arXiv subjects

Rio Saitou

Publications and source records attributed to Rio Saitou.

15 recordsLinked to original sources

arXiv2024

Parametrized-Post-Newtonian Test of Black Hole Spacetime for Galactic Center Massive Black Hole Sgr A*: Formulation and $χ^2$ Fitting

We have performed a parametrized post-Newtonian (PPN) test of a black hole spacetime using observational data of the star S0-2/S2 orbiting the massive black hole at our galactic center Sgr A*. After introducing our PPN model of black hole spacetime, we report the result of $χ^2$ fitting of the PPN model with the observational data. A new finding through our PPN model is a detectability of the gravitational lens effect on the null geodesics connecting S0-2 and observer under the present observational uncertainties, if a PPN parameter is about one order larger than the value for general relativity case. On the other hand, the effect of black hole spin on the S0-2's motion is not detectable. Thus our present PPN test is performed with spherically symmetric vacuum black hole spacetime. The resultant value of the PPN parameter, which corresponds to the minimum $χ^2$, implies that the gravitational field of Sgr A* is not of Schwarzschild metric or that there exists a sufficient amount of dark matters around Sgr A* to be detected by present telescopes. However, the difference between the minimum $χ^2$ and the $χ^2$ of Schwarzschild case is not large enough to ensure a statistical significance of non-Schwarzschild result. A more precise statistical analysis than $χ^2$ statistics is necessary to extract a statistically significant information of the gravitational field of Sgr A* from present observational data. We will report a result by a Bayesian analysis in next paper.

gr-qc↗

arXiv2020

Light deflection in Observation: Angle differences between two null geodesics on the de Sitter spacetime with multi-lensing objects

We derive angle differences between two null geodesics, propagating from light sources to an observer, on the de Sitter spacetime with multi-lensing objects. Assuming the lensing objects are mass monopoles on the de Sitter background, we derive the metric tensor by solving the Einstein equation perturbatively. On that spacetime, we solve a null geodesic parametrized by the coordinate time. Using the null geodesics, we define the angle differences in a coordinate invariant way. We take in the relativistic effects up to the first order of perturbation and clarify the magnitude of approximation errors. We find that the rest observer, who sees the isotropic cosmic space, implicitly observes the effect of the cosmological constant on the angle differences through the positions of the light sources. As a practical application, we regard the massive black hole at our galactic center (Sgr A*) and the solar system as the lensing objects, further a star and a flare around Sgr A* as the light sources. We write the angle differences between these light sources using their spatial coordinates. We find that deflections by Sgr A* remain in the angle differences while deflections by the solar system cancel out up to the first order of perturbation. The deflections by Sgr A* amounts around 10 microarcseconds, which is detectable in the near future observations.

gr-qc↗

arXiv2020

Constraints on the dark mass distribution surrounding Sgr A*: simple $χ^2$ analysis for the redshift of photons from orbiting stars

Sagittarius A* (Sgr A*) is the central supermassive black hole with the mass $\sim 4\times 10^6 M_{\odot}$ in the Milky Way and stars are orbiting around it. In May 2018, one of the nearest stars to Sgr A* named S0-2/S2 experienced the pericenter passage. The redshift of photons from S0-2 had varied from $4000\>{\rm km\>s^{-1}}$ to $-2000\>{\rm km\>s^{-1}}$ during the pericenter passage, which is within $0.5\>{\rm yr}$. In this paper, we show that this steep variation of the redshift gives a strong constraint on a dark mass distribution inside the orbit of S0-2. By applying a simple $χ^2$ analysis to the observed redshift, we can easily distinguish between the two models, the point mass model and the point mass plus an extended mass model without the best-fitting parameter search. Our redshift data during the pericenter passage in 2018 with Subaru/IRCS bound the amount of the extended mass inside the orbit of S0-2 less than $0.5\,\%$ ($\sim 2 \times 10^4 M_\odot$) of the mass of Sgr A*. This constraint obtained by our simple analysis is comparable to previous works with the best-fitting parameter search to the motion of S0-2 including the effect of the extended mass. We consider both the power-law and the Plummer models for the dark mass distribution model, but the significant difference between these results is not found.

