.

Phys. Rev.   Vol. 96 ( 12 ) page： 123527 - 123527   2017.12

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LIGO-Virgo collaboration has found black holes as heavy as $M \sim 30M_\odot$
through the detections of the gravitational waves emitted during their mergers.
Primordial black holes (PBHs) produced by inflation could be an origin of such
events. While it is tempting to presume that these PBHs constitute all Dark
Matter (DM), there exists a number of constraints for PBHs with $\mathcal{O} (10) M_\odot$ which contradict with the idea of PBHs as all DM. Also, it is
known that weakly interacting massive particle (WIMP) that is a common DM
candidate is almost impossible to coexist with PBHs. These observations
motivate us to pursue another candidate of DM. In this paper, we assume that
the string axion solving the strong CP problem makes up all DM, and discuss the
coexistence of string axion DM and inflationary PBHs for LIGO events.

16. Inomata, Keisuke, Kawasaki, Masahiro, Mukaida, Kyohei, Tada, Yuichiro, Yanagida, Tsutomu T.

Phys. Rev.   Vol. 96 ( 4 ) page： 043504 - 043504   2017.8

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Following a new microlensing constraint on primordial black holes (PBHs) with
$\sim10^{20}$--$10^{28}\,\mathrm{g}$~[1], we revisit the idea of PBH as all
Dark Matter (DM). We have shown that the updated observational constraints
suggest the viable mass function for PBHs as all DM to have a peak at $\simeq 10^{20}\,\mathrm{g}$ with a small width $\sigma \lesssim 0.1$, by imposing
observational constraints on an extended mass function in a proper way. We have
also provided an inflation model that successfully generates PBHs as all DM
fulfilling this requirement.

17. Inomata, Keisuke, Kawasaki, Masahiro, Mukaida, Kyohei, Tada, Yuichiro, Yanagida, Tsutomu T.

Phys. Rev.   Vol. 95 ( 12 ) page： 123510 - 123510   2017.6

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Primordial black holes (PBHs) are one of the candidates to explain the
gravitational wave (GW) signals observed by the LIGO detectors. Among several
phenomena in the early Universe, cosmic inflation is a major example to
generate PBHs from large primordial density perturbations. In this paper, we
discuss the possibility to interpret the observed GW events as mergers of PBHs
which are produced by cosmic inflation. The primordial curvature perturbation
should be large enough to produce a sizable amount of PBHs and thus we have
several other probes to test this scenario. We point out that the current
pulsar timing array (PTA) experiments already put severe constraints on GWs
generated via the second-order effects, and that the observation of the cosmic
microwave background (CMB) puts severe restriction on its $\mu$ distortion. In
particular, it is found that the scalar power spectrum should have a very sharp
peak at $k \sim 10^{6}$ Mpc$^{-1}$ to fulfill the required abundance of PBHs
while evading constraints from the PTA experiments together with the $\mu$
distortion. We propose a mechanism which can realize such a sharp peak. In the
future, simple inflation models that generate PBHs via almost Gaussian
fluctuations could be probed/excluded.

JCAP   Vol. 1702 ( 2 ) page： 021 - 021   2017.2

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The prospects of future galaxy surveys for non-Gaussianity measurements call
for the development of robust techniques for computing the bispectrum of
primordial cosmological perturbations. In this paper, we propose a novel
approach to the calculation of the squeezed bispectrum in multiple-field
inflation. With use of the $\delta N$ formalism, our framework sheds new light
on the recently pointed out difference between the squeezed bispectrum for
global observers and that for local observers, while allowing one to calculate
both. For local observers in particular, the squeezed bispectrum is found to
vanish in single-field inflation. Furthermore, our framework allows one to go
beyond the near-equilateral ("small hierarchy") limit, and to automatically
include intrinsic non-Gaussianities that do not need to be calculated
separately. The explicit computational programme of our method is given and
illustrated with a few examples.

