arXiv subjects

Shinji Mukohyama

Publications and source records attributed to Shinji Mukohyama.

At least 145 records · Page 8Linked to original sources

arXiv2019

Ghostfree quadratic curvature theories with massive spin-2 and spin-0 particles

We consider generic derivative corrections to the Einstein gravity and find new classes of theories without ghost around the Minkowski background by means of an extension of the spacetime geometry. We assume the Riemann-Cartan geometry, i.e. a geometry with a non-vanishing torsion, and consider all possible terms in the Lagrangian up to scaling dimension four. We first clarify the number, spins, and parities of all particle species around the Minkowski background and find that some of those particle species are ghosts for generic choices of parameters. For special choices of the parameters, on the other hand, those would-be ghosts become infinitely heavy and thus can be removed from the physical content of particle species. Imposing the conditions on the coupling constants to eliminate the ghosts, we find new quadratic curvature theories which are ghost-free around the Minkowski background for a range of parameters. A key feature of these theories is that there exist a non-ghost massive spin-2 particle and a non-ghost massive spin-0 particle in the graviton propagator, as well as the massless spin-2 graviton. In the limit of the infinite mass of the torsion, the Riemann-Cartan geometry reduces to the Riemannian geometry and thus the physical content of particle species coincides with that of the well-known quadratic curvature theory in the metric formalism, i.e. a massive spin-2 ghost, a massive spin-0 particle and the massless spin-2 graviton. Ghost-freedom therefore sets, besides other constraints, an upper bound on the mass of the torsion. In addition to the above mentioned particle species, the ghost-free theory contains either the set of a massive spin-1 and a massive spin-0 (Class I) or a couple of spin-1 (Class II). These additional particle species mediate gravity sourced by the spin of matter fields.

hep-th↗

arXiv2019

Primordial Tensor Non-Gaussianity from Massive Gravity

We calculate tensor bispectrum in a theory of massive tensor gravitons which predicts blue-tilted and largely amplified primordial gravitational waves. We find that a new 3-point interaction can produce a larger tensor bispectrum than the conventional one from general relativity. The bispectrum peaks at the squeezed configuration and its slope towards the squeezed limit is determined by the graviton mass. This squeezed tensor bispectrum may be observed as the quadrupolar modulation of the tensor power spectrum by interferometers.

astro-ph.CO↗

arXiv2019

Minimally Modified Gravity: a Hamiltonian Construction

Minimally modified gravity theories are modifications of general relativity with two local gravitational degrees of freedom in four dimensions. Their construction relies on the breaking of 4D diffeomorphism invariance keeping however the symmetry under 3D diffeomorphisms. Here, we construct these theories from a Hamiltonian point of view. We start with the phase space of general relativity in the ADM formalism. Then, we find the conditions that the Hamiltonian must satisfy for the theory to propagate (up to) two gravitational degrees of freedom with the assumptions that the lapse and the shift are not dynamical, and the theory remains invariant under 3D diffeomorphisms. This construction enables us to recover the well-known "cuscuton" class of scalar-tensor theories in the unitary gauge. We also exhibit a new class of interesting theories, that we dubb $f({\cal H})$ theories, where the usual Hamiltonian constraint $\cal H$ of general relativity is replaced by $f({\cal H})$ where $f$ is an arbitrary function.

gr-qc↗

arXiv2019

Gravitational scalar-tensor theory

We consider a new form of theories of gravity in which the action is written in terms of the Ricci scalar and its first and second derivatives. Despite the higher derivative nature of the action, the theory is free from ghost under an appropriate choice of the functional form of the Lagrangian. This model possesses $2+2$ physical degrees of freedom, namely $2$ scalar degrees and $2$ tensor degrees. We exhaust all such theories with the Lagrangian of the form $f(R, (\nabla R)^2, \Box R)$, where $R$ is the Ricci scalar, and then show some examples beyond this ansatz. In course of analysis, we prove the equivalence between these examples and generalized bi-Galileon theories.

