arXiv subjects

Hayato Motohashi

Publications and source records attributed to Hayato Motohashi.

At least 91 records · Page 5Linked to original sources

arXiv2016

Disformal invariance of curvature perturbation

We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that a similar result holds for any theory that is disformally related to Horndeski's scalar-tensor theory so long as the invertibility condition for the disformal transformation is satisfied. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Finally, we also discuss the counting of degrees of freedom in theories disformally related to Horndeski's.

gr-qc↗

arXiv2015

Nonlinear Excitations in Inflationary Power Spectra

We develop methods to calculate the curvature power spectrum in models where features in the inflaton potential nonlinearly excite modes and generate high frequency features in the spectrum. The first nontrivial effect of excitations generating further excitations arises at third order in deviations from slow roll. If these further excitations are contemporaneous, the series can be resummed, showing the exponential sensitivity of the curvature spectrum to potential features. More generally, this exponential approximation provides a power spectrum template which nonlinearly obeys relations between excitation coefficients and whose parameters may be appropriately adjusted. For a large sharp step in the potential, it greatly improves the analytic power spectrum template and its dependence on potential parameters. For axionic oscillations in the potential, it corrects the mapping between the potential and the amplitude, phase and zero point of the curvature oscillations, which might otherwise cause erroneous inferences in for example the tensor-scalar ratio, formally even when that amplitude is $10^3$ times larger than the slow roll power spectrum. It also estimates when terms that produce double frequency oscillations that are usually omitted when analyzing data should be included. These techniques should allow future studies of high frequency features in the CMB and large scale structure to extend to higher amplitude and/or higher precision.

astro-ph.CO↗

arXiv2015

Running from Features: Optimized Evaluation of Inflationary Power Spectra

In models like axion monodromy, temporal features during inflation which are not associated with its ending can produce scalar, and to a lesser extent, tensor power spectra where deviations from scale-free power law spectra can be as large as the deviations from scale invariance itself. Here the standard slow-roll approach breaks down since its parameters evolve on an efolding scale $ΔN$ much smaller than the efolds to the end of inflation. Using the generalized slow-roll approach, we show that the expansion of observables in a hierarchy of potential or Hubble evolution parameters comes from a Taylor expansion of the features around an evaluation point that can be optimized. Optimization of the leading-order expression provides a sufficiently accurate approximation for current data as long as the power spectrum can be described over the well-observed few efolds by the local tilt and running. Standard second-order approaches, often used in the literature, ironically are worse than leading-order approaches due to inconsistent evaluation of observables. We develop a new optimized next-order approach which predicts observables to $10^{-3}$ even for $ΔN\sim 1$ where all parameters in the infinite hierarchy are of comparable magnitude. For models with $ΔN \ll 1$, the generalized slow-roll approach provides integral expressions that are accurate to second order in the deviation from scale invariance. Their evaluation in the monodromy model provides highly accurate explicit relations between the running oscillation amplitude, frequency and phase in the curvature spectrum and parameters of the potential.

astro-ph.CO↗

arXiv2015

Stability of cosmological solutions in extended quasidilaton massive gravity

We consider the stability of self-accelerating solutions to extended quasidilaton massive gravity in the presence of matter. By making a second or extended fiducial metric dynamical in this model, matter can cause it to evolve from a Lorentzian to Euclidean signature, triggering a ghost instability. We study this possibility with scalar field matter as it can model a wide range of cosmological expansion histories. For the $Λ$CDM expansion history, stability considerations substantially limit the available parameter space while for a kinetic energy dominated expansion, no choice of quasidilaton parameters is stable. More generally these results show that there is no mechanism intrinsic to the theory to forbid such pathologies from developing from stable initial conditions and that stability can only be guaranteed for particular choices for the matter configuration.

hep-th↗

arXiv2015

Self-accelerating Massive Gravity: Superluminality, Cauchy Surfaces and Strong Coupling

Self-accelerating solutions in massive gravity provide explicit, calculable examples that exhibit the general interplay between superluminality, the well-posedness of the Cauchy problem, and strong coupling. For three particular classes of vacuum solutions, one of which is new to this work, we construct the conformal diagram for the characteristic surfaces on which isotropic stress-energy perturbations propagate. With one exception, all solutions necessarily possess spacelike characteristics, indicating perturbative superluminality. Foliating the spacetime with these surfaces gives a pathological frame where kinetic terms of the perturbations vanish, confusing the Hamiltonian counting of degrees of freedom. This frame dependence distinguishes the vanishing of kinetic terms from strong coupling of perturbations or an ill-posed Cauchy problem. We give examples where spacelike characteristics do and do not originate from a point where perturbation theory breaks down and where spacelike surfaces do or do not intersect all characteristics in the past light cone of a given observer. The global structure of spacetime also reveals issues that are unique to theories with two metrics: in all three classes of solutions, the Minkowski fiducial space fails to cover the entire de Sitter spacetime allowing worldlines of observers to end in finite proper time at determinant singularities. Characteristics run tangent to these surfaces requiring {\it ad hoc} rules to establish continuity across singularities.

