arXiv subjects
Publications and source records attributed to Misao Sasaki.
We present a canonical formulation of gravity theories whose Lagrangian is an arbitrary function of the Riemann tensor. Our approach allows a unified treatment of various subcases and an easy identification of the degrees of freedom of the theory.
Theories with curvature squared terms in the action are known to contain ghost modes in general. However, if we regard curvature squared terms as quantum corrections to the original theory, the emergence of ghosts may be simply due to the perturbative truncation of a full non-perturbative theory. If this is the case, there should be a way to live with ghosts. In this paper, we take the Euclidean path integral approach, in which ghost degrees of freedom can be, and are integrated out in the Euclideanized spacetime. We apply this procedure to Einstein gravity with a Weyl curvature squared correction in the inflationary background. We find that the amplitude of tensor perturbations is modified by a term of O(alpha^2 H^2) where alpha^2 is a coupling constant in front of the Weyl squared term and H is the Hubble parameter during inflation.
We present a class of dynamical solutions for intersecting D4-D8 and D3-D7 brane systems in ten-dimensional type IIA and IIB supergravity. We discuss if these solutions can be recovered in lower-dimensional effective theories for the warped compactification of a general p-brane system. It is found that an effective $p+1$-dimensional description is not possible in general due to the entanglement of the transverse coordinates and the $p+1$-dimensional coordinates in the metric components. For the D4-D8 brane system, the dynamical solutions reduces to a static warped ${\rm AdS_6}\times {\rm S}^4$ geometry in a certain spacetime region. For the D3-D7 brane system, we find a dynamical solution whose metric form is similar to that of a D3-brane solution. The main difference is the existence of a nontrivial dilaton configuration in the D3-D7 solution. Then we discuss cosmology of these solutions. We find that they behave like a Kasner-type cosmological solution at $τ\to\infty$, while it reduces to a warped static solution at $τ\to0$, where $τ$ is the cosmic time.
We study cosmology of the Einstein-Yang-Mills theory in ten dimensions with a quartic term in the Yang-Mills field strength. We obtain analytically a class of cosmological solutions in which the extra dimensions are static and the scale factor of the four-dimensional Friedmann-Lemaitre-Robertson-Walker metric is an exponential function of time. This means that the model can explain inflation. Then we look for solutions that describe dynamical compactification of the extra dimensions. The effective cosmological constant $λ_1$ in the four-dimensional universe is determined from the gravitational coupling, ten-dimensional cosmological constant, gauge coupling and higher derivative coupling. By numerical integration, the solution with $λ_1=0$ is found to behave as a matter-dominated universe which asymptotically approaches flat space-time, while the solution with a non-vanishing $λ_1$ approaches de Sitter space-time in the asymptotic future.
We consider the evaporation of rotating micro black holes produced in highly energetic particle collisions, taking into account the polarization due to the coupling between the spin of the emitted particles and the angular momentum of the black hole. The effect of rotation shows up in the helicity dependent angular distribution significantly. By using this effect, there is a possibility to determine the axis of rotation for each black hole formed, suggesting a way to improve the statistics. Deviation from thermal spectrum is also a signature of rotation. This deviation is due to the fact that rapidly rotating holes have an effective temperature $T_{\rm eff}$ significantly higher than the Hawking temperature $T_H$. The deformation of the spectral shape becomes evident only for very rapidly rotating cases. We show that, since the spectrum follows a blackbody profile with an effective temperature, it is difficult to determine both the number of extra-dimensions and the rotation parameter from the energy spectrum alone. We argue that the helicity dependent angular distribution may provide a way to resolve this degeneracy. We illustrate the above results for the case of fermions.
A model of multi-component hybrid inflation, dubbed multi-brid inflation, in which various observable quantities including the non-Gaussianity parameter f_{NL} can be analytically calculated was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories, provided that the ratio of the two masses is large. One might question whether the resulting large non-Gaussianity is specific to this particular form of the potential and the condition for the end of inflation. In this paper, we consider a model of multi-brid inflation with a potential given by an exponential function of terms quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation than those studied previously. Then, focusing on the case of two-brid inflation, we find that large non-Gaussianity is possible in the present model even for the equal-mass case. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.
