Shinji Mukohyama

Ghost condensation and a consistent infrared modification of gravity

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 has a constant velocity, = M2. 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 low-energy dispersion relation ω2 ~ 4/M2. If coupled to matter directly, it gives rise to small Lorentz-violating effects and a new long-range 1/r2 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 MPl/M2 and the time scale MPl2/M3. This theory opens up a number of new avenues for attacking cosmological problems, including inflation, dark matter and dark energy.

Scale-invariant cosmological perturbations from Hořava-Lifshitz gravity without inflation

Based on the renormalizable theory of gravitation recently proposed by Ho?ava, we present a simple scenario to generate almost scale-invariant, super-horizon curvature perturbations. The anisotropic scaling with dynamical critical exponent z = 3 implies that the amplitude of quantum fluctuations of a free scalar field generated in the early epoch of the expanding universe is insensitive to the Hubble expansion rate and, thus, scale-invariant. Those fluctuations are later converted to curvature perturbations by the curvaton mechanism or/and the modulated decay of heavy particles/oscillating fields. This scenario works, for example, for power law expansion at p with 1/3

Massive gravity: nonlinear instability of a homogeneous and isotropic universe.

> p>1/3 and, thus, does not require inflation. Also, this scenario does not rely on any additional assumptions such as the detailed balance condition.

Hořava-Lifshitz cosmology: a review

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.

Open FRW universes and self-acceleration from nonlinear massive gravity

Here we review the 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 mimics general relativity plus dark matter; (ii) higher spatial curvature terms allow bouncing and cyclic universes as regular solutions; (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.

Cosmological perturbations of self-accelerating universe in nonlinear massive gravity

In the context of a recently proposed nonlinear massive gravity with Lorentz-invariant mass terms, we investigate open Friedmann-Robertson-Walker (FRW) universes driven by arbitrary matter source. While the flat FRW solutions were recently shown to be absent, the proof does not extend to the open universes. We find three independent branches of solutions to the equations of motion for the Stuckelberg scalars. One of the branches does not allow any nontrivial FRW cosmologies, as in the previous no-go result. On the other hand, both of the other two branches allow general open FRW universes governed by the Friedmann equation with the matter source, the standard curvature term and an effective cosmological constant Λ± = c±mg2. Here, mg is the graviton mass, + and - represent the two branches, and c± are constants determined by the two dimensionless parameters of the theory. Since an open FRW universe with a sufficiently small curvature constant can approximate a flat FRW universe but there is no exactly flat FRW solution, the theory exhibits a discontinuity at the flat FRW limit.

Dynamic black-hole entropy

We study cosmological perturbations of self-accelerating universe solutions in the recently proposed nonlinear theory of massive gravity, with general matter content. While the broken diffeomorphism invariance implies that there generically are 2 tensor, 2 vector and 2 scalar degrees of freedom in the gravity sector, we find that the scalar and vector degrees have vanishing kinetic terms and nonzero mass terms. Depending on their nonlinear behavior, this indicates either nondynamical nature of these degrees or strong couplings. Assuming the former, we integrate out the 2 vector and 2 scalar degrees of freedom. We then find that in the scalar and vector sectors, gauge-invariant variables constructed from metric and matter perturbations have exactly the same quadratic action as in general relativity. The difference from general relativity arises only in the tensor sector, where the graviton mass modifies the dispersion relation of gravitational waves, with a time-dependent effective mass. This may lead to modification of stochastic gravitational wave spectrum.

Brane cosmology driven by the rolling tachyon

Abstract We consider two non-statistical definitions of the entropy of dynamic (non-stationary) black holes in a 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 Walds Noether-charge method, adapted to dynamic black holes by using the Kodama flow. Both definitions give the same value for the Einstein gravity: one-quarter the area of the trapping horizon.

Phenomenological aspects of Hořava-Lifshitz cosmology

Brane cosmology driven by the tachyon rolling down to its ground state is investigated. We adopt an effective field theoretical description for the tachyon and Randall-Sundrum type brane-world scenario. After formulating the basic equations, we show that the standard cosmology with the usual scalar field can mimic the low-energy behavior of the system near the tachyon ground state. We also investigate the qualitative behavior of the system beyond the low-energy regime for a positive, negative, and vanishing four-dimensional effective cosmological constant

Brane world solutions, standard cosmology, and dark radiation

{\ensuremath{\Lambda}}_{4}={\ensuremath{\kappa}}_{5}^{4}{V(T}_{0}{)}^{2}/12\ensuremath{-}|{\ensuremath{\Lambda}}_{5}|/2,