Seminars archive 

The standard cosmological model is recently suffering severe shortcomings and tensions due to the fact that, very likely, it has to be improved at IR and UV scales. In view to reconstruct a self-consistent cosmic history, cosmography revealed a model-independent approach capable of fixing reliable models starting from observations. Without claim to completeness, we are going to sketch an overview of the method and the possible realizations towards the solutions of various cosmological tensions.

In this seminar I will try to investigate the interplay between General Relativity (GR) and f(R) gravitational theories, exploring their implications for our understanding of the fundamental nature of gravity. I will delve into the theoretical frameworks of GR and f(R), examining the mathematical formulations and physical consequences of these two approaches on the construction of black holes.

We investigate the charged Vaidya spacetime with conformal symmetry by classifying the horizons and finding its connection to Hawking temperature. We find a conformal Killing vector whose existence requires the mass and electric charge functions to be proportional, as well as linear in time. Solving the Killing equations for the conformally transformed metric from the linear charged Vaidya metric yields the required form of the conformal factor. From the vanishing of the norm of the conformal Killing vector, we find three conformal Killing horizons which, under the transformation, are mapped to the Killing horizons of the associated static spacetime, if the spherical symmetry is maintained. We find that the conformal factor is not uniquely determined, but can take any function of the ratio of the radial coordinate to the dynamical mass. As an example, we illustrate a static spacetime with our choice of the conformal factor and explicitly show that the surface gravity of the conformal Killing horizons, which is conformally invariant, yield the expected Hawking temperature in the static spacetime. This static black hole spacetime contains a cosmological horizon, but it is not asymptotically de Sitter. We also investigate the case when the mass parameter is equal to the constant electric charge. While in this case the standard pair of horizons, the loci of the time component of the metric, degenerate, the conformal Killing horizons do not degenerate. This therefore leads to a non-zero Hawking temperature in the associated static spacetime. [Slides]

This lecture is intended to provide basic concepts of the global structure of spacetime in general relativity. For this purpose, we will take up some particular topics concerning theoretical and mathematical aspects of black hole spacetimes, including singularity theorems, black hole thermodynamics, and asymptotic symmetries, each of which points to some recent research directions.

Talk session: "Quantum black hole in the asymptotic safe gravity (漸近安全な量子重力における量子ブラックホール)" [Slides]

Talk session: "Crossing of observational cosmology and quantum gravity (観測的宇宙論と量子重力の交差点)"

It is explained the concept of generalised holographic dark energy. It is shown that entire evolution of the universe from the inflation till dark energy maybe provided by holographic dark energy with specific cut-offs. All known specific holographic dark energies, like Tsallis, Renyi, etc are shown to be particular examples of such generalised holographic dark energy introdced in Nojiri-Odintsov, Gen.Rel.Grav. 38 (2006) 1285-1304. The relation of holographic dark energy with modified gravity is also explained.

At the second part of talk novel 4 or 5 parameters dependent entropy which generalises the Bekenstein-Hawking, Tsallis, Renyi, Barrow, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies is introduced following Nojiri-Odintsov-Faraoni, Phys.Rev.D 105 (2022) 4, 044042. We address the implications of the generalized entropies on black hole thermodynamics as well as on cosmology, and discuss various constraints of the entropic parameters from different perspectives. The relation to holographic dark energy is briefly discussed. Our findings indicate that entropy is not fundamental quantity but may serve the basis for qualitatively new approaches to modern cosmology.

$F(R)$ gravity is one of the most successful extensions to General Relativity, which potentially provides us with a deeper understanding of the dark side of the Universe, i.e., dark energy, dark matter & inflation. Dark energy models in $F(R)$ gravity have been well-built to explain the late-time acceleration of expansion. Such models, however, generally contain a weak singularity. Fortunately, the singularity problem can be cured by adding high-order corrections, like an $R^2$ term. On the other hand, $R^2$ gravity is a very successful inflationary model. Thus, it is natural to consider a unified interpretation of the whole comic history from inflation to the dark energy epoch.

In this talk, I shall first review the singularity problem in dark energy models of $F(R)$ gravity and introduce its extension to higher-curvature corrected models. Then, I will show the pros and cons of this kind of theory. And finally, I will examine its validity in the early Universe. [Slides]

Talk session:
Expanding Edges of Quantum Hall Systems in a Cosmology Language – Hawking Radiation from de Sitter Horizon in Edge Modes

[Slides]

The Hubble tension is one of the most important problem in recent cosmology. As a possible attitude to the problem, the local variation of the expansion rate in an inhomogeneous universe has been proposed where the spatial averaging over a finite domain was introduced in order to construct local Friedmann spacetime. So far, however, this approach has considered in particular gauges, and it has been unclear whether the results obtained are gauge-invariant or not. We study the averaging scheme within the framework of the gauge-invariant linear cosmological perturbation theory, and found that the relation between locally and globally averaged cosmological parameters including Hubble parameter may be expressed in terms of gauge invariant quantities. This result reproduces previous results consistent and our question is positively resolved. [Slides]

Quantum mechanics allows matter to be in a quantum superposition state. In gravitational theory, matter generates a gravitational field. In the unified theory, quantum gravity, the quantum superposition of gravitational fields associated with superposed matters seems to be predicted. 

