arXiv subjects

Shuntaro Mizuno

Publications and source records attributed to Shuntaro Mizuno.

At least 37 records · Page 2Linked to original sources

arXiv2013

Influence of heavy modes on perturbations in multiple field inflation

We investigate linear cosmological perturbations in multiple field inflationary models where some of the directions are light while others are heavy (with respect to the Hubble parameter). By integrating out the massive degrees of freedom, we determine the multi-dimensional effective theory for the light degrees of freedom and give explicitly the propagation matrix that replaces the effective sound speed of the one-dimensional case. We then examine in detail the consequences of a sudden turn along the inflationary trajectory, in particular the possible breakdown of the low energy effective theory in case the heavy modes are excited. Resorting to a new basis in field space, instead of the usual adiabatic/entropic basis, we study the evolution of the perturbations during the turn. In particular, we compute the power spectrum and compare with the result obtained from the low energy effective theory.

hep-th↗

arXiv2013

Oscillatory features in the curvature power spectrum after a sudden turn of the inflationary trajectory

In the context of two-field inflation characterized by a light direction and a heavy direction, we revisit the question of the impact of the massive modes on the power spectrum produced after a turn in the inflationary trajectory. We consider in particular the resonant effect due to the background oscillations following a sharp turn. Working in the mass basis, i.e. in the basis spanned by the eigenvectors of the effective mass matrix for the perturbations, we provide an analytical estimate of the resonant effect, using the in-in formalism. In comparison with earlier estimates, we find the same the spectral dependence but a smaller amplitude. We also compute, again via the in-in formalism, the effect of the direct coupling between the light and heavy modes at the instant of the turn and confirm our previous results obtained via a different method.

hep-th↗

arXiv2012

Non-Gaussianities in multi-field DBI inflation with a waterfall phase transition

We study multi-field DBI inflation models with a waterfall phase transition. This transition happens for a D3 brane moving in the warped conifold if there is an instability along angular directions. The transition converts the angular perturbations into the curvature perturbation. Thanks to this conversion, multi-field models can evade the stringent constraints that strongly disfavour single field ultra-violet DBI inflation models in string theory. We explicitly demonstrate that our model satisfies current observational constraints on the spectral index and equilateral non-Gaussianity as well as the bound on the tensor to scalar ratio imposed in string theory models. In addition we show that large local type non-Gaussianity is generated together with equilateral non-Gaussianity in this model.

astro-ph.CO↗

arXiv2012

Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation

We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane is non-relativistic and we show that it tends to violate the null energy condition and to render cosmological fluctuations ghosts. There nonetheless exists an interesting parameter space in which a stable phase of quasi-exponential expansion can be achieved while the induced gravity leaves non trivial imprints. We derive the exact second-order action governing the dynamics of linear perturbations and we show that it can be simply understood through a bimetric perspective. In the relativistic regime, we also calculate the dominant contribution to the primordial bispectrum and demonstrate that large non-Gaussianities of orthogonal shape can be generated, for the first time in a concrete model. More generally, we find that the sign and the shape of the bispectrum offer powerful diagnostics of the precise strength of the induced gravity.

astro-ph.CO↗

arXiv2010

Primordial non-Gaussianity from the DBI Galileons

We study primordial fluctuations generated during inflation in a class of models motivated by the DBI Galileons, which are extensions of the DBI action that yield second order field equations. This class of models generalises the DBI Galileons in a similar way with K-inflation. We calculate the primordial non-Gaussianity from the bispectrum of the curvature perturbations at leading order in the slow-varying approximations. We show that the estimator for the equilateral-type non-Gaussianity, $f_{\rm NL} ^{equil}$, can be applied to measure the amplitude of the primordial bispectrum even in the presence of the Galileon-like term although it gives a slightly different momentum dependence from K-inflation models. For the DBI Galileons, we find $-0.32 /c_s^2 < f_{\rm NL} ^{equil} < -0.16/c_s^2$ and large primordial non-Gaussianities can be obtained when $c_s$ is much smaller than 1 as in the usual DBI inflation. In G-inflation models, where a de Sitter solution is obtained without any potentials, the non-linear parameter is given by $f_{\rm NL}^{equil} = 4.62 r^{-2/3}$ where $r$ is the tensor to scalar ratio, giving a stringent constraint on the model.

