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The Eisenhart lift of Riemannian type describes the motion of a particle as a geodesic in a higher-dimensional Riemannian manifold with one additional coordinate. It has recently been generalized to a scalar field system by introducing one additional vector field. We apply this approach to a scalar field system in the FLRW (Friedmann-Lemaitre-Robertson-Walker) universe and classify the symmetries of the system. In particular, we find nontrivial (conformal) Killing vector field and Killing tensor fields for a scalar field potential consisting of the square of a combination of exponential functions with specific index $e^{\pm\frac{\sqrt{6}}{4}\phi}$. Moreover, we find nontrivial conformal Killing vector fields for a potential which is written as an exponentiation of a combination of exponential potentials with general index. Complete solutions to the equations of motion are given. We also classify the symmetries of multiple scalar field system., Comment: 22 pages

A scalar field with an exponential potential has been proposed as a model of inflation (called power-law inflation). Although it admits an exact solution, the integrability of the system has not been shown.We uncover the hidden symmetries behind the system by utilising the Eisenhart lift of field theories. We find that a conformal Killing vector field in the field space exists only for a particular combination of exponential functions that includes a single exponential potential. This implies the existence of additional conserved quantity and explains the integrability of the system., Comment: 6 pages, to appear in CQG

We derive the time dilation formula for charged quantum clocks in electromagnetic fields. As a concrete example of non-inertial motion, we consider a cyclotron motion in a uniform magnetic field. Applying the time dilation formula to coherent state of the charged quantum clock, we evaluate the time dilation quantum-mechanically., Comment: 11 pages, 2 figures, to appear in PRD

A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation., Comment: 12 pages, 2 figures, version published in PRD

Motivated by constant-G theory, we introduce a one-parameter family of scalar-tensor theories as an extension of constant-G theory in which the conformal symmetry is a cosmological attractor. Since the model has the coupling function of negative curvature, we expect spontaneous scalarization occurs and the parameter is constrained by pulsar-timing measurements. Modeling neutron stars with realistic equation of states, we study the structure of neutron stars and calculate the effective scalar coupling with the neutron star in these theories. We find that within the parameter region where the observational constraints are satisfied, the effective scalar coupling almost coincides with that derived using the quadratic model with the same curvature. This indicates that the constraints obtained by the quadratic model will be used to limit the curvature of the coupling function universally in the future., Comment: 15 pages, 7 figures, updated to match the published version

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy., Comment: 10 pages, 3 figures

We study the frame dependence/independence of cosmological observables under disformal transformations, extending the previous results regarding conformal transformations, and provide the correspondence between Jordan-frame and Einstein-frame variables. We consider quantities such as the gravitational constant in the Newtonian limit, redshift, luminosity and angular diameter distances, as well as the distance-duality relation. Also, the Boltzmann equation, the observed specific intensity, and the adiabaticity condition are discussed. Since the electromagnetic action changes under disformal transformations, photons in the Einstein frame no longer propagate along null geodesics. As a result, several quantities of cosmological interest are modified. Nevertheless, we show that the redshift is invariant and the distance-duality relation (the relation between the luminosity distance and the angular diameter distance) still holds in general spacetimes even though the reciprocity relation (the relation between two geometrical distances) is modified., Comment: 29 pages, 1 figure. v3: updated subsection 4.3 and fixed minor typos

Redshifts of an astronomical body measured at multiple epochs (e.g., separated by 10 years) are different due to the cosmic expansion. This so-called Sandage-Loeb test offers a direct measurement of the expansion rate of the Universe. However, acceleration in the motion of Solar System with respect to the cosmic microwave background also changes redshifts measured at multiple epochs. If not accounted for, it yields a biased cosmological inference. To address this, we calculate the acceleration of Solar System with respect to the Local Group of galaxies to quantify the change in the measured redshift due to local motion. Our study is motivated by the recent determination of the mass of Large Magellanic Cloud (LMC), which indicates a significant fraction of the Milky Way mass. We find that the acceleration towards the Galactic Center dominates, which gives a redshift change of 7 cm/s in 10 years, while the accelerations due to LMC and M31 cannot be ignored depending on lines of sight. We create all-sky maps of the expected change in redshift and the corresponding uncertainty, which can be used to correct for this effect., Comment: 6 pages, 3 figures. Accepted for publication in PASJ

Stochastic gravitational wave backgrounds, predicted in many models of the early universe and also generated by various astrophysical processes, are a powerful probe of the Universe. The spectral shape is key information to distinguish the origin of the background since different production mechanisms predict different shapes of the spectrum. In this paper, we investigate how precisely future gravitational wave detectors can determine the spectral shape using single and broken power-law templates. We consider the detector network of Advanced-LIGO, Advanced-Virgo and KAGRA and the space-based gravitational-wave detector DECIGO, and estimate the parameter space which could be explored by these detectors. We find that, when the spectrum changes its slope in the frequency range of the sensitivity, the broken power-law templates dramatically improve the $\chi^2$ fit compared with the single power-law templates and help to measure the shape with a good precision., Comment: 45 pages, 20 figures