19. Kawasaki, Masahiro, Kusenko, Alex, er, Tada, Yuichiro, Yanagida, Tsutomu T.

Phys. Rev.   Vol. 94 ( 8 ) page： 083523 - 083523   2016.10

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We propose a novel scenario to produce abundant primordial black holes (PBHs) in new inflation which is a second phase of a double inflation in the supergravity frame work. In our model, some preinflation phase before the new inflation is assumed and it would be responsible for the primordial curvature perturbations on the cosmic microwave background scale, while the new inflation produces only the small scale perturbations. Our new inflation model has linear, quadratic, and cubic terms in its potential and PBH production corresponds with its flat inflection point. The linear term can be interpreted to come from a supersymmetry-breaking sector, and with this assumption, the vanishing cosmological constant condition after inflation and the flatness condition for the inflection point can be consistently satisfied.

20. Inomata, Keisuke, Kawasaki, Masahiro, Tada, Yuichiro

Phys. Rev.   Vol. 94 ( 4 ) page： 043527 - 043527   2016.8

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We revisit the constraints on the small scale density perturbations
($10^4\,\mathrm{Mpc}^{-1}\lesssim k \lesssim10^5\,\mathrm{Mpc}^{-1}$) from the
modification of the freeze-out value of the neutron-proton ratio at big-bang
nucleosynthesis era. Around the freeze-out temperature $T\sim 0.5\,\mathrm{MeV}$, the universe can be divided into several local patches
which have different temperatures since any perturbation which enters the
horizon after the neutrino decoupling has not diffused yet. Taking account of
this situation, we calculate the freeze-out value in detail. We find that the
small scale perturbations decrease the n-p ratio in contrast to previous works.
With use of the latest observed $^4$He abundance, we obtain the constraint on
the power spectrum of the curvature perturbations as
$\Delta^2_\mathcal{R}\lesssim 0.018$ on $10^4\,\mathrm{Mpc}^{-1}\lesssim k \lesssim 10^5\,\mathrm{Mpc}^{-1}$.

JCAP   Vol. 1608 ( 8 ) page： 041 - 041   2016.8

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We studied the possibility whether the massive primordial black holes (PBHs)
surviving today can be produced in hybrid inflation. Though it is of great
interest since such PBHs can be the candidate for dark matter or seeds of the
supermassive black holes in galaxies, there have not been quantitatively
complete works yet because of the non-perturbative behavior around the critical
point of hybrid inflation. Therefore, combining the stochastic and $\delta N$
formalism, we numerically calculated the curvature perturbations in a
non-perturbative way and found, without any specific assumption of the types of
hybrid inflation, PBHs are rather overproduced when the waterfall phase of
hybrid inflation continues so long that the PBH scale is well enlarged and the
corresponding PBH mass becomes sizable enough.

22. Determination of n-p ratio in small scale perturbations

Inomata Keisuke, Kawasaki Masahiro, Tada Yuichiro

Meeting Abstracts of the Physical Society of Japan   Vol. 71   page： 328 - 328   2016

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Language：Japanese   Publisher：The Physical Society of Japan

Phys. Rev.   Vol. 91 ( 12 ) page： 123534 - 123534   2015.6

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Language：Japanese   Publishing type：Research paper (scientific journal)

Primordial black holes (PBHs) are theoretical black holes which may be formed
during the radiation dominant era and, basically, caused by the gravitational
collapse of radiational overdensities. It has been well known that in the
context of the structure formation in our Universe such collapsed objects,
e.g., halos/galaxies, could be considered as bias tracers of underlying matter
fluctuations and the halo/galaxy bias has been studied well. Employing a
peak-background split picture which is known to be a useful tool to discuss the
halo bias, we consider the large scale clustering behavior of the PBH and
propose an almost mass-independent constraint to the scenario that dark matters
(DMs) consist of PBHs. We consider the case where the statistics of the
primordial curvature perturbations is almost Gaussian, but with small
local-type non-Gaussianity. If PBHs account for the DM abundance, such a large
scale clustering of PBHs behaves as nothing but the matter isocurvature
perturbation and constrained strictly by the observations of cosmic microwave
backgrounds (CMB). From this constraint, we show that, in the case a certain
single field causes both CMB temperature perturbations and PBH formations, the
PBH-DM scenario is excluded even with quite small local-type non-Gaussianity,
$|f_\mathrm{NL}|\sim\mathcal{O}(0.01)$, while we give the constraints to
parameters in the case where the source field of PBHs is different from CMB
perturbations.

