We propose a new scenario for early cosmology, where an inflationary de Sitter phase is obtained with a ghost condensate. The transition to radiation dominance is triggered by the ghost itself, without any slow-roll potential. Density perturbations are generated by fluctuations around the ghost condensate and can be reliably computed in the effective field theory. The fluctuations are scale invariant as a consequence of the de Sitter symmetries, however, the size of the perturbations are parametrically different from conventional slow-roll inflation, and the inflation happens at far lower energy scales. The model makes definite predictions that distinguish it from standard inflation, and can be sharply excluded or confirmed by experiments in the near future. The tilt in the scalar spectrum is predicted to vanish (n s = 1), and the gravity wave signal is negligible. The non-Gaussianities in the spectrum are predicted to be observable: the 3-point function is determined up to an overall O(1) constant, and its magnitude is much bigger than in conventional inflation, with an equivalent f NL ≃ 100, not far from the present WMAP bounds.

This article reviews basic construction and cosmological implications of a power-counting renormalizable theory of gravitation recently proposed by Hořava. We explain that (i) at low energy this theory does not exactly recover general relativity but instead mimic general relativity plus dark matter; that (ii) higher spatial curvature terms allow bouncing and cyclic universes as regular solutions; and that (iii) the anisotropic scaling with the dynamical critical exponent z = 3 solves the horizon problem and leads to scale-invariant cosmological perturbations even without inflation. We also comment on issues related to an extra scalar degree of freedom called scalar graviton. In particular, for spherically-symmetric, static, vacuum configurations we prove non-perturbative continuity of the λ → 1 + 0 limit, where λ is a parameter in the kinetic action and general relativity has the value λ = 1. We also derive the condition under which linear instability of the scalar graviton does not show up.(IPMU10-0120)

DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the future Japanese space gravitational wave antenna. DECIGO is expected to open a new window of observation for gravitational wave astronomy especially between 0.1 Hz and 10 Hz, revealing various mysteries of the universe such as dark energy, formation mechanism of supermassive black holes, and inflation of the universe. The pre-conceptual design of DECIGO consists of three drag-free spacecraft, whose relative displacements are measured by a differential Fabry-Perot Michelson interferometer. We plan to launch two missions, DECIGO pathfinder and pre-DECIGO first and finally DECIGO in 2024.

We argue that all homogeneous and isotropic solutions in nonlinear massive gravity are unstable. For this purpose, we study the propagating modes on a Bianchi type-I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theory. This ghost mode is interpreted as a leading nonlinear perturbation around a homogeneous and isotropic background.

DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the future Japanese space gravitational wave antenna. It aims at detecting various kinds of gravitational waves between 1 mHz and 100 Hz frequently enough to open a new window of observation for gravitational wave astronomy. The pre-conceptual design of DECIGO consists of three drag-free satellites, 1000 km apart from each other, whose relative displacements are measured by a Fabry–Perot Michelson interferometer. We plan to launch DECIGO in 2024 after a long and intense development phase, including two pathfinder missions for verification of required technologies.

We propose a theoretically consistent modification of gravity in the infrared, which is compatible with all current experimental observations. This is an analog of the Higgs mechanism in general relativity, and can be thought of as arising from ghost condensation-a background where a scalar field φ has a constant velocity, φ = M 2 . The ghost condensate is a new kind of fluid that can fill the universe, which has the same equation of state, ρ = −p, as a cosmological constant, and can hence drive de Sitter expansion of the universe. However, unlike a cosmological constant, it is a physical fluid with a physical scalar excitation, which can be described by a systematic effective field theory at low energies. The excitation has an unusual lowenergy dispersion relation ω 2 ∼ k 4 /M 2 . If coupled to matter directly, it gives rise to small Lorentz-violating effects and a new long-range 1/r 2 spin dependent force. In the ghost condensate, the energy that gravitates is not the same as the particle physics energy, leading to the possibility of both sources that can gravitate and anti-gravitate. The Newtonian potential is modified with an oscillatory behavior starting at the distance scale M Pl /M 2 and the time scale M 2 Pl /M 3 . This theory opens up a number of new avenues for attacking cosmological problems, including inflation, dark matter and dark energy.

We consider two non-statistical definitions of entropy for dynamic (non-stationary) black holes in spherical symmetry. The first is analogous to the original Clausius definition of thermodynamic entropy: there is a first law containing an energy-supply term which equals surface gravity times a total differential. The second is Wald's Noether-charge method, adapted to dynamic black holes by using the Kodama flow. Both definitions give the same answer for Einstein gravity: one-quarter the area of the trapping horizon. 04.70.-sIt is widely believed that black holes possess a gravitational entropy, given in Einstein gravity by A/4, where A is the black-hole area and units are such that c = G = h = k = 1. The original reasoning stemmed from two discoveries: (i) Hawking's result [1] that for stationary black holes, quantum fields radiate with a thermal spectrum at temperature κ/2π, where κ is the surface gravity of the black hole; and (ii) previously discovered properties of stationary black holes [2] which are analogous to the laws of thermodynamics, in particular a first law of the form δm = κδA/8π plus work terms, where δ is a perturbation of a stationary black-hole solution of mass m. This has been called the first law of black-hole statics to stress that it concerns stationary black holes [3]. Most discussions of black-hole entropy concern the stationary case, which is analogous to thermostatics rather than thermodynamics. Since entropy is a fundamental quantity in thermodynamics and not just thermostatics, one expects that dynamic (i.e. non-stationary) black holes should also possess an entropy.This leads to two questions about potential generalizations of the above facts. (i) Do dynamic black holes have a local Hawking temperature in some sense? (ii) Is there a first law of black-hole dynamics? The latter question was recently answered in Ref.[3] in spherical symmetry. The method is based on earlier work which defined dynamic black holes in terms of trapping horizons and derived a corresponding second law of black-hole dynam- * hayward@yukawa.kyoto-u.ac.jp † mukoyama@yukawa.kyoto-u.ac.jp ‡ ashworth@th.phys.titech.ac.jp ics [4]. Moreover, this first law of black-hole dynamics is encoded in a unified first law which also encodes a first law of relativistic thermodynamics. A possible answer to the former question was also suggested, by a local definition of surface gravity for a dynamic black hole. Whether this really determines a local Hawking temperature is still unknown. It is generally thought that black-hole entropy should have a statistical origin, presumably in a quantum theory of gravity. This is, of course, due to the definition of entropy in statistical mechanics. However, it should be remembered that the original concept of entropy was not statistical [5]. The original argument of Clausius was that, in a cyclic reversible process, the total heat supply δQ divided by temperature ϑ should vanish. Thus in any reversible process, δQ/ϑ should be the total differential dS of a state function S, the entropy. M...

We investigate the universal low-energy dynamics of the simplest Higgs phase for gravity, 'ghost condensation.' We show that the nonlinear dynamics of the 'ghostone' field dominate for all interesting gravitational sources. Away from caustic singularities, the dynamics is equivalent to the irrotational flow of a perfect fluid with equation of state p ∝ ρ 2 , where the fluid particles can have negative mass. We argue that this theory is free from catastrophic instabilities due to growing modes, even though the null energy condition is violated. Numerical simulations show that solutions generally have singularities in which negative energy regions shrink to zero size. We exhibit partial UV completions of the theory in which these singularities are smoothly resolved, so this does not signal any inconsistency in the effective theory. We also consider the bounds on the symmetry breaking scale M in this theory. We argue that the nonlinear dynamics cuts off the Jeans instability of the linear theory, and allows M < ∼ 100 GeV.