Recent cosmological observations are in good agreement with the scalar spectral index $n_s$ with $n_s-1\simeq -2/N$, where $N$ is the number of e-foldings. In the previous work, the reconstruction of the inflaton potential for a given $n_s$ was studied, and it was found that for $n_s-1=-2/N$, the potential takes the form of either $\alpha$-attractor model or chaotic inflation model with $\phi^2$ to the leading order in the slow-roll approximation. Here we consider the reconstruction of $f(R)$ gravity model for a given $n_s$ both in the Einstein frame and in the Jordan frame. We find that for $n_s-1=-2/N$ (or more general $n_s-1=-p/N$), $f(R)$ is given parametrically and is found to asymptote to $R^2$ for large $R$. This behavior is generic as long as the scalar potential is of slow-roll type., Comment: 8 pages, 2 figures, references added, version to appear in PTEP

We estimate the spin distribution of primordial black holes based on the recent study of the critical phenomena in the gravitational collapse of a rotating radiation fluid. We find that primordial black holes are mostly slowly rotating., Comment: 12 pages, 2 figures, references added, version to appear in PTEP

We present cosmological constraints on the scalar-tensor theory of gravity by analyzing the angular power spectrum data of the cosmic microwave background obtained from the Planck 2015 results together with the baryon acoustic oscillations (BAO) data. We find that the inclusion of the BAO data improves the constraints on the time variation of the effective gravitational constant by more than $10\%$, that is, the time variation of the effective gravitational constant between the recombination and the present epochs is constrained as $G_{\rm rec}/G_0-1 <1.9\times 10^{-3}\ (95.45\%\ {\rm C.L.})$ and $G_{\rm rec}/G_0-1 <5.5\times 10^{-3}\ (99.99 \%\ {\rm C.L.})$. We also discuss the dependence of the constraints on the choice of the prior., Comment: 16 pages, 13 figures, version to appear in PTEP

We study timelike and null geodesics in a non-singular black hole metric proposed by Hayward. The metric contains an additional length-scale parameter $\ell$ and approaches the Schwarzschild metric at large radii while approaches a constant at small radii so that the singularity is resolved. We tabulate the various critical values of $\ell$ for timelike and null geodesics: the critical values for the existence of horizon, marginally stable circular orbit and photon sphere. We find the photon sphere exists even if the horizon is absent and two marginally stable circular orbits appear if the photon sphere is absent and a stable circular orbit for photons exists for a certain range of $\ell$. We visualize the image of a black hole and find that blight rings appear even if the photon sphere is absent., Comment: 14 pages, 10 figures, typos corrected, to appear in PTEP

Cosmological constraints on the scalar-tensor theory of gravity by analyzing the angular power spectrum data of the cosmic microwave background (CMB) obtained from the Planck 2015 results are presented. We consider the harmonic attractor model, in which the scalar field has a harmonic potential with curvature ($\beta$) in the Einstein frame and the theory relaxes toward the Einstein gravity with time. Analyzing the {\it TT}, {\it EE}, {\it TE} and lensing CMB data from Planck by the Markov chain Monte Carlo method, we find that the present-day deviation from the Einstein gravity (${\alpha_0}^2$) is constrained as ${\alpha_0}^2<2.5\times10^{-4-4.5\beta^2}\ (95.45\% {\rm\ C.L.})$ and ${\alpha_0}^2<6.3\times10^{-4-4.5\beta^2}\ (99.99\%\ {\rm C.L.})$ for $0<\beta<0.4$. The time variation of the effective gravitational constant between the recombination and the present epochs is constrained as $G_{\rm rec}/G_0<1.0056\ (95.45\% {\rm\ C.L.})$ and $G_{\rm rec}/G_0<1.0115\ (99.99 \%{\rm\ C.L.})$. We also find that the constraints are little affected by extending to nonflat cosmological models because the diffusion damping effect revealed by Planck breaks the degeneracy of the projection effect., Comment: 7 pages, 10 figures, version to appear in PRD

Recent cosmological observations are in good agreement with the scalar spectral index $n_s$ with $n_s-1\sim -2/N$, where $N$ is the number of e-foldings. Quadratic chaotic model, Starobinsky model and Higgs inflation or $\alpha$-attractors connecting them are typical examples predicting such a relation. We consider the problem in the opposite: given $n_s$ as a function of $N$, what is the inflaton potential $V(\phi)$. We find that for $n_s-1=-2/N$, $V(\phi)$ is either $\tanh^2(\gamma\phi/2)$ ("T-model") or $\phi^2$ (chaotic inflation) to the leading order in the slow-roll approximation. $\gamma$ is the ratio of $1/V$ at $N\rightarrow \infty$ to the slope of $1/V$ at a finite $N$ and is related to "$\alpha$" in the $\alpha$-attractors by $\gamma^2=2/3\alpha$. The tensor-to-scalar ratio $r$ is $r=8/N(\gamma^2 N +1) $. The implications for the reheating temperature are also discussed. We also derive formulas for $n_s-1=-p/N$. We find that if the potential is bounded from above, only $p>1$ is allowed. Although $r$ depends on a parameter, the running of the spectral index is independent of it, which can be used as a consistency check of the assumed relation of $n_s(N)$., Comment: 15 pages, 3 figures, published version