hep-th↗

arXiv2010

Trispectrum estimator in equilateral type non-Gaussian models

We investigate an estimator to measure the primordial trispectrum in equilateral type non-Gaussian models such as k-inflation, single field DBI inflation and multi-field DBI inflation models from Cosmic Microwave Background (CMB) anisotropies. The shape of the trispectrum whose amplitude is not constrained by the bispectrum in the context of effective theory of inflation and k-inflation is known to admit a separable form of the estimator for CMB anisotropies. We show that this shape is $87 \%$ correlated with the full quantum trispectrum in single field DBI inflation, while it is $33 \%$ correlated with the one in multi-field DBI inflation when curvature perturbation is originated from purely entropic contribution. This suggests that $g_{\rm NL} ^{equil}$, the amplitude of this particular shape, provides a reasonable measure of the non-Gaussianity from the trispectrum in equilateral non-Gaussian models. We relate model parameters such as the sound speed, $c_s$ and the transfer coefficient from entropy perturbations to the curvature perturbation, $T_{\mathcal{R} S}$ with $g_{\rm NL} ^{equil}$, which enables us to constrain model parameters in these models once $g_{\rm NL}^{equil}$ is measured in WMAP and Planck.

hep-th↗

arXiv2010

Cosmological Dynamics of a Dirac-Born-Infeld field

We analyze the dynamics of a Dirac-Born-Infeld (DBI) field in a cosmological set-up which includes a perfect fluid. Introducing convenient dynamical variables, we show the evolution equations form an autonomous system when the potential and the brane tension of the DBI field are arbitrary power-law or exponential functions of the DBI field. In particular we find scaling solutions can exist when powers of the field in the potential and warp-factor satisfy specific relations. A new class of fixed-point solutions are obtained corresponding to points which initially appear singular in the evolution equations, but on closer inspection are actually well defined. In all cases, we perform a phase-space analysis and obtain the late-time attractor structure of the system. Of particular note when considering cosmological perturbations in DBI inflation is a fixed-point solution where the Lorentz factor is a finite large constant and the equation of state parameter of the DBI field is $w=-1$. Since in this case the speed of sound $c_s$ becomes constant, the solution can be thought to serve as a good background to perturb about.

hep-th↗

arXiv2009

On the full quantum trispectrum in multi-field DBI inflation

We compute the leading order connected four-point function of the primordial curvature perturbation coming from the four-point function of the fields in multi-field DBI inflation models. We confirm that the consistency relations in the squeezed limit and in the counter-collinear limit hold as in single field models thanks to special properties of the DBI action. We also study the momentum dependence of the trispectra coming from the adiabatic, mixed and purely entropic contributions separately and we find that they have different momentum dependence. This means that if the amount of the transfer from the entropy perturbations to the curvature perturbation is significantly large, the trispectrum can distinguish multi-field DBI inflation models from single field DBI inflation models. A large amount of transfer $T_{\mathcal{RS}} \gg 1 $ suppresses the tensor to scalar ratio $r \propto T_{\mathcal{RS}}^{-2}$ and the amplitude of the bispectrum $f_{NL}^{equi} \propto T_{\mathcal{RS}}^{-2}$ and so it can ease the severe observational constraints on the DBI inflation model based on string theory. On the other hand, it enhances the amplitude of the trispectrum $τ_{NL}^{equi} \propto T_{\mathcal{RS}}^2 f_{NL}^{equi 2}$ for a given amplitude of the bispectrum.

hep-th↗

arXiv2009

Lorentz boost and non-Gaussianity in multi-field DBI-inflation

We show that higher-order actions for cosmological perturbations in the multi-field DBI-inflation model are obtained by a Lorentz boost from the rest frame of the brane to the frame where the brane is moving. We confirm that this simple method provides the same third- and fourth- order actions at leading order in slow-roll and in the small sound speed limit as those obtained by the usual ADM formalism. As an application, we compute the leading order connected four-point function of the primordial curvature perturbation coming from the intrinsic fourth-order contact interaction in the multi-field DBI-inflation model. At the third order, the interaction Hamiltonian arises purely by the boost from the second-order action in the rest frame of the brane. The boost acts on the adiabatic and entropy modes in the same way thus there exists a symmetry between the adiabatic and entropy modes. But at fourth order this symmetry is broken due to the intrinsic fourth-order action in the rest frame and the difference between the Lagrangian and the interaction Hamiltonian. Therefore, contrary to the three-point function, the momentum dependence of the purely adiabatic component and the components including the entropic contributions are different in the four-point function. This suggests that the trispectrum can distinguish the multi-field DBI-inflation model from the single field DBI-inflation model.