24. Fujita, Tomohiro, Namba, Ryo, Tada, Yuichiro, Takeda, Naoyuki, Tashiro, Hiroyuki

JCAP   Vol. 1505 ( 5 ) page： 054 - 054   2015.5

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Language：Japanese   Publishing type：Research paper (scientific journal)

There has been a growing evidence for the existence of magnetic fields in the
extra-galactic regions, while the attempt to associate their origin with the
inflationary epoch alone has been found extremely challenging. We therefore
take into account the consistent post-inflationary evolution of the magnetic
fields that are originated from vacuum fluctuations during inflation. In the
model of our interest, the electromagnetic (EM) field is coupled to a
pseudo-scalar inflaton $\phi$ through the characteristic term $\phi F\tilde F$,
breaking the conformal invariance. This interaction dynamically breaks the
parity and enables a continuous production of only one of the polarization
states of the EM field through tachyonic instability. The produced magnetic
fields are thus helical. We find that the dominant contribution to the observed
magnetic fields in this model comes from the modes that leave the horizon near
the end of inflation, further enhanced by the tachyonic instability right after
the end of inflation. The EM field is subsequently amplified by parametric
resonance during the period of inflaton oscillation. Once the thermal plasma is
formed (reheating), the produced helical magnetic fields undergo a turbulent
process called inverse cascade, which shifts their peak correlation scales from
smaller to larger scales. We consistently take all these effects into account
within the regime where the perturbation of $\phi$ is negligible and obtain
$B_{\rm eff} \sim 10^{-19}$G, indicating the necessity of additional mechanisms
to accommodate the observations.

25. Ota, Atsuhisa, Sekiguchi, Toyokazu, Tada, Yuichiro, Yokoyama, Shuichiro

JCAP   Vol. 1503 ( 3 ) page： 013 - 013   2015.3

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We calculate the CMB $\mu$-distortion and the angular power spectrum of its
cross-correlation with the temperature anisotropy in the presence of the
non-Gaussian neutrino isocurvature density (NID) mode. While the pure Gaussian
NID perturbations give merely subdominant contribution to $<\mu>$ and vanishing
$< \mu T>$, the latter quantity can be large enough to be detected in the
future when the NID perturbations $\mathcal S(\mathbf x)$ are proportional to
the square of a Gaussian field $g(\mathbf x)$, i.e. $\mathcal S({\mathbf x})\propto g^2({\mathbf x})$. In particular, large $< \mu T>$ can be realized
since Gaussian-squared perturbations can yield a relatively large bispectrum,
satisfying the constraints from the power spectrum of CMB anisotropies, i.e.
$\mathcal{P}_\mathcal{SS}(k_0) \sim\mathcal{P}_g^2(k_0)\lesssim10^{-10}$ at
$k_0=0.05$ Mpc$^{-1}$. We also forecast constraints from the CMB temperature
and E-mode polarisation bispectra, and show that
$\mathcal{P}_g(k_0)\lesssim10^{-5}$ would be allowed from Planck data. We find
that $< \mu >$ and $|l(l+1)C^{\mu T}_l|$ can respectively be as large as
$10^{-9}$ and $10^{-14}$ with uncorrelated scale-invariant NID perturbations
for $\mathcal{P}_g(k_0)=10^{-5}$. When the spectrum of the Gaussian field is
blue-tilted (with spectral index $n_g \simeq 1.5$), $< \mu T>$ can be enhanced
by an order of magnitude.