hep-th↗

arXiv2015

Consistency relation for $R^p$ inflation

We consider $R^p$ inflation with $p \approx 2$, allowing small deviation from $R^2$ inflation. Using the inflaton potential in the Einstein frame, we construct a consistency relation between the scalar spectral index, the tensor-to-scalar ratio, as well as the running of the scalar spectral index, which will be useful to constrain a deviation from $R^2$ inflation in future observations.

astro-ph.CO↗

arXiv2015

Third order equations of motion and the Ostrogradsky instability

It is known that any nondegenerate Lagrangian containing time derivative terms higher than first order suffers from the Ostrogradsky instability, pathological excitation of positive and negative energy degrees of freedom. We show that, within the framework of analytical mechanics of point particles, any Lagrangian for third order equations of motion, which evades the nondegeneracy condition, still leads to the Ostrogradsky instability. Extension to the case of higher odd order equations of motion is also considered.

physics.class-ph↗

arXiv2014

Loop contribution to inflationary magnetic field

Within the framework of the standard quantum electrodynamics, we compute contribution of vacuum polarization at one-loop order to the power spectrum of the magnetic field on inflationary (de Sitter) background. It is found that the one-loop term exhibits the infrared secular growth that is proportional to the number of $e$-folds. The use of the dynamical renormalization group method, which amounts to partial resummation of higher loop diagrams, shows that the resummed power spectrum is free from the secular growth and the loop effect only changes the power from $(k/a)^4$ at the tree level to ${(k/a)}^{4-ν}$, where $ν$ represents the contribution from vacuum polarization. The parameter $ν$, being proportional to the square of the gauge coupling constant as well as the number of fermion species, is a simple function of a ratio of fermion mass to the Hubble parameter and is positive irrespective of the fermion mass. Thus, the loop effect always enhances the infrared magnetic field strength. We find that $ν\simeq 5 \times 10^{-3}$ is the possible maximum contribution to $ν$ from a single fermion. This estimate suggests that either large number of fermion species or large coupling constant is a necessary condition for the loop effect to be responsible for the seed of the cosmic magnetic fields.

astro-ph.CO↗

arXiv2014

Constraint on reheating after f(R) inflation from gravitational waves

Recently, a combined model of the primordial inflation and the present cosmic acceleration has been proposed in the context of f(R) gravity. This model is composed of the late-time acceleration term and an R2 term, which enables the model to avoid high curvature singularity and describe a quasi-de Sitter inflationary phase in the early Universe. An interesting feature of this model is that the reheating dynamics after the inflation is significantly modified, in contrast to the original R2 model, and affects the shape of a gravitational wave background (GWB) spectrum. Here we investigate the production of a GWB during the inflation and reheating eras in the R2-corrected f(R) model and compute a GWB spectrum. We found that interesting region of the model parameters has already been excluded by the cosmological limit on abundance of GWs.

astro-ph.CO↗

arXiv2013

Langevin description of gauged scalar fields in a thermal bath

We study the dynamics of the oscillating gauged scalar field in a thermal bath. A Langevin type equation of motion of the scalar field, which contains both dissipation and fluctuation terms, is derived by using the real-time finite temperature effective action approach. The existence of the quantum fluctuation-dissipation relation between the non-local dissipation term and the Gaussian stochastic noise terms is verified. We find the noise variables are anti-correlated at equal-time. The dissipation rate for the each mode is also studied, which turns out to depend on the wavenumber.

hep-ph↗

arXiv2013

Detecting cosmic string passage through the Earth by consequent global earthquake

Effects invoked by the passage of the cosmic string through the Earth are investigated. The cosmic string induces global oscillations of the Earth whose amplitude and acceleration both linearly depend on the string line density. For the line density maximally allowed by the cosmic observations, the oscillations are perceivable even to human beings and may cause serious damages to the environment. Use of the sophisticated accelerograph enables us to detect the string of a line density down to ten orders of magnitude smaller than the cosmologically relevant value.

astro-ph.CO↗

arXiv2013

Cosmology Based on f(R) Gravity Admits 1 eV Sterile Neutrinos

It is shown that the tension between recent neutrino oscillation experiments, favoring sterile neutrinos with masses of the order of 1 eV, and cosmological data which impose stringent constraints on neutrino masses from the free streaming suppression of density fluctuations, can be resolved in models of the present accelerated expansion of the Universe based on f(R) gravity.