gr-qc↗

arXiv2019

Kinetic equation for Lifshitz scalar

Employing the method of Wigner functions on curved spaces, we study classical kinetic (Boltzmann-like) equations of distribution functions for a real scalar field with the Lifshitz scaling. In particular, we derive the kinetic equation for $z=2$ on general curved spaces and for $z=3$ on spatially flat spaces under the projectability condition $N=N(t)$, where $z$ is the dynamical critical exponent and $N$ is the lapse function. We then conjecture a form of the kinetic equation for a real scalar field with a general dispersion relation in general curved geometries satisfying the projectability condition, in which all the information about the non-trivial dispersion relation is included in the group velocity and which correctly reproduces the equations for the $z=2$ and $z=3$ cases as well as the relativistic case. The method and equations developed in the present paper are expected to be useful for developments of cosmology in the context of Hořava-Lifshitz gravity.

hep-th↗

arXiv2019

Cosmology in Mimetic SU(2) Gauge Theory

It is well known that the standard scalar field mimetic cosmology provides a dark matter-like energy density component. Considering $SU(2)$ gauge symmetry, we study the gauge field extension of the mimetic scenario in spatially flat and curved FLRW spacetimes. Because of the mimetic constraint, the standard Yang-Mills term plays the role of the cosmological constant while the mimetic term provides two different contributions: one is the standard radiation scaling like $ a^{-4}$ while the other contribution in energy density scales as $\propto a^{-2}$. Consequently, in the Friedmann equation we have two different energy densities which scale as $\propto a^{-2}$: one is the mimetic spatial curvature-like and the other is the standard spatial curvature which can compete with each other. The degeneracy between these two contributions are disentangled in this scenario since the mimetic spatial curvature-like term shows up only at the dynamical level while the standard spatial curvature term shows up at both dynamical and kinematical levels.

gr-qc↗

arXiv2019

Shape dependence of spontaneous scalarization

Spontaneous scalarization is an interesting mechanism for modification of gravity by nonminimal coupling of a scalar field to matter or curvature invariants in the context of scalar-tensor theories, and its onset is signaled by linear instability of the scalar field around the corresponding general relativity solution. We thus perform the linear stability analysis of the scalar field about general relativity solutions and highlight a crucial difference between a spherically symmetric profile and a planar symmetric profile. We clarify that the critical value for the instability is sensitive to the morphology and that the spontaneous scalarization occurs much more easily with the planar symmetric shape than with the spherically symmetric shape.

gr-qc↗

arXiv2019

Phenomenology in type-I minimally modified gravity

We study cosmology in a class of minimally modified gravity (MMG) with two local gravitational degrees of freedom. We classify modified gravity theories into type-I and type-II: theories of type-I have an Einstein frame and can be recast by change of variables as general relativity (GR) with a non-minimal matter coupling, while theories of type-II have no Einstein frame. Considering a canonical transformation of the lapse, the 3-dimensional induced metric and their conjugate momenta we generate type-I MMG. We then show that phenomenological deviations from GR, such as the speed of gravitational waves $c_T$ and the effective gravitational constant for scalar perturbations $G_{\rm eff}$, are characterized by two functions of an auxiliary variable. We study the phenomenology of several models all having $c_T=1$. We obtain a scenario with $c_T=1$ in which the effective equation-of-state parameter of dark energy is different from $-1$ even though the cosmic acceleration is caused by a bare cosmological constant, and we find that it is possible to reconstruct the theory on choosing a selected time-evolution for the effective dark energy component.

gr-qc↗

arXiv2018

Gravitational collapse and formation of universal horizons in Einstein-aether theory

We numerically study the gravitational collapse of a massless scalar field with spherical symmetry in Einstein-aether theory, and show that apparent, spin-0 and dynamical universal horizons (dUHs) can be all formed. The spacetime and the aether field are well-behaved and regular, including regions nearby these horizons (but away from the center of spherical symmetry). The spacetime outside the apparent and spin-0 horizons settles down to a static configuration, and some of such resulting static black holes were already found numerically in the literature. On the other hand, the proper distance of the outermost dUH from the apparent (or spin-0) horizon keeps increasing on $\mboxæ$ther-orthogonal time slices. This indicates that the outermost dUH is evolving into the causal boundary, even for excitations with large speeds of propagation.

