arXiv subjects
Publications and source records attributed to Misao Sasaki.
We show that in the single component situation all perturbation variables in the comoving gauge are conformally invariant to all perturbation orders. Generally we identify a special time slicing, the uniform-conformal transformation slicing, where all perturbations are again conformally invariant to all perturbation orders. We apply this result to the delta N formalism, and show its conformal invariance.
We study the Gregory-Laflamme instability of a 5-dimensional slowly rotating black string in which the 4-dimensional section is described by the Kerr black hole. We treat the rotation in a perturbative way introducing a small parameter for the rotation. It is found that rotation makes the Gregory-Laflamme instability stronger. Both the critical wavelength at the onset of instability and the growth time-scale are found to decrease as the rotation increases.
We study carefully the contribution of the waterfall field to the curvature perturbation at the end of hybrid inflation. In particular we clarify the parameter dependence analytically under reasonable assumptions on the model parameters. After calculating the mode function of the waterfall field, we use the delta N formalism and confirm the previously obtained result that the power spectrum is very blue with the index 4 and is absolutely negligible on large scales. However, we also find that the resulting curvature perturbation is highly non-Gaussian and hence we calculate the bispectrum. We find that the bispectrum is at leading order independent of momentum and exhibits its peak at the equilateral limit, though it is unobservably small on large scales. We also present the one-point probability distribution function of the curvature perturbation.
It is known that the curvature perturbation on uniform energy density (or comoving or uniform Hubble) slices on superhorizon scales is conserved to full nonlinear order if the pressure is only a function of the energy density (ie, if the perturbation is purely adiabatic), independent of the gravitational theory. Here we explicitly show that the same conservation holds for a universe dominated by a single scalar field provided that the field is in an attractor regime, for a very general class of scalar field theories. However, we also show that if the scalar field equation contains a second time derivative of the metric, as in the case of the Galileon theory, one has to invoke the gravitational field equations to show the conservation.
As we shall briefly recall, Nordström's theory of gravity is observationally ruled out. It is however an interesting example of non-minimal coupling of matter to gravity and of the role of conformal transformations. We show in particular that they could be useful to extend manifolds through curvature singularities.
In order to assess the role of ghosts in cosmology, we study the evolution of linear cosmological perturbations during inflation when a Weyl term is added to the action. Our main result is that vector perturbations can no longer be ignored and that scalar modes diverge in the newtonian gauge but remain bounded in the comoving slicing.
We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of of non-local gravity with the Lagrangian of the form, $R+f(\Box^{-1}R)-2Λ$ where $f(X)$ is a quadratic function of $X$, there is a flat spacetime solution despite the presence of the cosmological constant $Λ$. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of `time'. Nevertheless our result suggests the possibility of solving the cosmological constant problem in the context of non-local gravity.
We study the kinematic Sunyaev-Zel'dovich (kSZ) effect in a Lemître-Tolman-Bondi (LTB) universe model whose distance-redshift relation agrees with that of the concordance $Λ$CDM model at redshifts $z\lesssim2$. This LTB universe model has a void with size comparable to the Hubble horizon scale. We first determine the decoupling epoch in this LTB universe model by an approximate analytical condition under a few simplified assumptions on the physical quantities at that epoch. Then we calculate the cosmic microwave background (CMB) anisotropy observed in the rest frame of clusters of galaxies which are assumed to be at rest in the spatial comoving coordinates of the LTB universe model. We find that the obtained temperature anisotropies are dominated by dipole, although there may exist higher multi-poles in general. We may interpret this dipole anisotropy as the drift velocity of a cluster of galaxies relative to the CMB rest frame. Hence it gives rise to the kSZ effect. We calculate this effect and compare it with observational data. We find that if we assume the conventional adiabatic perturbation scenario at the time of decoupling, the drift velocity of clusters of galaxies becomes unacceptably large. Conversely, this observational constraint may be relaxed by introducing a non-adiabatic (i.e., primordially isocurvature) component of inhomogeneities at the time of decoupling. However, our result indicates that the necessary isocurvature perturbation amplitude is very large.