As can be seen from this speculation, understanding ``Gravity of Quantum matters” is a key foothold to clarify quantum gravity. Regarding this, the following two questions have been discussed: what happens in the dynamics of superposed massive particles? what implications on the quantization of gravitational field can be obtained from the dynamics of superposed massive particles? In our work, we address the parallel questions on the dynamics of superposed charged particles: what happens in the dynamics of superposed charged particles? what implications on the quantization of electromagnetic field can be obtained from the dynamics of superposed charged particles? These questions are important for giving a solid understanding based on a well-established theory and discussing the similarities or differences between gravity and electromagnetism in a quantum regime. In this talk, I want to share the current status of our work. [Slides]

The gravitational lens plays an important role in astronomy and gravitational physics. The conventional method of the gravitational lens is described in terms of perturbations for which backgrounds are usually assumed a flat spacetime leading to Euclidean geometry. As a further theoretical study of gravitational lenses, it is significant to analyze lensing effects for various gravity models since the geometrical structure may be different between the standard general relativity and other models. In this talk, we will introduce an optical metric for the background spacetime from the null condition. Then we will develop an “optical constant-curvature approach” for which the curvature of the background optical space is assumed to be constant. As a concrete example, we show that de Sitter and anti-de Sitter background optical spaces have negative and positive constant curvature, respectively. Therefore, these backgrounds are hyperbolic and spherical geometry, respectively. By using the associated trigonometry, we derive the exact lens equations. We also discuss the background dependence of the deflection angle of light. Finally, we will mention a possible contribution of the cosmological constant to the gravitational lens. [slides]

In this talk, I will introduce and explain the geometrical role of torsion and nonmetricity tensor by considering post-Riemannian manifolds to construct theories of gravity. Then the trinity of gravity will be presented. After that, I will discuss a gravitational model which allows the independent dynamical behaviour of the torsion and nonmetricity fields to be displayed in the framework of Metric-Affine gauge theory of gravity. It will be shown that it is possible to construct exact black hole solutions within this theory. Particularly, I will show the first known isolated gravitational spherically symmetric system characterized by a metric tensor with independent spin and dilation charges. Finally, I will show a new axially symmetric solution in our theory which describes a Plebansky-Damiansky type D black hole solution valid in the decoupling limit between the orbital and the spin angular momentum. [slides]

Primordial gravitational waves (GWs) carry the imprints of the dynamics of the universe during its earliest stages. With a variety of GW detectors being proposed to operate over a wide range of frequencies, there is great expectation that observations of primordial GWs can provide us with an unprecedented window to the physics operating during inflation and reheating. In this work, we closely examine the effects of the regime of reheating on the spectrum of primordial GWs observed today. We consider a scenario wherein the phase of reheating is described by an averaged equation of state (EoS) parameter with an abrupt transition to radiation domination as well as a scenario wherein there is a gradual change in the effective EoS parameter to that of radiation due to the perturbative decay of the inflaton. We show that the perturbative decay of the inflaton leads to oscillations in the spectrum of GWs, which, if observed, can possibly help us decipher finer aspects of the reheating mechanism. We also examine the effects of a secondary phase of reheating arising due to a brief epoch driven possibly by an exotic, non-canonical, scalar field. Interestingly, we find that, for suitable values of the EoS parameter governing the secondary phase of reheating, the GWs can be of the strength as suggested by the recent NANOGrav observations. [slides]

  Unruh effect is a theoretical prediction that a uniformly accelerated observer sees the vacuum state in an inertial frame as a thermally excited state. The straight derivation would be performing the Bogoliubov transformation between operators of the scalar field defined in Rindler frame and Minkowski frame. We analytically investigated the massive 4dimensional Dirac field in Minkowski spacetime covered with Kasner and Rindler coordinate and derived the vacuum state with the entangled form. The analytic solution of the Dirac field given in this process is also applied to the research on the relativistic effect on the energy state of bouncing ultra-cold neutron trapped on the floor by the uniform gravity. In this talk, I'll discuss the detail of the analysis and introduce some related topics in QFT in curved spacetime. [Slides] 