gr-qc↗

arXiv2018

Blue-tilted Primordial Gravitational Waves from Massive Gravity

We study a theory of massive tensor gravitons which predicts blue-tilted and largely amplified primordial gravitational waves. After inflation, while their mass is significant until it diminishes to a small value, gravitons are diluted as non-relativistic matter and hence their amplitude can be substantially amplified compared to the massless gravitons which decay as radiation. We show that such gravitational waves can be detected by interferometer experiments, even if their signal is not observed on the CMB scales.

gr-qc↗

arXiv2018

Gauge Field Mimetic Cosmology

We extend the mimetic cosmology to models containing gauge invariant $p$-forms. The $0$-form case reproduces the well-known results of the mimetic dark matter, the $1$-form corresponds to the gauge field mimetic model while the $2$-form model is the Hodge dual of the $0$-form model in $4$ spacetime dimensions. We study the cosmological applications of the new gauge field mimetic model and show that it generates an energy density component which mimics the roles of spatial curvature. In the presence of the Maxwell term, the model also supports the flat, open and closed de Sitter-like cosmological backgrounds while the spatial geometry is flat for all three cases. We perform the cosmological perturbations analysis and show that the model is stable in the case of open de Sitter-like solution while it suffers from ghost instabilities in the case of the closed de Sitter-like solution.

hep-th↗

arXiv2018

Stability of stealth magnetic field in de Sitter spacetime

A detailed stability analysis is presented for the de Sitter solution with a homogeneous magnetic field that was recently found in the context of a $U(1)$ gauge theory nonminimally coupled to scalar-tensor gravity. The magnetic field is `stealth' in the sense that the corresponding stress-energy tensor is of the form of an effective cosmological constant and thus is isotropic despite the fact that the magnetic field has a preferred spatial direction. We study the stability of the solution against linear perturbations in the subhorizon and superhorizon limits. We then present some explicit examples that satisfy all stability conditions. The stable de Sitter solution with a homogeneous magnetic field opens up a new possibility for inflationary magnetogenesis, in which magnetic fields in the Universe at all scales may originate from a classical, homogeneous magnetic field sustained during inflation.

hep-th↗

arXiv2018

The Ogievetsky-Polubarinov massive gravity and the benign Boulware-Deser mode

We present our analysis of the theory constructed in 1965 by Ogievetsky and Polubarinov (OP) -- the first ever theory of interacting massive gravitons. Its mass term is adjusted in such a way that the non-linear field equations imply as a consequence the linear Hilbert-Lorentz condition, which restricts the spin of states in the theory. Strikingly, for special parameter values this theory coincides with one of the "ghost-free" massive gravity models rediscovered only in 2010. For generic parameter values, however, it propagates 6 degrees of freedom and shows ghost around flat space. Surprizingly, we find that the de Sitter space remains stable for a large region of the parameter space, provided that the Hubble expansion rate is large enough, hence the Boulware-Deser mode is benign in this case. We study also other solutions and find that the Milne universe -- a sector of Minkowski space -- is stable in the UV limit. This presumably implies that at the non-linear level the ghost instability in flat space develops only for long waves, similarly to the classical Jeans instability.

hep-th↗

arXiv2018

Black holes and stars in the minimal theory of massive gravity

In this letter, we show that any solution of general relativity (GR) that can be rendered spatially flat by a coordinate change is also a solution of the self-accelerating branch of the minimal theory of massive gravity (MTMG), with or without matter. We then for the first time obtain black hole and star solutions in a theory of massive gravity that agree with the corresponding solutions in GR and that are free from strong coupling issues. This in particular implies that the parametrized post-Newtonian parameters $β^{\rm PPN}$ and $γ^{\rm PPN}$ are unity, as in GR. We further show how these solutions can be embedded in a cosmological setting. While cosmological scales have already been considered in previous works, this is the first study of the phenomenology at shorter scales of the self-accelerating branch of MTMG.