As is well-known, Kerr-Schild metrics linearize the Einstein tensor. We shall see here that they also simplify the Gauss-Bonnet tensor, which turns out to be only quadratic in the arbitrary Kerr-Schild function f when the seed metric is maximally symmetric. This property allows us to give a simple analytical expression for its trace, when the seed metric is a five dimensional maximally symmetric spacetime in spheroidal coordinates with arbitrary parameters a and b. We also write in a (fairly) simple form the full Einstein-Gauss-Bonnet tensor (with a cosmological term) when the seed metric is flat and the oblateness parameters are equal, a=b. Armed with these results we give in a compact form the solution of the trace of the Einstein-Gauss-Bonnet field equations with a cosmological term and a different than b. We then examine whether this solution for the trace does solve the remaining field equations. We find that it does not in general, unless the Gauss-Bonnet coupling is such that the field equations have a unique maximally symmetric solution.
In the inflationary cosmology it occurs frequently that the inflaton field is trapped in a local, transient minimum with non-zero vacuum energy. The difficulty regarding the curvature perturbation produced during such a stage is that classically the inflaton does not move so that the comoving hypersurfaces are not well defined at linear order in the scalar field perturbation. In this paper, assuming a mechanism of trapping which resembles a high temperature correction to the potential, we explicitly calculate for the first time the resulting power spectrum of the curvature perturbation by evaluating the quantum two-point correlation function directly. The spectrum is steeply blue with the spectral index n_R = 4.
The impact of particle production during inflation on the primordial curvature perturbation spectrum is investigated both analytically and numerically. We obtain an oscillatory behavior on small scales, while on large scales the spectrum is unaffected. The amplitude of the oscillations is proportional to the number of coupled fields, their mass, and the square of the coupling constant. The oscillations are due a discontinuity in the second time derivative of the inflaton, arising from a temporary violation of the slow-roll conditions. A similar effect on the power spectrum should be produced also in other inflationary models where the slow-roll conditions are temporarily violated.
We consider a class of multi-component hybrid inflation models whose evolution may be analytically solved under the slow-roll approximation. We call it multi-brid inflation (or $n$-brid inflation where $n$ stands for the number of inflaton fields). As an explicit example, we consider a two-brid inflation model, in which the inflaton potentials are of exponential type and a waterfall field that terminates inflation has the standard quartic potential with two minima. Using the $δN$ formalism, we derive an expression for the curvature perturbation valid to full nonlinear order. Then we give an explicit expression for the curvature perturbation to second order in the inflaton perturbation. We find that the final form of the curvature perturbation depends crucially on how the inflation ends. Using this expression, we present closed analytical expressions for the spectrum of the curvature perturbation ${\cal P}_{S}(k)$, the spectral index $n_S$, the tensor to scalar ratio $r$, and the non-Gaussian parameter $f_{NL}^{\rm local}$, in terms of the model parameters. We find that a wide range of the parameter space $(n_S, r, f_{NL}^{\rm local})$ can be covered by varying the model parameters within a physically reasonable range. In particular, for plausible values of the model parameters, we may have large non-Gaussianity $f_{NL}^{\rm local}\sim 10$--100. This is in sharp contrast to the case of single-field hybrid inflation in which these parameters are tightly constrained.
We propose a practical method for analyzing stability of Q-balls for the whole parameter space, which includes the intermediate region between the thin-wall limit and thick-wall limit as well as Q-bubbles (Q-balls in false vacuum), using the catastrophe theory. We apply our method to the two concrete models, $V_3=m^2ϕ^2/2-μϕ^3+λϕ^4$ and $V_4=m^2ϕ^2/2-λϕ^4+ϕ^6/M^2$. We find that $V_3$ and $V_4$ Models fall into {\it fold catastrophe} and {\it cusp catastrophe}, respectively, and their stability structures are quite different from each other.
In gravity theories derived from a f(R) Lagrangian, matter is usually supposed to be minimally coupled to the metric, which hence defines a ``Jordan frame.'' However, since the field equations are fourth order, gravity possesses an extra degree of freedom on top of the standard graviton, as is manifest from its equivalent description in the conformally related, Einstein, frame. We introduce explicitly this extra scalar degree of freedom in the action and couple it to matter, so that the original metric no longer defines a Jordan frame. This ``detuning'' puts f(R) gravity into a wider class of scalar--tensor theories. We argue that a ``chameleon-like'' detuning tracing the background matter density may provide purely gravitational models which account for the present acceleration of the universe and evade local gravity constraints.