hep-th↗

arXiv2009

On the full trispectrum in single field DBI-inflation

We compute the tree-level connected four-point function of the primordial curvature perturbation for a fairly general minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the scalar field and its first derivatives. This model includes K-inflation and DBI-inflation as particular cases. We show that, at the leading order in the slow-roll expansion and in the small sound speed limit, there are two important tree-level diagrams for the trispectrum. One is a diagram where a scalar mode is exchanged and the other is a diagram where the interaction occurs at a point, i.e. a contact interaction diagram. The scalar exchange contribution is comparable to the contact interaction contribution. For the DBI-inflation model, in the so-called equilateral configuration, the scalar exchange trispectrum is maximized when the angles between the four momentum vectors are equal and in this case the amplitude of the trispectrum from the scalar exchange is one order of magnitude higher than the contact interaction trispectrum.

hep-th↗

arXiv2009

Non-Gaussianities from ekpyrotic collapse with multiple fields

We compute the non-Gaussianity of the curvature perturbation generated by ekpyrotic collapse with multiple fields. The transition from the multi-field scaling solution to a single-field dominated regime converts initial isocurvature field perturbations to an almost scale-invariant comoving curvature perturbation. In the specific model of two fields, $ϕ_1$ and $ϕ_2$, with exponential potentials, $-V_i \exp (-c_i ϕ_i)$, we calculate the bispectrum of the resulting curvature perturbation. We find that the non-Gaussianity is dominated by non-linear evolution on super-Hubble scales and hence is of the local form. The non-linear parameter of the curvature perturbation is given by $f_{NL} = 5 c_j^2 /12$, where $c_j$ is the exponent of the potential for the field which becomes sub-dominant at late times. Since $c_j^2$ must be large, in order to generate an almost scale invariant spectrum, the non-Gaussianity is inevitably large. By combining the present observational constraints on $f_{\rm NL}$ and the scalar spectral index, the specific model studied in this paper is thus ruled out by current observational data.

hep-th↗

arXiv2009

Dynamics of a scalar field in Robertson-Walker spacetimes

We analyze the dynamics of a single scalar field in Friedmann-Robertson-Walker universes with spatial curvature. We obtain the fixed point solutions which are shown to be late time attractors. In particular, we determine the corresponding scalar field potentials which correspond to these stable solutions. The analysis is quite general and incorporates expanding and contracting universes with both positive and negative scalar potentials. We demonstrate that the known power law, exponential, and de-Sitter solutions are certain limits of our general set of solutions.

astro-ph.CO↗

arXiv2009

Curvature perturbations from ekpyrotic collapse with multiple fields

A scale-invariant spectrum of isocurvature perturbations is generated during collapse in the ekpyrotic scaling solution in models where multiple fields have steep negative exponential potentials. The scale invariance of the spectrum is realized by a tachyonic instability in the isocurvature field. This instability drives the scaling solution to the late time attractor that is the old ekpyrotic collapse dominated by a single field. We show that the transition from the scaling solution to the single field dominated ekpyrotic collapse automatically converts the initial isocurvature perturbations about the scaling solution to comoving curvature perturbations about the late-time attractor. The final amplitude of the comoving curvature perturbation is determined by the Hubble scale at the transition.

hep-th↗

arXiv2008

Non-gaussianity from the bispectrum in general multiple field inflation

We study the non-gaussianity from the bispectrum in multi-field inflation models with a general kinetic term. The models include the multi-field K-inflation and the multi-field Dirac-Born-Infeld (DBI) inflation as special cases. We find that, in general, the sound speeds for the adiabatic and entropy perturbations are different and they can be smaller than 1. Then the non-gaussianity can be enhanced. The multi-field DBI-inflation is shown to be a special case where both sound speeds are the same due to a special form of the kinetic term. We derive the exact second and third order actions including metric perturbations. In the small sound speed limit and at leading order in the slow-roll expansion, we derive the three point function for the curvature perturbation which depends on both adiabatic and entropy perturbations. The contribution from the entropy perturbations has a different momentum dependence if the sound speed for the entropy perturbations is different from the adiabatic one, which provides a possibility to distinguish the multi-field models from single field models. On the other hand, in the multi-field DBI case, the contribution from the entropy perturbations has the same momentum dependence as the pure adiabatic contributions and it only changes the amplitude of the three point function. This could help to ease the constraints on the DBI-inflation models.