gr-qc↗

arXiv2018

Vector disformal transformation of generalized Proca theory

Motivated by the GW170817/GRB170817A constraint on the deviation of the speed of gravitational waves from that of photons, we study disformal transformations of the metric in the context of the generalized Proca theory. The constraint restricts the form of the gravity Lagrangian, the way the electromagnetism couples to the gravity sector on cosmological backgrounds, or in general a combination of both. Since different ways of coupling matter to gravity are typically related to each other by disformal transformations, it is important to understand how the structure of the generalized Proca Lagrangian changes under disformal transformations. For disformal transformations with constant coefficients we provide the complete transformation rule of the Lagrangian. We find that additional terms, which were considered as beyond generalized Proca in the literature, are generated by the transformations. Once these additional terms are included, on the other hand, the structure of the gravity Lagrangian is preserved under the transformations. We then derive the transformation rules for the sound speeds of the scalar, vector and tensor perturbations on a homogeneous and isotropic background. We explicitly show that they transform following the natural expectation of metric transformations, that is, according to the transformation of the background lightcone structure. We end by arguing that inhomogeneities due to structures in the universe, e.g. dark matter halos, generically changes the speed of gravitational waves from its cosmological value. We give a rough estimate of the effect of inhomogeneities and find that the fine-tuning should not depend on the background or that the fine-tuned theory has to be further fine-tuned to pass the tight constraint.

gr-qc↗

arXiv2018

Integrated Sachs-Wolfe-galaxy cross-correlation bounds on the two branches of the minimal theory of massive gravity

The minimal theory of massive gravity (MTMG) has two branches of stable cosmological solutions: a self-accelerating branch, which, except for the mass of tensor modes has exactly the same behavior of linear perturbations as $Λ$CDM in general relativity (GR), and a normal branch with nontrivial behavior. We explore the influence of the integrated Sachs-Wolfe-galaxy correlation constraints on the normal branch of MTMG, which, in its simplest implementation, has one free parameter more than $Λ$CDM in GR (or the self-accelerating branch of MTMG): $θ$. This parameter is related to the graviton mass and only affects the behavior of the cosmological linear perturbation dynamics. Using 2d-mass and SDSS data, we check which values of $θ$ lead to a positive or negative cross-correlation. We find that positive cross-correlation is achieved for a large parameter-space interval. Within this allowed region of parameter space, we perform a $χ^2$ analysis in terms of the parameter $θ$, while keeping the other background parameters fixed to the best-fit values of Planck. We then infer that the normal branch of MTMG fits the data well in a nontrivial portion of the parameter space, and future experiments should be able to distinguish such a model from $Λ$CDM in GR (or the self-accelerating branch of MTMG).

astro-ph.CO↗

arXiv2018

Constraints on Einstein-aether theory after GW170817

In this paper, we carry out a systematic analysis of the theoretical and observational constraints on the dimensionless coupling constants $c_i$ ($i=1,2,3,4$) of the Einstein-aether theory, taking into account the events GW170817 and GRB 170817A. The combination of these events restricts the deviation of the speed $c_T$ of the spin-2 graviton to the range, $- 3\times 10^{-15} < c_T -1 < 7\times 10^{-16}$, which for the Einstein-aether theory implies $\left|c_{13}\right| \le 10^{-15}$ with $c_{ij} \equiv c_{i} + c_{j}$. The rest of the constraints are divided into two groups: those on the ($c_1, c_{14}$)-plane and those on the ($c_2, c_{14}$)-plane, except the strong-field constraints. The latter depend on the sensitivities $σ_æ$ of neutron stars, which are not known at present in the new ranges of the parameters found in this paper.

gr-qc↗

arXiv2018

Quantum Entanglement in Multi-field Inflation

We study the emergence of quantum entanglement in multi-field inflation. In this scenario, the perturbations of one field contribute to the observable curvature perturbation, while multi-field dynamics with the other fields affect the curvature perturbation through particle production and entanglement. We develop a general formalism which defines the quantum entanglement between the perturbations of the multiple fields both in the Heisenberg and Schrödinger pictures, and show that entanglement between different fields can arise dynamically in the context of multi-field inflationary scenarios. We also present a simple model in which a sudden change in the kinetic matrix of the scalar fields generates entanglement and an oscillatory feature appears in the power spectrum of the inflaton perturbation.

astro-ph.CO↗