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A bstract We compute the leading order non-Gaussianity, i.e., the bispectrum, of the tensor perturbation in the general α -vacuum on de Sitter space in general relativity. In addition to the well-known Bunch-Davies (BD) vacuum, there exits an infinite number of de Sitter invariant vacua represented by a real parameter α and a phase ϕ , with α = 0 being the BD vacuum. They are called α -vacua. In the standard slow-roll inflation, as de Sitter invariance no longer applies, the α -vacua lose its relevance in the rigorous sense. Nevertheless, if we assume that the parameter α is only weakly dependent on the wavenumber with an appropriate UV cutoff, we may consider pseudo- α -vacua. In the case of false vacuum inflation where the background spacetime is pure de Sitter, a non-trivial (non-BD) α -vacuum could indeed be realized. We find an intriguing result that the bispectrum may be exponentially enhanced to be detectable by observation even if the spectrum is too small to be detected.

A bstract We show that the general vacuum states that respect the de Sitter symmetry, known as the α -vacua, can introduce non-vanishing parity-violating tensor non-Gaussianities. This is due to the mixing by the Bogoliubov transformation of the positive and negative frequency modes of the Bunch-Davies vacuum. We calculate explicitly the bispectra of tensor perturbations and show that the amplitude can be exponentially enhanced for certain choices of the squeezing parameter α and the phase ϕ of the α -vacua. We find a new shape for the parity-violating tensor bispectrum which peaks in the flattened configuration.

A bstract The radiation-dominated universe is a key ingredient of the standard Big Bang cosmology. Radiation comprises numerous quantum elementary particles, and the macroscopic behavior of radiation is described by taking the quantum thermal average of its constituents. While the interactions between individual particles and gravitational waves are often neglected in this context, it raises the question of whether these elementary particles interact with gravitational waves in the framework of quantum field theory. To address this question, this paper aims to explore the quantum mechanical aspects of gravitational waves in a universe dominated by a massless scalar field, whose averaged energy-momentum tensor plays the role of background radiation. We establish the equivalence between the classical Einstein equation and the mean-field approximation of the Heisenberg equation in a local thermal state. Beyond the mean-field approximation, we analyze the quantum corrections to gravitational waves, particularly focusing on the thermal radiation loop corrections. Interestingly, we find the 1-loop correction surpasses the tree-level spectrum of primordial gravitational waves, which is O ( α 2 ) where α = H inf . /M pl is the ratio of the inflationary Hubble parameter to the Planck mass. This indicates break down of the perturbative analysis. Then, to see if this result persists even if we take into account the higher order loop corrections, we schematically discuss two-loop diagrams that may give O ( α 2 ) contributions. We leave explicit computations of these diagrams for future studies. Thus, although we cannot claim that the whole loop corrections exceed the tree-level spectrum at the moment, our findings highlight the significance of considering quantum effects when studying the interaction between radiation and gravitational waves in the cosmological context.

There have been various interpretations of Hawking radiation proposed based on the perturbative approach, and all have confirmed Hawking’s original finding. One major conceptual challenge of Hawking evaporation is the associated black hole information loss paradox, which remains unresolved. A key factor to the issue is the end-stage of the black hole evaporation. Unfortunately by then the evaporation process becomes non-perturbative. Aspired to provide a tool for the eventual solution to this problem, here we introduce a new interpretation of Hawking radiation as the tunneling of instantons. We study instantons of a massless scalar field in Einstein gravity. We consider a complex-valued instanton that connects an initial pure black hole state to a black hole with a scalar field that represents the Hawking radiation at future null infinity, where its action depends only on the areal entropy difference. By comparing it with several independent approaches to Hawking radiation in the perturbative limit, we conclude that Hawking radiation may indeed be described by a family of instantons. Since the instanton approach can describe non-perturbative processes, we hope that our new interpretation and holistic method may shed lights on the information loss problem.

