arXiv subjects

Shinji Mukohyama

Publications and source records attributed to Shinji Mukohyama.

At least 91 records · Page 5Linked to original sources

arXiv2022

Cosmological memory effect in scalar-tensor theories

The cosmological memory effect is a permanent change in the relative separation of test particles located in a FLRW spacetime due to the passage of gravitational waves. In the case of a spatially flat FLRW spacetime filled with a perfect fluid in general relativity, it is known that only tensor perturbations contribute to the memory effect while scalar and vector perturbations do not. In this paper, we show that in the context of scalar-tensor theories, the scalar perturbations associated to the scalar graviton contribute to the memory effect as well. We find that, depending on the mass and coupling, the influence of cosmic expansion on the memory effect due to the scalar perturbations can be either stronger or weaker than the one induced by the tensor perturbations. As a byproduct, in an appendix, we develop a general framework which can be used to study coupled wave equations in any curved spacetime region which admits a foliation by time slices.

gr-qc↗

arXiv2022

Extended minimal theories of massive gravity

In this work, we introduce a class of extended Minimal Theories of Massive Gravity (eMTMG), without requiring a priori that the theory should admit the same homogeneous and isotropic cosmological solutions as the de Rham-Gabadadze-Tolley massive gravity. The theory is constructed as to have only two degrees of freedom in the gravity sector. In order to perform this step we first introduce a precursor theory endowed with a general graviton mass term, to which, at the level of the Hamiltonian, we add two extra constraints as to remove the unwanted degrees of freedom, which otherwise would typically lead to ghosts and/or instabilities. On analyzing the number of independent constraints and the properties of tensor mode perturbations, we see that the gravitational waves are the only propagating gravitational degrees of freedom which do acquire a non-trivial mass, as expected. In order to understand how the effective gravitational force works for this theory we then investigate cosmological scalar perturbations in the presence of a pressureless fluid. We then restrict the whole class of models by imposing the following conditions at all times: 1) it is possible to define an effective gravitational constant, $G_{\rm eff}$; 2) the value $G_{\text{eff}}/G_{N}$ is always finite but not always equal to unity (as to allow some non-trivial modifications of gravity, besides the massive tensorial modes); and 3) the square of mass of the graviton is always positive. These constraints automatically make also the ISW-effect contributions finite at all times. Finally we focus on a simple subclass of such theories, and show they already can give a rich and interesting phenomenology.

gr-qc↗

arXiv2022

DeWitt wave function in Hořava-Lifshitz cosmology with tensor perturbation

We present a well-tempered DeWitt wave function, which vanishes at the classical big-bang singularity, in Hořava-Lifshitz (HL) cosmology with tensor perturbation, both analytically and numerically. In general relativity, the DeWitt wave function is ill-behaved once the tensor perturbation is taken into account. This is essentially because the amplitude of the perturbation diverges at the singularity and the perturbative expansion completely breaks down. On the other hand, in HL gravity it is known that the higher dimensional operators required by the perturbative renormalizability render the tensor perturbation scale-invariant and regular all the way up to the singularity. In this paper we analytically show that in $d+1$ dimensional HL gravity the DeWitt wave function for tensor perturbation is indeed well-defined around the classical big-bang singularity. Also, we numerically demonstrate the well-behaved DeWitt wave function for tensor perturbation from the big-bang to a finite size of the Universe.

gr-qc↗

arXiv2022

Reheating after relaxation of large cosmological constant

We present a cosmological model of an early-time scenario that incorporates a relaxation process of the would-be large vacuum energy, followed by a reheating era connecting to the standard hot big bang universe. Avoiding fine-tuning the cosmological constant is achieved by the dynamics of a scalar field whose kinetic term is modulated by an inverse power of spacetime curvature. While it is at work against radiative corrections to the dark energy, this mechanism alone would wipe out not only the vacuum energy but also all other matter contents. Our present work aims to complete the scenario by exploiting a null-energy-condition violating sector whose energy is eventually transferred to a reheating sector. We provide an explicit example of this process and thus a concrete scenario of the cosmic onset that realizes the thermal history of the Universe with a negligible cosmological constant.

hep-th↗

arXiv2022

Junction conditions and sharp gradients in generalized coupling theories

In this article, we develop the formalism for singular hypersurfaces and junction conditions in generalized coupling theories using a variational approach. We then employ this formalism to examine the behavior of sharp matter density gradients in generalized coupling theories. We find that such gradients do not necessarily lead to the pathologies present in other theories of gravity with auxiliary fields. A detailed example, based on a simple instance of a generalized coupling theory called the MEMe model, is also provided. In the static case, we show that sharp boundaries do not generate singularities in the dynamical frame despite the presence of an auxiliary field. Instead, in the case of a collapsing spherical density distribution with a general profile an additional force compresses over-densities and expands underdensities. These results can also be used to deduce additional constraints on the parameter of this model.

gr-qc↗

arXiv2022

Static and spherically symmetric general relativity solutions in Minimal Theory of Bigravity