hep-th↗

arXiv2008

Constraints on scalar-tensor models of dark energy from observational and local gravity tests

We construct a family of viable scalar-tensor models of dark energy (DE) which possess a phase of late-time acceleration preceded by a standard matter era, while at the same time satisfying the local gravity constraints (LGC). The coupling Q between the scalar field and the non-relativistic matter in the Einstein frame is assumed to be constant in our scenario, which is a generalization of f(R) gravity theories corresponding to the coupling Q=-1/sqrt{6}. We find that these models can be made compatible with local gravity constraints even when |Q| is of the order of unity through a chameleon mechanism, if the scalar-field potential is chosen to have a sufficiently large mass in the high-curvature regions. We show that these models generally lead to the divergence of the equation of state of DE, which occur at smaller redshifts as the deviation from the LambdaCDM model become more significant. We also study the evolution of matter density perturbations and employ them to place bounds on the coupling |Q| as well as model parameters of the field potential from observations of the matter power spectrum and the CMB anisotropies. We find that, as long as |Q| is smaller than the order of unity, there exist allowed parameter regions that are consistent with both observational and local gravity constraints.

astro-ph↗

arXiv2007

Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations

We explore the initial conditions for cosmological N-body simulations suitable for calculating the skewness and kurtosis of the density field. In general, the initial conditions based on the perturbation theory (PT) provide incorrect second-order and higher-order growth. These errors implied by the use of the perturbation theory to set up the initial conditions in N-body simulations are called transients. Unless these transients are completely suppressed compared with the dominant growing mode, we can not reproduce the correct evolution of cumulants with orders higher than two, even though there is no problem with the numerical scheme. We investigate the impact of transients on the observable statistical quantities by performing $N$-body simulations with initial conditions based on Lagrangian perturbation theory (LPT). We show that the effects of transients on the kurtosis from the initial conditions, based on second-order Lagrangian perturbation theory (2LPT) have almost disappeared by $z\sim5$, as long as the initial conditions are set at $z > 30$. This means that for practical purposes, the initial conditions based on 2LPT are accurate enough for numerical calculations of skewness and kurtosis.

astro-ph↗

arXiv2007

Non-Gaussianity of the density distribution in accelerating universes II:N-body simulations

We explore the possibility of putting constraints on dark energy models with statistical property of large scale structure in the non-linear region. In particular, we investigate the $w$ dependence of non-Gaussianity of the smoothed density distribution generated by the nonlinear dynamics. In order to follow the non-linear evolution of the density fluctuations, we apply N-body simulations based on $P^3 M$ scheme. We show that the relative difference between non-Gaussianity of $w=-0.8$ model and that of $w=-1.0$ model is $0.67 %$ (skewness) and $1.2 %$ (kurtosis) for $R=8h^{-1}$ Mpc. We also calculate the correspondent quantities for $R=2h^{-1}$ Mpc, $3.0 %$ (skewness) and $4.5 %$ (kurtosis), and the difference turn out to be greater, even though non-linearity in this scale is so strong that the complex physical processes about galaxy formation affect the galaxy distribution. From this, we can expect that the difference can be tested by all sky galaxy surveys with the help of mock catalogs created by selection functions, which suggests that non-Gaussianity of the density distribution potentially plays an important role for extracting information on dark energy.

astro-ph↗

arXiv2006

Inflaton perturbations in brane-world cosmology with induced gravity

We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass $m^2 = -2(2\ell-1) (\ell +1) H^2$ and $m^2 = -2\ell(2\ell+3) H^2$ where $\ell$ is an integer. There are two branches ($\pm$ branches) of solutions for the background spacetime. In the $+$ branch, which includes the self-accelerating universe, a resonance appears for a mode with $m^2 = 2 H^2$ due to a spin-0 perturbation with $m^2 = 2H^2$. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with $m^2 = 2H^2$. In the $-$ branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related to the disappearance of van Dam-Veltman-Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the lineariaed gravity on the brane is well described by the Brans-Dicke theory with $ω=3Hr_c$ in $-$ branch and $ω= -3H r_c$ in $+$ branch, respectively, which confirms the existence of the ghost in $+$ branch. We also study large scale perturbations. In $+$ branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of Weyl tensor in the bulk, but no instability is shown to exist on the brane.

gr-qc↗