26. Fujita, Tomohiro, Kawasaki, Masahiro, Tada, Yuichiro

JCAP   Vol. 1410 ( 10 ) page： 030 - 030   2014.10

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Language：Japanese   Publishing type：Research paper (scientific journal)

In our previous paper, we have proposed a new algorithm to calculate the
power spectrum of the curvature perturbations generated in inflationary
universe with use of the stochastic approach. Since this algorithm does not
need the perturbative expansion with respect to the inflaton fields on
super-horizon scale, it works even in highly stochastic cases. For example,
when the curvature perturbations are very large or the non-Gaussianities of the
curvature perturbations are sizable, the perturbative expansion may break down
but our algorithm enables to calculate the curvature perturbations. We apply it
to two well-known inflation models, chaotic and hybrid inflation, in this
paper. Especially for hybrid inflation, while the potential is very flat around
the critical point and the standard perturbative computation is problematic, we
successfully calculate the curvature perturbations.

27. Fujita, Tomohiro, Kawasaki, Masahiro, Tada, Yuichiro, Takesako, Tomohiro

JCAP   Vol. 1312 ( 12 ) page： 036 - 036   2013.12

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Language：Japanese   Publishing type：Research paper (scientific journal)

We propose a new approach for calculating the curvature perturbations
produced during inflation in the stochastic formalism. In our formalism, the
fluctuations of the e-foldings are directly calculated without perturbatively
expanding the inflaton field and they are connected to the curvature
perturbations by the $\delta N$ formalism. The result automatically includes
the contributions of the higher order perturbations because we solve the
equation of motion non-perturbatively. In this paper, we analytically prove
that our result (the power spectrum and the nonlinearity parameter) is
consistent with the standard result in single field slow-roll inflation. We
also describe the algorithm for numerical calculations of the curvature
perturbations in more general inflation models.

### MISC 2

1. Albert Escrivà, Yuichiro Tada, Shuichiro Yokoyama, Chul-Moon Yoo

2022.2

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In this work, we have performed numerical simulations of primordial black
hole (PBH) formation in the Friedman-Lema\^itre-Robertson-Walker universe
filled by radiation fluid, introducing the local-type non-Gaussianity to the
primordial curvature fluctuation. We have compared the numerical results from
simulations with previous analytical estimations on the threshold value for PBH
formation done in the previous paper arXiv:2109.00791, particularly for
negative values of the non-linearity parameter $f_{\rm NL}$. Our numerical
results show the existence of PBH formation of (the so-called) type I also in
the case $f_{\rm NL} \lesssim -0.336$, which was not found in the previous
analytical expectations using the critical averaged compaction function. In
particular, although the universal value for the averaged critical compaction
function $\bar{\mathcal{C } }_{c}=2/5$ found previously in the literature is not
satisfied for all the profiles considered in this work, an alternative direct
analytical estimate has been found to be roughly accurate to estimate the
thresholds, which gives the value of the critical averaged density with a few
$\%$ deviation from the numerical one for $f_{\rm NL}\gtrsim -1$.

2021.10

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We investigate the UV-completion of the Higgs inflation in the metric and the
Palatini formalisms. It is known that the cutoff scales for the perturbative
unitarity of these inflation models become much smaller than the Planck scale
to be consistent with observations. Expecting that the low cutoff scale
originates in the curvature of a field-space spanned by the Higgs fields, we
consider embedding the curved field-space into a higher dimensional flat space
and apply this procedure to the metric-Higgs and the Palatini-Higgs scenarios.
The new field introduced in this way successfully flattens the field-space and
UV-completes the Higgs inflation in the metric formalism. However, in the
Palatini formalism, the new field cannot uplift the cutoff up to the Planck
scale. We also discuss the unavoidable low cutoff in the Palatini formalism in
the context of the local conformal symmetry.

