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We study cosmological dynamics of the Cuscuta–Galileon gravity with a potential term by using the dynamical system approach. This model is galileon generalization of the cuscuton gravity where we add a potential term to the theory in order to obtain the radiation and matter dominated eras. The exponential potential can provide the sequence of the thermal history of the Universe correctly, i.e. starting from radiation dominance, passing through matter dominant era, and then approaching de Sitter expansion stage. This model has no ghosts and the Laplacian instability for both scalar and tensor perturbations. We also discuss the observational constraints on the model parameters. It turns out that the model actually has three degrees of freedom unlike the original cuscuton theory.

A bstract We study gravitational theories with a cosmological constant and the Gauss-Bonnet curvature squared term and analyze the possibility of de Sitter expanding spacetime with a constant internal space. We find that there are two branches of the de Sitter solutions: both the curvature of the internal space and the cosmological constant are (1) positive and (2) negative. From the stability analysis, we show that the de Sitter solution of the case (1) is unstable, while that in the case (2) is stable. Namely de Sitter solution in the present system is stable if the cosmological constant is negative. We extend our analysis to the gravitational theories with higher-order Lovelock curvature terms. Although the existence and the stability of the de Sitter solutions are very complicated and highly depend on the coupling constants, there exist stable de Sitter solutions similar to the case (2). We also find de Sitter solutions with Hubble scale much smaller than the scale of a cosmological constant, which may explain a discrepancy between an inflation energy scale and the Planck scale.

Abstract We discuss cosmology based on the cuscuton gravity theory to resolve the anomaly of the observational 4He abundance reported by the EMPRESS collaboration. We find that the gravitational constant Gcos in the Friedmann equation should be smaller than Newton’s constant GN such that ${\\Delta G_{\\rm N}}/{G_{\\rm N}} \\equiv (G_{\\rm cos}-G_{\\rm N})/{G_{\\rm N}} = -0.085_{-0.028}^{+0.026} \\ (68 \\% \\text{ C.L.})$ in terms of big-bang nucleosynthesis, which excludes ΔGN = 0 at more than 95% C.L. To fit the data, we obtain a negative mass squared of a non-dynamical scalar field with the Planck-mass scale as $\\sim - {\\mathcal {O}}(1) {M_{\\rm PL}^2} ({\\mu }/{0.5 M_{\\rm PL}})^{4}$ with the cuscuton mass parameter μ. This fact could suggest the need for modified gravity theories such as the cuscuton gravity theory with a quadratic potential, which can be regarded as the low-energy Hořava–Lifshitz gravity, and might give a hint of quantum gravity.

We study cosmological solutions in the effective heterotic string theory with α ′-correction terms in the string frame. It is pointed out that the effective theory has an ambiguity via field redefinition and we analyze generalized effective theories due to this ambiguity. We restrict our analysis to the effective theories which give equations of motion of second order in the derivatives, just as “Galileon” field theory. This class of effective actions contains two free coupling constants. We find de Sitter solutions as well as the power-law expanding universes in our four-dimensional Einstein frame. The accelerated expanding universes are always attractors in the present dynamical system.

Abstract Energy extraction from a rotating or charged black hole is one of the fascinating issues in general relativity. The collisional Penrose process is one such extraction mechanism and has been reconsidered intensively since Bañados, Silk, and West pointed out the physical importance of very high energy collisions around a maximally rotating black hole. In order to get results analytically, the test particle approximation has been adopted so far. Successive works based on this approximation scheme have not yet revealed the upper bound on the efficiency of the energy extraction because of the lack of backreaction. In the Reissner–Nordström spacetime, by fully taking into account the self-gravity of the shells, we find that there is an upper bound on the extracted energy that is consistent with the area law of a black hole. We also show one particular scenario in which almost the maximum energy extraction is achieved even without the Bañados–Silk–West collision.

We analyze the collisional Penrose process between a particle on the innermost stable circular orbit (ISCO) orbit around an extreme Kerr black hole and a particle impinging from infinity. We consider both cases with non-spinning and spinning particles. We evaluate the maximal efficiency, $\\eta_{\\text{max}}=(\\text{extracted energy})/(\\text{input energy})$, for the elastic collision of two massive particles and for the photoemission process, in which the ISCO particle will escape to infinity after a collision with a massless impinging particle. For non-spinning particles, the maximum efficiency is $\\eta_{\\text{max}} \\approx 2.562$ for the elastic collision and $\\eta_{\\text{max}} \\approx 7$ for the photoemission process. For spinning particles we obtain the maximal efficiency $\\eta_{\\text{max}} \\approx 8.442$ for the elastic collision and $\\eta_{\\text{max}} \\approx 12.54$ for the photoemission process.

We construct a general family of supersymmetric solutions in time- and space-dependent wave backgrounds in general supergravity theories describing single and intersecting p -branes embedded into time-dependent dilaton-gravity plane waves of an arbitrary (isotropic) profile, with the brane world-volume aligned parallel to the propagation direction of the wave. We discuss how many degrees of freedom we have in the solutions. We also propose that these solutions can be used to describe higher-dimensional time-dependent “black holes”, and discuss their property briefly.

The scalar-tensor theory of gravitation is one of the most popular alternatives to Einstein's theory of gravitation. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar fields and placing them in context with a discussion of Brans-Dicke theory. Topics covered include the cosmological constant problem, time variability of coupling constants, higher dimensional space-time, branes and conformal transformations. The authors emphasize the physical applications of the scalar-tensor theory and thus provide a pedagogical overview of the subject, keeping more mathematically detailed sections for the appendices. This book is suitable for graduate courses in cosmology, gravitation and relativity. It will also provide a valuable reference for researchers.

We study a stationary black brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in D-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). General solutions are constructed by superposition of a complete set of those harmonic functions. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field ij, which is a rotational part of gravity, is self-dual.

We study a stationary black brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in D-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). General solutions are constructed by superposition of a complete set of those harmonic functions. Using the hyperspherical coordinate system, we explicitly give the solutions in 11-dimensional M theory for the case with M2⊥M5 intersecting branes and a traveling wave. Compactifying these solutions into five dimensions, we show that these solutions include the BMPV black hole and the Brinkmann wave solution. We also find new solutions similar to the Brinkmann wave. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field ij, which is a rotational part of gravity, is self-dual. We also discuss non-spherical black objects (e.g., a ring topology and an elliptical shape) by use of other curvilinear coordinates.