We investigate static and spherically symmetric solutions in the Minimal Theory of Bigravity (MTBG). First, we show that a pair of Schwarzschild-de Sitter spacetimes with different cosmological constants and black hole masses written in the spatially-flat Gullstrand-Painlevé (GP) coordinates is a solution in the self-accelerating branch of MTBG, while it cannot be a solution in the normal branch. We then illustrate how Schwarzschild-de Sitter solutions can become compatible with the normal branch when using different coordinates. We also confirm that the self-accelerating branch of MTBG admits static and spherically symmetric general relativity solutions with matter written in the spatially-flat coordinates, including neutron stars with arbitrary matter equations of state. Finally, we show that in the self-accelerating branch nontrivial solutions are given by the Schwarzschild-de Sitter metrics written in nonstandard coordinates.

gr-qc↗

arXiv2022

Dark Matter from Entropy Perturbations in Curved Field Space

The accumulated energy density of the excited entropy modes in multiple field inflationary scenarios can play the role of dark matter. In the usual case of a flat field space without any turning trajectory, only light superhorizon entropy modes can be excited through the gravitational instability. In the case of a negatively curved field space, we show that subhorizon entropy modes can be excited as well through the tachyonic instability induced by the negative curvature of the field space. The latter allows for production of entropy modes with masses larger than or at the order of the Hubble expansion rate during inflation, leading to a new dark matter scenario. Due to the contribution of subhorizon modes, the corresponding spectral density has a peak at a scale smaller than its counterpart in the models based on a flat field space. This difference makes our model observationally distinguishable.

gr-qc↗

arXiv2022

Disformal map and Petrov classification in modified gravity

Disformal transformation provides a map relating different scalar-tensor and vector-tensor theories and gives access to a powerful solution-generating method in modified gravity. In view of the vast family of new solutions one can achieve, it is crucial to design suitable tools to guide their construction. In this work, we address this question by revisiting the Petrov classification of disformally constructed solutions in modified gravity theories. We provide close formulas which relate the principal nulls directions as well as the Weyl scalars before and after the disformal transformation. These formulas allow one to capture if and how the Petrov type of a given seed geometry changes under a disformal transformation. Finally, we apply our general setup to three relevant disformally constructed solutions for which the seeds are respectively homogeneous and isotropic, static spherically symmetric and stationary axisymmetric. For the first two cases, we show that the Petrov type O and Petrov type D remain unchanged after a disformal transformation while we show that disformed Kerr black hole is no longer of type D but of general Petrov type I. The results presented in this work should serve as a new toolkit when constructing and comparing new disformal solutions in modified gravity.

gr-qc↗

arXiv2022

Inflation with $0 \leq c_{\rm s} \leq 1$

We investigate a novel single field inflationary scenario which allows a transition between a slow-roll k-inflation with $c_{\rm s}$ of order unity and a ghost inflation with $ c_{\rm s} \simeq 0$, where $ c_{\rm s}$ is the sound speed for the curvature perturbations. We unify the two phases smoothly by appropriately taking into account a higher derivative scordatura term, which is always there from the effective field theory point of view but which becomes important only in the $c_{\rm s} \simeq 0$ regime. The model achieves the whole range of $0 \leq c_{\rm s} \leq 1$ avoiding strong coupling and gradient instability, and allows us to access the $c_{\rm s} \simeq 0$ regime in a self-consistent manner. We also discuss implications to the formation of primordial black holes.

hep-th↗

arXiv2022

The Effective Field Theory of Vector-Tensor Theories

We investigate a systematic formulation of vector-tensor theories based on the effective field theory (EFT) approach. The input of our EFT is that the spacetime symmetry is spontaneously broken by the existence of a preferred timelike direction in accordance with the cosmological principle. After clarifying the difference of the symmetry breaking pattern from the conventional EFT of inflation/dark energy, we find an EFT description of vector-tensor theories around the cosmological background. This approach not only serves as a unified description of vector-tensor theories but also highlights universal differences between the scalar-tensor theories and the vector-tensor theories. The theories having different symmetry breaking patterns are distinguished by a phenomenological function and consistency relations between the EFT coefficients. We study the linear cosmological perturbations within our EFT framework and discuss the characteristic properties of the vector-tensor theories in the context of dark energy. In particular, we compute the effective gravitational coupling and the slip parameter for the matter density contrast in terms of the EFT coefficients.

hep-th↗

arXiv2021

Shift-symmetric $SO(N)$ multi-Galileon

A Poincarè invariant, local scalar field theory in which the Lagrangian and the equation of motion contain only up to second-order derivatives of the fields is called generalized Galileon. The covariant version of it in four dimensions is called Horndeski theory, and has been vigorously studied in applications to inflation and dark energy. In this paper, we study a class of multi-field extensions of the generalized Galileon theory. By imposing shift and $SO(N)$ symmetries on all the currently known multi-Galileon terms in general dimensions, we find that the structure of the Lagrangian is uniquely determined and parameterized by a series of coupling constants. We also study tensor perturbation in the shift-symmetric $SO(3)$ multi-Galileon theory in four dimensions. The tensor perturbations can obtain a mass term stemming from the same symmetry breaking pattern as the solid inflation. We also find that the shift-symmetric $SO(3)$ multi-Galileon theory gives rise to new cubic interactions of the tensor modes, suggesting the existence of a new type of tensor primordial non-Gaussianity.