### Presentations 9

1. 多田祐一郎

名古屋大学・名古屋市科学館 公開オンラインセミナー  2021.8.22

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech

2. 宇宙の「インフレ」と「金融工学」 Invited

多田祐一郎

名大発アカデミックフラッシュ 第2報  2021.9.3

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Language：Japanese   Presentation type：Oral presentation (general)

3. 粗視化曲率ゆらぎの確率密度関数

多田祐一郎, Vincent Vennin

日本物理学会秋季大会  2021.9.14

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Language：Japanese   Presentation type：Oral presentation (general)

4. Primordial black holes in peak theory with a non-Gaussian tail

Naoya Kitajima, Yuichiro Tada, Shuichiro Yokoyama, Chul-Moon Yoo

The KEK-PH + KEK-Cosmo joint workshop on "Primordial Black Holes"  2021.10.19

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Language：Japanese   Presentation type：Oral presentation (general)

5. Primordial black holes in peak theory with a non-Gaussian tail Invited

Naoya Kitajima, Yuichiro Tada, Shuichiro Yokoyama, Chul-Moon. Yoo

2021 NRF-JSPS Workshop in particle physics, cosmology, and gravitation  2021.7.21

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Language：English   Presentation type：Oral presentation (general)

6. Probability density functions of coarse-grained curvature and density perturbations in stochastic inflation

JGRG30  2021.12.9

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Language：English   Presentation type：Oral presentation (general)

7. Probability density functions of coarse-grained curvature and density perturbations in stochastic inflation

COSMO'21  2021.8.2

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Language：English   Presentation type：Poster presentation

8. Self-introduction, or a biased view of what theoretical cosmologists are recently interested in Invited

E-lab seminar, Nagoya U.  2021.5.25

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech

9. インフレーションの「現在」と重力波 Invited

多田祐一郎

DECIGO ワークショップ  2021.12.11

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Language：Japanese   Presentation type：Oral presentation (general)

### KAKENHI (Grants-in-Aid for Scientific Research) 4

1. Grant number：21K13918  2021.4 - 2024.3

Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists  Grant-in-Aid for Early-Career Scientists

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Authorship：Principal investigator

Grant amount：\4680000 （ Direct Cost: \3600000 、 Indirect Cost：\1080000 ）

2. Grant number：19K14707  2019.4 - 2021.3

Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists  Grant-in-Aid for Early-Career Scientists

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Authorship：Principal investigator

Grant amount：\1560000 （ Direct Cost: \1200000 、 Indirect Cost：\360000 ）

3. Curvature Perturbations and Primordial Black Hole Formation in the Inflationary Universe

Grant number：18J01992  2018.4 - 2021.3

Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows  Grant-in-Aid for JSPS Fellows

4. 小スケール曲率ゆらぎの観測とインフレーション

Grant number：15J10829  2015.4 - 2017.3

日本学術振興会  科学研究費助成事業 特別研究員奨励費  特別研究員奨励費

多田 祐一郎

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昨年度は5本の論文 (arXiv:1605.04646, 1606.07631, 1609.08876, 1611.06130, 1701.02544) を提出した。1つ目の論文では小スケールにもし大きな曲率ゆらぎが生じていた場合、それがビッグバン元素合成に与える影響について再考察し、既存の結果が定性的レベルで修正されることを示した。また3つ目の論文では、曲率ゆらぎのスクィーズド極限バイスペクトルに関し、近年指摘されているゲージ依存効果についての新たな理解を示し、簡単な計算アルゴリズムを提唱した。これは今後、実際に何らかの観測 (宇宙背景放射や銀河バイアス等) によってバイスペクトルを測定し、それを宇宙初期の物理と対応させるときに非常に重要になってくる。残りの論文では原始ブラックホールについて議論している。昨年 LIGO グループが初の重力波直接検出を発表し話題になったが、この重力波は重いブラックホール連星の合体から来ており、こうしたブラックホールが原始ブラックホールである可能性も注目されてきている。また伴って、原始ブラックホールが暗黒物質である可能性も再注目されてきた。そこで我々は実際に具体的なインフレーション模型を構築し、原始ブラックホールが LIGO の重力波イベントや暗黒物質を説明しうるか、また他に検出方法があるかどうかなどを検証した。
これら研究成果に関し、国際会議で2度, 国内会議で1度口頭発表を行った. また国内外合わせて4つの研究機関でセミナー発表を行った.

### Teaching Experience (Off-campus) 1

1. Classical mechanics 1, 2

2019.4 Daido University）