In the theory of General Relativity, gravity is described by a metric which couples minimally to the fields representing matter. We consider here its "veiled" versions where the metric is conformally related to the original one and hence is no longer minimally coupled to the matter variables. We show on simple examples that observational predictions are nonetheless exactly the same as in General Relativity, with the interpretation of this "Weyl" rescaling "à la Dicke", that is, as a spacetime dependence of the inertial mass of the matter constituents.
We estimate large-scale curvature perturbations from isocurvature fluctuations in the waterfall field during hybrid inflation, in addition to the usual inflaton field perturbations. The tachyonic instability at the end of inflation leads to an explosive growth of super-Hubble scale perturbations, but they retain the steep blue spectrum characteristic of vacuum fluctuations in a massive field during inflation. The power spectrum thus peaks around the Hubble-horizon scale at the end of inflation. We extend the usual delta-N formalism to include the essential role of these small fluctuations when estimating the large-scale curvature perturbation. The resulting curvature perturbation due to fluctuations in the waterfall field is second-order and the spectrum is expected to be of order 10^{-54} on cosmological scales.
In this short note, we obtain the necessary and sufficient condition for a class of non-canonical single scalar field models to be exactly equivalent to barotropic perfect fluids, under the assumption of an irrotational fluid flow. An immediate consequence of this result is that the non-adiabatic pressure perturbation in this class of scalar field systems vanishes exactly at all orders in perturbation theory and on all scales. The Lagrangian for this general class of scalar field models depends on both the kinetic term and the value of the field. However, after a field redefinition, it can be effectively cast in the form of a purely kinetic K-essence model.
We present a new analytical method to calculate the small angle CMB temperature angular power spectrum due to cosmic (super-)string segments. In particular, using our method, we clarify the dependence on the intercommuting probability $P$. We find that the power spectrum is dominated by Poisson-distributed string segments. The power spectrum for a general value of $P$ has a plateau on large angular scales and shows a power-law decrease on small angular scales. The resulting spectrum in the case of conventional cosmic strings is in very good agreement with the numerical result obtained by Fraisse et al.. Then we estimate the upper bound on the dimensionless tension of the string for various values of $P$ by assuming that the fraction of the CMB power spectrum due to cosmic (super-)strings is less than ten percents at various angular scales up to $\ell=2000$. We find that the amplitude of the spectrum increases as the intercommuting probability. As a consequence, strings with smaller intercommuting probabilities are found to be more tightly constrained.
Acoustic peaks in the spectrum of the cosmic microwave background in spherically symmetric inhomogeneous cosmological models are studied. At the photon-baryon decoupling epoch, the universe may be assumed to be dominated by non-relativistic matter, and thus we may treat radiation as a test field in the universe filled with dust which is described by the Lemaître-Tolman-Bondi (LTB) solution. First, we give an LTB model whose distance-redshift relation agrees with that of the concordance $Λ$CDM model in the whole redshift domain and which is well approximated by the Einstein-de Sitter universe at and before decoupling. We determine the decoupling epoch in this LTB universe by Gamow's criterion and then calculate the positions of acoustic peaks. Thus obtained results are not consistent with the WMAP data. However, we find that one can fit the peak positions by appropriately modifying the LTB model, namely, by allowing the deviation of the distance-redshift relation from that of the concordance $Λ$CDM model at $z>2$ where no observational data are available at present. Thus there is still a possibility of explaining the apparent accelerated expansion of the universe by inhomogeneity without resorting to dark energy if we abandon the Copernican principle. Even if we do not take this extreme attitude, it also suggests that local, isotropic inhomogeneities around us may seriously affect the determination of the density contents of the universe unless the possible existence of such inhomogeneities is properly taken into account.