gr-qc↗

arXiv2021

Nonlinear definition of the shadowy mode in higher-order scalar-tensor theories

We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode in a generic coordinate system. We show that the extra mode satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface, and hence it does not propagate. We clarify how to treat this "shadowy" mode at both the linear and the nonlinear levels.

gr-qc↗

arXiv2021

Static, spherically symmetric objects in Type-II minimally modified gravity

Static, spherically symmetric solutions representing stars made of barotropic perfect fluid are studied in the context of two theories of type-II minimally modified gravity, VCDM and VCCDM. Both of these theories share the property that no additional degree of freedom is introduced in the gravity sector, and propagate only two gravitational waves besides matter fields, as in General Relativity (GR). We find that, on imposing physical boundary conditions on the Misner-Sharp mass of the system, the solutions in V(C)CDM exactly coincide with the ones in GR, namely they also satisfy the Tolman-Oppenheimer-Volkoff equation.

gr-qc↗

arXiv2021

On the assumptions leading to the information loss paradox

The information loss paradox is usually stated as an incompatibility between general relativity and quantum mechanics. However, the assumptions leading to the problem are often overlooked and, in fact, a careful inspection of the main hypothesises suggests a radical reformulation of the problem. Indeed, we present a thought experiment involving a black hole that emits radiation and, independently of the nature of the radiation, we show the existence of an incompatibility between (i) the validity of the laws of general relativity to describe infalling matter far from the Planckian regime, and (ii) the so-called central dogma which states that as seen from an outside observer a black hole behaves like a quantum system whose number of degrees of freedom is proportional to the horizon area. We critically revise the standard arguments in support of the central dogma, and argue that they cannot hold true unless some new physics is invoked even before reaching Planck scales. This suggests that the information loss problem, in its current formulation, is not necessarily related to any loss of information or lack of unitarity. Therefore, in principle, semiclassical general relativity and quantum mechanics can be perfectly compatible before reaching the final stage of the black hole evaporation where, instead, a consistent theory of quantum gravity is needed to make any prediction.

hep-th↗

arXiv2021

Positivity vs. Lorentz-violation: an explicit example

We show how a class of multi-field scalar-field theories in a Lorentz-breaking background imposes consistency conditions on its effective theory of a single field and provides an example of order-unity violation of a naively applied positivity bound, assuming a large hierarchy between the masses of the lightest field and the others.

hep-th↗

arXiv2021

Minimal theory of massive gravity and constraints on the graviton mass

The Minimal theory of Massive Gravity (MTMG) is endowed non-linearly with only two tensor modes in the gravity sector which acquire a non-zero mass. On a homogeneous and isotropic background the theory is known to possess two branches: the self-accelerating branch with a phenomenology in cosmology which, except for the mass of the tensor modes, exactly matches the one of $Λ$CDM; and the normal branch which instead shows deviation from General Relativity in terms of both background and linear perturbations dynamics. For the latter branch we study using several early and late times data sets the constraints on today's value of the graviton mass $μ_{0}$, finding that $(μ_{0}/H_{0})^{2}=0.119_{-0.098}^{+0.12}$ at $68\%$ CL, which in turn gives an upper bound at $95\%$ CL as $μ_{0}<8.4\times10^{-34}$ eV. This corresponds to the strongest bound on the mass of the graviton for the normal branch of MTMG.

astro-ph.CO↗

arXiv2021

Ghosts without runaway

We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e. with a ghost. We prove analytically that the classical motion of the system is completely stable for all initial conditions, notwithstanding that the conserved Hamiltonian is unbounded from below and above. This is fully supported by numerical computations. Systems with negative kinetic terms often appear in modern cosmology, quantum gravity and high energy physics and are usually deemed as unstable. Our result demonstrates that for mechanical systems this common lore can be too naive and that living with ghosts can be stable.

gr-qc↗

arXiv2021

Spherically symmetric exact vacuum solutions in Einstein-aether theory

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlevè-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both time-dependent and time-independent exact vacuum solutions. In particular, in the isotropic coordinates we find a class of exact static solutions characterized by a single parameter $c_{14}$ in closed forms, which satisfies all the current observational constraints of the theory, and reduces to the Schwarzschild vacuum black hole solution in the decoupling limit ($c_{14} = 0$). However, as long as $c_{14} \not= 0$, a marginally trapped throat with a finite non-zero radius always exists, and in one side of it the spacetime is asymptotically flat, while in the other side the spacetime becomes singular within a finite proper distance from the throat, although the geometric area is infinitely large at the singularity. Moreover, the singularity is a strong and spacetime curvature singularity, at which both of the Ricci and Kretschmann scalars become infinitely large.

gr-qc↗