Chaotic dynamics in preheating after inflation

We study chaotic dynamics in preheating after inflation in which an inflaton $\phi$ is coupled to another scalar field $\chi$ through an interaction $(1/2)g^2\phi^2\chi^2$. We first estimate the size of the quasi-homogeneous field $\chi$ at the beginning of reheating for large-field inflaton potentials $V(\phi)=V_0\phi^n$ by evaluating the amplitude of the $\chi$ fluctuations on scales larger than the Hubble radius at the end of inflation. Parametric excitations of the field $\chi$ during preheating can give rise to chaos between two dynamical scalar fields. For the quartic potential ($n=4$, $V_0=\lambda/4$) chaos actually occurs for $g^2/\lambda <{\cal O}(10)$ in a linear regime before which the backreaction of created particles becomes important. This analysis is supported by several different criteria for the existence of chaos. For the quadratic potential ($n=2$) the signature of chaos is not found by the time at which the backreaction begins to work, similar to the case of the quartic potential with $g^2/\lambda \gg 1$.Comment: 12 pages, 10 figures, Version to appear in Classical and Quantum Gravit

Density perturbations in f(R) gravity theories in metric and Palatini formalisms

We make a detailed study of matter density perturbations in both metric and Palatini formalisms in theories whose Lagrangian density is a general function, f(R), of the Ricci scalar. We derive these equations in a number of gauges. We show that for viable models that satisfy cosmological and local gravity constraints (LGC), matter perturbation equations derived under a sub-horizon approximation are valid even for super-Hubble scales provided the oscillating mode (scalaron) does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism because of the absence of scalarons. Using these equations we make a comparative study of the behaviour of density perturbations as well as gravitational potentials for a number of classes of theories. In the metric formalism the parameter m=Rf_{,RR}/f_{,R} characterising the deviation from the Lambda CDM model is constrained to be very small during the matter era in order to ensure compatibility with LGC, but the models in which m grows to the order of 10^{-1} around the present epoch can be allowed. These models also suffer from an additional fine tuning due to the presence of scalaron modes which are absent in the Palatini case. In Palatini formalism LGC and background cosmological constraints provide only weak bounds on |m| by constraining it to be smaller than ~ 0.1. This is in contrast to matter density perturbations which, on galactic scales, place far more stringent constraints on the present deviation parameter m of the order of |m| < 10^{-5} - 10^{-4}. This is due to the peculiar evolution of matter perturbations in the Palatini case which exhibits a rapid growth or a damped oscillation depending on the sign of m.Comment: 36 pages including 8 figures. Accepted for publication in Physical Review

Density perturbations in general modified gravitational theories

We derive the equations of linear cosmological perturbations for the general Lagrangian density $f (R,\phi, X)/2+L_c$, where $R$ is a Ricci scalar, $\phi$ is a scalar field, and $X=-(\nabla \phi)^2/2$ is a field kinetic energy. We take into account a nonlinear self-interaction term $L_c$ recently studied in the context of "Galileon" cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasi-static approximation on sub-horizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature and thus it is convenient to test the viability of such models from both theoretical and observational points of view.Comment: 17 pages, no figure

Power-law inflation with a nonminimally coupled scalar field

We consider the dynamics of power-law inflation with a nonminimally coupled scalar field $\phi$. It is well known that multiple scalar fields with exponential potentials $V(\phi)=V_0 {\rm exp}(-\sqrt{16\pi/p m_{\rm pl}^2} \phi)$ lead to an inflationary solution even if the each scalar field is not capable to sustain inflation. In this paper, we show that inflation can be assisted even in the one-field case by the effect of nonminimal coupling. When $\xi$ is positive, since an effective potential which arises by a conformal transformation becomes flatter compared with the case of $\xi=0$ for $\phi>0$, we have an inflationary solution even when the universe evolves as non-inflationary in the minimally coupled case. For the negative $\xi$, the assisted inflation can take place when $\phi$ evolves in the region of $\phi<0$ \.Comment: 12 pages, 6 figures, to appear in Phys. Rev.

Are Kaluza-Klein modes enhanced by parametric resonance?

We study parametric amplification of Kaluza-Klein (KK) modes in a higher $D$-dimensional generalized Kaluza-Klein theory, which was originally considered by Mukohyama in the narrow resonance case. It was suggested that KK modes can be enhanced by an oscillation of a scale of compactification by the $d$-dimensional sphere $S^d~(d=D-4)$ and by the direct product $S^{d_1}\times S^{d_2}~(d_1+d_2=D-4)$. We extend this past work to the more general case where initial values of the scale of compactification and the quantum number of the angular momentum $l$ of KK modes are not small. We perform analytic approaches based on the Mathieu equation as well as numerical calculations, and find that the expansion of the universe rapidly makes the KK field deviate from instability bands. As a result, KK modes are not enhanced sufficiently in an expanding universe in these two classes of models.Comment: 15 pages, 5 figure

New constraints on multi-field inflation with nonminimal coupling

We study the dynamics and perturbations during inflation and reheating in a multi-field model where a second scalar field $\chi$ is nonminimally coupled to the scalar curvature $(\frac12 \xi R\chi^2$). When $\xi$ is positive, the usual inflationary prediction for large-scale anisotropies is hardly altered while the $\chi$ fluctuation in sub-Hubble modes can be amplified during preheating for large $\xi$. For negative values of $\xi$, however, long-wave modes of the $\chi$ fluctuation exhibit exponential increase during inflation, leading to the strong enhancement of super-Hubble metric perturbations even when $|\xi|$ is less than unity. This is because the effective $\chi$ mass becomes negative during inflation. We constrain the strength of $\xi$ and the initial $\chi$ by the amplitude of produced density perturbations. One way to avoid nonadiabatic growth of super-Hubble curvature perturbations is to stabilize the $\chi$ mass through a coupling to the inflaton. Preheating may thus be necessary in these models to protect the stability of the inflationary phase.Comment: 20 pages, 8 figures, submitted to Physical Review

Generalized Brans-Dicke theories

In Brans-Dicke theory a non-linear self interaction of a scalar field allows a possibility of realizing the late-time cosmic acceleration, while recovering the General Relativistic behavior at early cosmological epochs. We extend this to more general modified gravitational theories in which a de Sitter solution for dark energy exists without using a field potential. We derive a condition for the stability of the de Sitter point and study the background cosmological dynamics of such theories. We also restrict the allowed region of model parameters from the demand for the avoidance of ghosts and instabilities. A peculiar evolution of the field propagation speed allows us to distinguish those theories from the LCDM model.Comment: 14 pages, 4 figures, version to appear in JCA

Brane preheating

We study brane-world preheating in massive chaotic inflationary scenario where scalar fields are confined on the 3-brane. Assuming that quadratic contribution in energy densities dominates the Hubble expansion rate during preheating, the amplitude of inflaton decreases slowly relative to the standard dust-dominated case. This leads to an efficient production of $\chi$ particles via nonperturbative decay of inflaton even if its coupling is of order $g=10^{-5}$. We also discuss massive particle creation heavier than inflaton, which may play important roles for the baryo- and lepto-genesis scenarios.Comment: 6 pages, 2 figures, submitted to Physical Review

Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether Symmetry Approach. A general formalism in the metric framework is developed considering a point-like f(R)-Lagrangian where spherical symmetry is required. Examples of exact solutions are given.Comment: 17 pages, to appear in Class. Quant. Gra