We compute the one-point probability distribution function of small-angle cosmic microwave background temperature fluctuations due to curved cosmic (super-)strings with a simple model of string network by performing Monte Carlo simulations. Taking into account of the correlation between the curvature and the velocity of string segments, there appear non-Gaussian features, specifically non-Gaussian tails and a skewness, in the one-point pdf. The obtained sample skewness for the conventional field-theoretic cosmic strings is $g_1\approx -0.14$, which is consistent with the result reported by Fraisse et al.. We also discuss the dependence of the pdf on the intercommuting probability. We find that the standard deviation of the Gaussian part increases and non-Gaussian features are suppressed as the intercommuting probability decreases. For sufficiently small intercommuting probability, the skewness is given by $\lesssim$ (a\ few) $\times 10^{-2}$.
We investigate the linear cosmological perturbations in Hořava-Lifshitz gravity with a scalar field. Starting from the most general expressions of the metric perturbations as well as that of a canonical scalar field, we decompose the scalar, vector and tensor parts of the perturbed action. By reducing the Hamiltonian, we find that there are two independent degrees of freedom for the tensor perturbations while none for the vector perturbations. For the scalar perturbations, the remaining number of degrees of freedom, which are all gauge invariant, depends on whether the projectable condition is applied or not. For both cases, we lose the time reparametrization symmetry of any kind.
We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a single scalar field with a general kinetic term and a general form of the potential. We employ the ADM formalism and the spatial gradient expansion approach, characterised by $O(ε^m)$, where $ε=1/(HL)$ is a small parameter representing the ratio of the Hubble radius to the characteristic length scale $L$ of perturbations. We obtain the general solution for a full nonlinear version of the curvature perturbation valid up through second-order in $ε$ ($m=2$). We find the solution satisfies a nonlinear second-order differential equation as an extension of the equation for the linear curvature perturbation on the comoving hypersurface. Then we formulate a general method to match a perturbative solution accurate to $n$-th-order in perturbation inside the horizon to our nonlinear solution accurate to second-order ($m=2$) in the gradient expansion on scales slightly greater than the Hubble radius. The formalism developed in this paper allows us to calculate the superhorizon evolution of a primordial non-Gaussianity beyond the so-called $δN$ formalism or separate universe approach which is equivalent to leading order ($m=0$) in the gradient expansion. In particular, it can deal with the case when there is a temporary violation of slow-roll conditions. As an application of our formalism, we consider Starobinsky's model, which is a single field model having a temporary non-slow-roll stage due to a sharp change in the potential slope. We find that a large non-Gaussianity can be generated even on superhorizon scales due to this temporary suspension of slow-roll inflation.
We study the effect on the primordial cosmological perturbations of a sharp transition from inflationary to a radiation and matter dominated epoch respectively. We assume that the perturbations are generated by the vacuum fluctuations of a scalar field slowly rolling down its potential, and that the transition into the subsequent epoch takes place much faster than a Hubble time. The behaviour of the superhorizon perturbations corresponding to cosmological scales in this case is well known. However, it is not clear how perturbations on scales of and smaller than the Hubble horizon scale at the end of inflation may evolve through such a transition. We derive the evolution equation for the gravitational potential $Ψ$, which allows us to study the evolution of the perturbations on all scales under these circumstances. We show that for a certain range of scales inside the horizon at the end of inflation, the amplitude of the perturbations are enhanced relative to the superhorizon scales. This enhancement may lead to the overproduction of Primordial Black Holes (PBHs), and therefore constrain the dynamics of the transitions that take place at the end of inflation.
We compute analytically the small-scale temperature fluctuations of the cosmic microwave background from cosmic (super-)strings and study the dependence on the string intercommuting probability $P$. We develop an analytical model which describes the evolution of a string network and calculate the numbers of string segments and kinks in a horizon volume. Then we derive the probability distribution function (pdf) which takes account of finite angular resolution of observation. The resultant pdf consists of a Gaussian part due to frequent scatterings by long string segments and a non-Gaussian tail due to close encounters with kinks. The dispersion of the Gaussian part is reasonably consistent with that obtained by numerical simulations by Fraisse et al.. On the other hand, the non-Gaussian tail contains two phenomenological parameters which are determined by comparison with the numerical results for P=1. Extrapolating the pdf to the cases with $P<1$, we predict that the non-Gaussian feature is suppressed for small $P$.