We present a class of dynamical solutions for an intersecting D4-D8 brane system in ten-dimensional type IIA supergravity. The dynamical solutions reduces to a static warped AdS_6 x S^4 geometry in a certain spacetime region. We also consider lower-dimensional effective theories for the warped compactification of general p-brane system. It is found that an effective (p+1)-dimensional description is not possible in general due to the entanglement of the transverse coordinates and the (p+1)-dimensional coordinates in the metric components. Then we discuss cosmological solutions. We find a solution that behaves like a Kasner-type cosmological solution at $τ\to\infty$, while it reduces to a warped static solution at $τ\to0$, where $τ$ is the cosmic time.
We present Feynman type diagrams for calculating the n-point function of the primordial curvature perturbation in terms of scalar field perturbations during inflation. The diagrams can be used to evaluate the corresponding terms in the n-point function at tree level or any required loop level. Rules are presented for drawing the diagrams and writing down the corresponding terms in real space and Fourier space. We show that vertices can be renormalised to automatically account for diagrams with dressed vertices. We apply these rules to calculate the primordial power spectrum up to two loops, the bispectrum including loop corrections, and the trispectrum.
Taking advantage of the conformal equivalence of f(R) theories of gravity with General Relativity coupled to a scalar field we generalize the Israel junction conditions for this class of theories by direct integration of the field equations. We suggest a specific non-minimal coupling of matter to gravity which opens the possibility of a new class of braneworld scenarios.
We investigate the Kaluza-Klein braneworld cosmology from the point of view of observers on the brane. We first generalize the Shiromizu-Maeda-Sasaki (SMS) equations to higher dimensions. As an application, we study a (4+n)-dimensional brane with n dimensions compactified on the brane, in a (5+n)-dimensional bulk. By assuming that the size of the internal space is static, that the bulk energy-momentum tensor can be neglected, we determine the effect of the bulk geometry on the Kaluza-Klein braneworld. Then we derive the effective Friedmann equation on the brane. It turns out that the Friedmann equation explicitly depends on the equation of state, in contrast to the braneworld in a 5-dimensional bulk spacetime. In particular, in a radiation-dominated era, the effective Newton constant depends on the scale factor logarithmically. If we include a pressureless matter on the brane, this dependence disappears after the radiation-matter equality. This may be interpreted as stabilization of the Newton constant by the matter on the brane. Our findings imply that the Kaluza-Klein braneworld cosmology is quite different from the conventional Kaluza-Klein cosmology even at low energy.
We consider a brane world in an arbitrary number of dimensions without Z_2 symmetry and derive the effective Einstein equation on the brane, where its right-hand side is given by the matter on the brane and the curvature in the bulk. This is achieved by first deriving the junction conditions for a non-Z_2 symmetric brane and second solving the Gauss equation, which relates the mean extrinsic curvature of the brane to the curvature in the bulk, with respect to the mean extrinsic curvature. The latter corresponds to formulating an explicit junction condition on the mean of the extrinsic curvature, analogue to the Israel junction condition for the jump of the extrinsic curvature. We find that there appears a new type of an effective anisotropic fluid on the right-hand side of the effective Einstein equation due to the fact that there is no Z_2 symmetry. The derived equation is a basic equation for the study of Kaluza-Klein brane worlds in which some dimensions on the brane are compactified or for a regularization scheme for a higher codimension brane world, where the Kaluza-Klein compactification on the brane is regarded as a means to regularize the uncontrollable spacetime singularity caused by the higher codimension brane.
We formulate nonlinear perturbations of a scalar field dominated universe on super-horizon scales. We consider the case of a single scalar field. We take the gradient expansion approach. We adopt the uniform Hubble slicing and derive the general solution valid to $O(ε^2)$, where $ε$ is the expansion parameter associated with a spatial derivative, which includes both the scalar and tensor modes. In particular, the $O(ε^2)$ correction terms to the nonlinear curvature perturbation, which become important in models with a non-slowroll stage during inflation, are explicitly obtained.