astro-ph.CO↗

arXiv2012

Ultra Slow-Roll Inflation and the non-Gaussianity Consistency Relation

Ultra slow-roll inflation has recently been used to challenge the non-Gaussianity consistency relation. We show that this inflationary scenario belongs to a one parameter class of models and we study its properties and observational predictions. We demonstrate that the power spectrum remains scale-invariant and that the bi-spectrum is of the local type with fnl=5(3-ns)/4 which, indeed, represents a modification of the consistency relation. However, we also show that the system is unstable and suffers from many physical problems among which is the difficulty to correctly WMAP normalize the model. We conclude that ultra slow-roll inflation remains a very peculiar case, the physical relevance of which is probably not sufficient to call into question the validity of the consistency relation.

astro-ph.CO↗

arXiv2012

Consequences of a stochastic approach to the conformal invariance of inflationary correlators

We provide a general formalism to calculate the infrared correlators of multiple interacting scalar fields in the de Sitter space by means of the stochastic approach. These scalar fields are treated as test fields and hence our result is applicable to the models such as the curvaton scenario where the fields that yield initially isocurvature modes do not contribute to the cosmic energy density during inflationary expansion. The stochastic formalism combined with the argument of conformal invariance of the correlators reflecting the de Sitter isometries allows us to fix the form and amplitude of the three-point functions completely and partially for the four-point functions in terms of calculable quantities. It turns out that naive scaling argument employed in the previous literature does not necessarily hold and we derive the necessary and sufficient condition for the correlator to obey the naive scaling. We also find that correlation functions can in principle exhibit more complicated structure than argued in the literature.

hep-th↗

arXiv2012

Black hole perturbation in nondynamical and dynamical Chern-Simons gravity

Chern-Simons gravitational theories are extensions of general relativity in which the parity is violated due to the Chern-Simons term. We study linear perturbations on the static and spherically symmetric background spacetime both for nondynamical and dynamical Chern-Simons theories. We do not make an assumption that the background Chern-Simons scalar field vanishes, which has been adopted in the literature. By eliminating nondynamical variables using their constraint equations, we derive the reduced second order action from which a set of closed evolution equations containing only dynamical variables are immediately obtained and therefore the number of propagating degrees of freedom as well. It is found that ghost is present both for the nondynamical case and for the dynamical case unless the background Chern-Simons scalar field vanishes. It is also found that if the background scalar field vanishes, ghost degrees of freedom are killed and all the modes propagate at the speed of light.

gr-qc↗

arXiv2012

Self-accelerating solutions in massive gravity on an isotropic reference metric

Within the framework of the recently proposed ghost-free massive gravity, a cosmological constant-type self-accelerating solution has been obtained for Minkowski and de Sitter reference metrics. We ease the assumption on the reference metric and find the self-accelerating solution for the reference metric respecting only isotropy, thus considerably extending the range of known solutions.

hep-th↗

arXiv2012

Reheating after f(R) inflation

The reheating dynamics after the inflation induced by $R^2$-corrected $f(R)$ model is considered. To avoid the complexity of solving the fourth order equations, we analyze the inflationary and reheating dynamics in the Einstein frame and its analytical solutions are derived. We also perform numerical calculation including the backreaction from the particle creation and compare the results with the analytical solutions. Based on the results, observational constraints on the model are discussed.

astro-ph.CO↗

arXiv2011

Black hole perturbation in parity violating gravitational theories

We study linear perturbations around the static and spherically symmetric spacetime for the gravitational theories whose Lagrangian depends on Ricci scalar and the parity violating Chern-Simons term. By an explicit construction, we show that Hamiltonian for the perturbation variables is not bounded from below in general, suggesting that such a background spacetime is unstable against perturbations. This gives a strong limit on a phenomenological gravitational model which violates parity. We also provide a necessary and sufficient condition for the theory to belong to a special class in which no such instability occurs. For such theories, the number of propagating modes for $\ell \ge 2$ is three, one from the odd and the other two from the even. Unlike in the case of $f(R)$ theories, those modes are coupled each other, which can be used as a distinctive feature to test the parity violating theories from observations. All the modes propagate at the speed of light. No-ghost condition and no-tachyon condition are the same as those in $f(R)$ theories. For the dipole perturbations, the odd and the even modes completely decouple. The odd mode gives a slowly-rotating BH solution whose metric is linearized in its angular momentum. We provide an integral expression of such a solution. On the other hand, the even mode propagates at the speed of light. For the monopole perturbation, in addition to a mode which just shifts the mass of the background BH, there is also one even mode that propagates at the speed of light.

gr-qc↗