astro-ph.GA↗

arXiv2019

Inflationary spectral tilts as a result of the dilatation symmetry breaking

We derive the spectral indices and their runnings of single inflation models by a new approach. We perform a dilatation transformation to the linear cosmological perturbations and derive a current (non-)conservation law. Using it, we construct a dilatation charge and a Ward-Takahashi identity for the two-point correlators, and derive two \textit{exact} expressions for the tree-level spectral indices. First, we apply the slow roll expansion to one of the exact expressions. We calculate the spectral indices and their runnings up to the second and the third order of slow roll parameters respectively, with use of the "horizon crossing formalism". By construction, our results are more rigorous and generic than the previous works. Then, we analyze another exact expression to understand how the perturbations and the slow roll parameters contribute to the spectral indices. By a numerical calculation, we confirm that only the behaviors of the slow roll parameters during a few e-folds around the horizon crossing affect significantly to the values of spectral indices. The analysis in this article indicates that if one cannot use the slow roll parameters, regardless of their values, as the expansion parameters around the horizon crossing, then one can no longer apply the slow roll expansion to the spectral indices, and it is thus necessary to apply the more generic method introduced here.

hep-th↗

arXiv2019

Stochastic approach to de Sitter instability and eternal inflation

We investigate when effective theories of a scalar field on (quasi-)de Sitter background break down through the stochastic formalism. We derive the Fokker-Planck equation leaving the second order time derivative of the scalar field. Assuming there exists an equilibrium distribution for the field velocity, we obtain a mean value and a variance of the field velocity caused by the quantum fluctuation. Introducing coarse-grained Einstein equations, we obtain bounds for the non-eternal inflation phase and for maintaining the exact de Sitter background. We point out that those bounds derived in our formalism correspond to the de Sitter entropy bound proposed by Arkani-Hamed, \textit{et.al.}, up to $O(1)$ factor, even for a massless free scalar field on exact de Sitter background. We discuss connections of our results to the quantum field theory also.

gr-qc↗

arXiv2018

Generic analysis of kinetically driven inflation

We perform a model-independent analysis of kinetically driven inflation (KDI) which (partially) includes Generalized G-inflation and Ghost inflation. We evaluate the background evolution splitting into the inflationary attractor and the perturbation around it. We also consider the quantum fluctuation of scalar mode with a usual scaling and derive the spectral index ignoring the contribution from the second order products of slow-roll parameters. Using these formalisms, we find that within our generic framework, the models of KDI which possess the shift symmetry of scalar field cannot create the quantum fluctuation consistent to the observation. Breaking the shift symmetry, we obtain a few essential conditions for viable models of KDI associated with the graceful exit.

hep-th↗

arXiv2017

de Sitter spacetime with a Becchi-Rouet-Stora quartet

We generalize the topological model recently proposed and investigate the cosmological perturbations of the model. The model has an exact de Sitter background solution associated with a Becchi-Rouet-Stora(BRS) quartet terms which are regarded as a Lagrangian density of the topological field theory. The de Sitter solution can be selected without spontaneously breaking the BRS symmetry, and be interpreted as a gauge fixing of de Sitter spacetime. The BRS symmetry is preserved for the perturbations around the de Sitter background before we solve the constraints of general relativity. We derive action to the second order of the perturbations and confirm that even after solving the constraints, we have the BRS symmetry at least for the second order action. We construct the cosmological perturbation theory involving the BRS sector, and obtain the two point correlation functions for the curvature perturbation and the isocurvature perturbations which compose the BRS sector. Our result gives a new description for de Sitter spacetime and the quantum field theory in de Sitter spacetime.

hep-th↗

arXiv2016

Canonical invariance of spatially covariant scalar-tensor theory

We investigate invariant canonical transformations of a spatially covariant scalar-tensor theory of gravity, called the XG theory, by which the action or the Hamiltonian and the primary constraints keep their forms invariant. We derive the Hamiltonian in a non perturbative manner and complete the Hamiltonian analysis for all regions of the theory. We confirm that the theory has at most 3 degrees of freedom in all regions of the theory as long as the theory has the symmetry under the spatial diffeormorphism. Then, we derive the invariant canonical transformation by using the infinitesimal transformation. The invariant metric transformation of the XG theory contains a vector product as well as the disformal transformation. The vector product and the disformal factor can depend on the higher order derivative terms of the scalar field and the metric. In addition, we discover the invariant canonical transformation which transforms the momentum of the metric. Using the invariant transformation, we study the relation between the Horndeski theory and the GLPV theory, and find that we can not obtain the arbitrary GLPV theory from the Horndeski theory through the invariant canonical transformation we have found.

hep-th↗

arXiv2016

Ghost inflation and de Sitter entropy

In the setup of ghost condensation model the generalized second law of black hole thermodynamics can be respected under a radiatively stable assumption that couplings between the field responsible for ghost condensate and matter fields such as those in the Standard Model are suppressed by the Planck scale. Since not only black holes but also cosmology are expected to play important roles towards our better understanding of gravity, we consider a cosmological setup to test the theory of ghost condensation. In particular we shall show that the de Sitter entropy bound proposed by Arkani-Hamed, et.al. is satisfied if ghost inflation happened in the early epoch of our universe and if there remains a tiny positive cosmological constant in the future infinity. We then propose a notion of cosmological Page time after inflation.