A bstract We investigate thermal activation of thin-shells around anti-de Sitter black holes. Under the thin-shell approximation, we extensively study the parameter region that allows a bubble nucleation bounded by a thin-shell out of a thermal bath. We show that in general if one fixes the temperature outside the shell, one needs to consider the presence of a conical deficit inside the shell in the Euclidean manifold, due to the lack of solutions with a smooth manifold. We show that for a given set of theoretical parameters, i.e., vacuum and shell energy density, there is a finite range of black hole masses that allow this transition. Most interestingly, one of them describes the complete evaporation of the initial black hole.

The information loss paradox associated with black hole Hawking evaporation is an unresolved problem in modern theoretical physics. In a recent brief essay, we revisited the evolution of the black hole entanglement entropy via the Euclidean path integral (EPI) of the quantum state and allow for the branching of semi-classical histories along the Lorentzian evolution. We posited that there exist at least two histories that contribute to EPI, where one is an information-losing history, while the other is an information-preserving one. At early times, the former dominates EPI, while at the late times, the latter becomes dominant. By doing so, we recovered the essence of the Page curve, and thus, the unitarity, albeit with the turning point, i.e., the Page time, much shifted toward the late time. In this full-length paper, we fill in the details of our arguments and calculations to strengthen our notion. One implication of this modified Page curve is that the entropy bound may thus be violated. We comment on the similarity and difference between our approach and that of the replica wormholes and the islands’ conjectures.

We review the analytic methods used to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive, compact body, based on black hole perturbation theory. There exist two different methods of performing the post-Newtonian expansion. Both are based on the Teukolsky equation. In one method, the Teukolsky equation is transformed into a Regge-Wheeler type equation that reduces to the standard Klein Gordon equation in the flat-space limit, while in the other method (which was introduced by Mano, Suzuki, and Takasugi relatively recently, the Teukolsky equation is used directly in its original form. The former's advantage is that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one goes to higher and higher post-Newtonian orders. In contrast, the latter's advantage is that a systematic calculation to higher post-Newtonian orders can be implemented relatively easily, but otherwise, it is so mathematical that it is hard to understand the interplay of higher order terms. In this paper, we review both methods so that their pros and cons may be seen clearly. We also review some results of calculations of gravitational radiation emitted by a particle orbiting a black hole.

A bstract We show that the ghost degrees of freedom of Einstein gravity with a Weyl term can be tamed by a simple mechanism that invokes local Lorentz symmetry breaking. We demonstrate how the mechanism works in a cosmological setting. The presence of the Weyl term forces a redefinition of the quantum vacuum state of the tensor perturbations. As a consequence the amplitude of their spectrum blows up when the Lorentz-violating scale becomes comparable to the Hubble radius. Such a behaviour is in sharp contrast to what happens in standard Weyl gravity where the gravitational ghosts smoothly damp out the spectrum of primordial gravitational waves.

A bstract We compute the entanglement entropy of a free massive Dirac field between two causally disconnected open charts in de Sitter space. We first derive the Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no supercurvature mode for the Dirac field. We then give the Bogoliubov transformation between the Bunch-Davies vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that the Dirac field becomes more entangled than a scalar field as m 2 /H 2 becomes small, and the difference is maximal in the massless limit.

DECIGO (DECi-hertz Interferometer Gravitational wave Observatory) is the planned Japanese space gravitational wave antenna, aiming to detect gravitational waves from astrophysically and cosmologically significant sources mainly between 0.1 Hz and 10 Hz and thus to open a new window for gravitational wave astronomy and for the universe. DECIGO will consists of three drag-free spacecraft arranged in an equilateral triangle with 1000 km arm lengths whose relative displacements are measured by a differential Fabry-Perot interferometer, and four units of triangular Fabry-Perot interferometers are arranged on heliocentric orbit around the sun. DECIGO is vary ambitious mission, we plan to launch DECIGO in era of 2030s after precursor satellite mission, B-DECIGO. B-DECIGO is essentially smaller version of DECIGO: B-DECIGO consists of three spacecraft arranged in an triangle with 100 km arm lengths orbiting 2000 km above the surface of the earth. It is hoped that the launch date will be late 2020s for the present..