 We investigate the relation perturbative unitarity and renormalizablility in quantum gravity.
  In particle theories point of view, Llewellyn Smith conjectured that renormalizablility and tree-unitarity at high energy give the same conditions for theories. If we apply this conjecture to gravity theory, it is shown that Einstein gravity is not renormalizable and does not hold perturbative unitarity at high energy.
  One candidate of quantum gravity, the quadratic gravity ($R_{\mu\nu}^2$ gravity or higher derivative gravity), is a renormalizable theory, but it contains negative norm states and hence does not satisfy tree-unitarity. This gives that the quadratic gravity is one of a counterexample of Llewellyn Smith's conjecture.
  In this talk, I introduce that Llewellyn Smith's conjecture and our contribution. Especially, we show that in a higher derivative theory, the unitarity bound at tree level (tree unitarity) is violated but $S$-matrix unitarity ($SS^{\dagger}=1$ or often called pseudo-unitarity) is satisfied. The point is our new conjecture that renormalizablility and $S$-matrix unitarity at high energy give the same conditions for theories. [Slides] 

 Infrared divergence due to the contribution from long wavelength modes in loop correction exists in the calculation of the initial density fluctuation in the inflationary universe scenario, which is the standard in cosmology. The purpose of this lecture is to clarify what is currently understood as the basis for the calculation method of initial density fluctuation in the inflationary universe scenario, focusing on the effect of infrared divergence on observables and to There are two main goals: 1) clarifying the relationship between the adiabatic mode generated by "large gauge transformations" and infrared divergence, giving a unified understanding of the dynamics of long wavelength modes in cosmological perturbation theory such as the δN formalism, 2) providing a method for estimating finite observables without infrared divergence based on the stochastic interpretation of the infrared divergence problem that appears in loop correction. [Slides]

Talk Session:
"Towards the Exploration of String Axion Using Gravitational Waves"

 We have been developing a gauge-invariant perturbation theory on a generic background spacetime from 2003. In 2013, we proposed "zero-mode problem" for linear metric perturbations as the essential problem in this formulation. In the perturbation theory on the Schwarzschild background spacetime, l=0,1 modes of perturbations correspond to the above "zero-mode" and the gauge-invariant treatments of these modes is a famous non-trivial problem in perturbation theories on the Schwarzschild background spacetime. In this talk, we propose a gauge-invariant treatment of the l=0,1-mode perturbations on the Schwarzschild background spacetime. Through this gauge-invariant treatment, we derive the solutions to the linearized Einstein equation for these modes with a generic matter field. In the vacuum case, these solutions include the Kerr parameter perturbations in the l=1 odd modes and the additional mass parameter perturbations of the Schwarzschild mass in the l=0 even modes. Then, the linearized version of Birkhoff's theorem is confirmed in a gauge-invariant manner. In this sense, our proposal is reasonable. In addition, formal solutions of the any-order mass, angular-momentum, dipole perturbations on the same background spacetime are derived along this proposal. This talk is based on our recent works [K. Nakamura, arXiv:2102.00830v3 [gr-qc]; K. Nakamura, arXiv:2102.10650 [gr-qc]]. [Slides]

 In this seminar, I will talk about the recent developments on the analytical estimation for the threshold of PBH formation under spherical symmetry on a FRW universe filled with a perfect fluid, thanks to the use of numerical simulations done using pseudo-spectral methods. Moreover, I will show the effect of the accretion and sizes of the PBHs formed in terms of the specific shape of the initial curvature profile. Finally, I will comment on the effect of the non-gaussianities on the threshold for PBH formation and its consequences on the PBHs coming from false vacuum regions in comparison with those coming from the collapse of large adiabatic overdensities. [Slides]

 Axion like particle (ALP) is a well-motivated hypothetical particle beyond the standard model and attracts growing attention. In this seminar, I discuss the possible roles of ALPs in the Universe and their experimental/observational tests. Recently, a re-analysis of Planck satellite data found the cosmic birefringence with the statistical significance of 2.4σ. This is a signal beyond the ΛCDM standard cosmology and can be explained by a slow-rolling ALP with a Chern-Simons coupling to photons which is responsible for dark energy. Alternatively, if the ALP rolls down its potential before the CMB emission, it not only explains the observed cosmic birefringence but also alleviates the Hubble tension problem. Furthermore, ALP with a tiny mass is a promising candidate for dark matter, because its extended de Broglie wave naturally resolves the core-cusp problem. We are running three independent ALP dark matter search projects in the ultra-light mass range 10^{-22}eV < m < 10^{-10}eV. I would like to introduce them, when time allows.  [Slides]