hep-th↗

arXiv2015

Derivative-dependent metric transformation and physical degrees of freedom

We study metric transformations which depend on a scalar field $ϕ$ and its first derivatives and confirm that the number of physical degrees of freedom does not change under such transformations, as long as they are not singular. We perform a Hamiltonian analysis of a simple model in the gauge $ϕ= t$. In addition, we explicitly show that the transformation and the gauge fixing do commute in transforming the action. We then extend the analysis to more general gravitational theories and transformations in general gauges. We verify that the set of all constraints and the constraint algebra are left unchanged by such transformations and conclude that the number of degrees of freedom is not modified by a regular and invertible generic transformation among two metrics. We also discuss the implications on the recently called "hidden" constraints and on the case of a singular transformation, a.k.a. mimetic gravity.

hep-th↗

arXiv2015

Hamiltonian analysis of nonprojectable Hořava-Lifshitz gravity with $U(1)$ symmetry

We study the nature of constraints and count the number of degrees of freedom in the nonprojectable version of the $U(1)$ extension of Hořava-Lifshitz gravity, using the standard method of Hamiltonian analysis in the classical field theory. This makes it possible for us to investigate the condition under which the scalar graviton is absent at a fully nonlinear level. We show that the scalar graviton does not exist at the classical level if and only if two specific coupling constants are exactly zero. The operators corresponding to these two coupling constants are marginal for any values of the dynamical critical exponent of the Lifshitz scaling and thus should be generated by quantum corrections even if they are eliminated from the bare action. We thus conclude that the theory in general contains the scalar graviton.

hep-th↗

arXiv2015

A general method for the construction of stable Galileon models consistent with the Planck data results

The reconstruction procedure, which has proven quite useful to obtain viable models of the universe evolution, is here employed in order to construct inflation models. It has the advantages that it ensures full consistency with astronomical observations and that it allows to evaluate the stability of the resulting cosmological model quite easily. The reconstruction for two different types of Lagrangian, included in the frame of G-inflation, is carried out in detail and explicit models for each Lagrangian are constructed. As a bonus for having used this reconstruction formalism, the final models are easily adjusted to satisfy the observational constraints---imposed by the most recent data releases of the Planck mission---on the spectral index, the tensor to scalar ratio, and the running of the spectral index. Further, it turns also to be not difficult to make the models stable. Thus, the method here developed provides a general and very efficient tool, a quite natural procedure to construct models consistent with very precise observations. It can also be applied to other models, besides the ones here considered.

hep-th↗

arXiv2014

Hamiltonian structure of scalar-tensor theories beyond Horndeski

We study the nature of constraints and the Hamiltonian structure in a scalar-tensor theory of gravity recently proposed by Gleyzes, Langlois, Piazza and Vernizzi (GLPV). For the simple case with A_5 = 0, namely when the canonical momenta conjugate to the spatial metric are linear in the extrinsic curvature, we prove that the number of physical degrees of freedom is three at fully nonlinear level, as claimed by GLPV. Therefore, while this theory extends Horndeski's scalar-tensor gravity theory, it is protected against additional degrees of freedom.

hep-th↗

arXiv2012

Stable phantom-divide crossing in two scalar models with matter

We construct cosmological models with two scalar fields, which has the structure as in the ghost condensation model or k-essence model. The models can describe the stable phantom crossing, which should be contrasted with one scalar tensor models, where the infinite instability occurs at the crossing the phantom divide. We give a general formulation of the reconstruction in terms of the e-foldings N by including the matter although in the previous two scalar models, which are extensions of the scalar tensor model, it was difficult to give a formulation of the reconstruction when we include matters. In the formulation of the reconstruction, we start with a model with some arbitrary functions, and find the functions which generates the history in the expansion of the universe. We also give general arguments for the stabilities of the models and the reconstructed solution. The viability of a model is also investigated by comparing the observational data.

hep-th↗

arXiv2011

The unification of inflation and late-time acceleration in the frame of $k$-essence

By using the formulation of the reconstruction, we explicitly construct models of $k$-essence, which unify the inflation in the early universe and the late accelerating expansion of the present universe by a single scalar field. Due to the higher derivative terms, the solution describing the unification can be stable in the space of solutions, which makes the restriction for the initial condition relaxed. The higher derivative terms also eliminate tachyon. Therefore we can construct a model describing the time development, which cannot be realized by a usual inflaton or quintessence models of the canonical scalar field due to the instability or the existence of tachyon. We also propose a mechanism of the reheating by the quantum effects coming from the variation of the energy density of the scalar field.

hep-th↗