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

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.

Avoidance of future singularities in loop quantum cosmology

We consider the fate of future singularities in the effective dynamics of loop quantum cosmology. Non-perturbative quantum geometric effects which lead to $\rho^2$ modification of the Friedmann equation at high energies result in generic resolution of singularities whenever energy density $\rho$ diverges at future singularities of Friedmann dynamics. Such quantum effects lead to the avoidance of a Big Rip, which is followed by a recollapsing universe stable against perturbations. Resolution of sudden singularity, the case when pressure diverges but energy density approaches a finite value depends on the ratio of the latter to a critical energy density of the order of Planck. If the value of this ratio is greater than unity, the universe escapes the sudden future singularity and becomes oscillatory.Comment: 6 pages, 2 figure

Loop quantum gravity effects on inflation and the CMB

In loop quantum cosmology, the universe avoids a big bang singularity and undergoes an early and short super-inflation phase. During super-inflation, non-perturbative quantum corrections to the dynamics drive an inflaton field up its potential hill, thus setting the initial conditions for standard inflation. We show that this effect can raise the inflaton high enough to achieve sufficient e-foldings in the standard inflation era. We analyze the cosmological perturbations generated when slow-roll is violated after super-inflation, and show that loop quantum effects can in principle leave an indirect signature on the largest scales in the CMB, with some loss of power and running of the spectral index.Comment: revtex4, 5 pages, 3 figures, significant improvements in explanation of quantization and perturbation issues; version to appear Classical and Quantum Gravit

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

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

String-inspired cosmology: Late time transition from scaling matter era to dark energy universe caused by a Gauss-Bonnet coupling

The Gauss-Bonnet (GB) curvature invariant coupled to a scalar field $\phi$ can lead to an exit from a scaling matter-dominated epoch to a late-time accelerated expansion, which is attractive to alleviate the coincident problem of dark energy. We derive the condition for the existence of cosmological scaling solutions in the presence of the GB coupling for a general scalar-field Lagrangian density $p(\phi, X)$, where $X=-(1/2)(\nabla \phi)^2$ is a kinematic term of the scalar field. The GB coupling and the Lagrangian density are restricted to be in the form $f(\phi) \propto e^{\lambda \phi}$ and $p=Xg (Xe^{\lambda \phi})$, respectively, where $\lambda$ is a constant and $g$ is an arbitrary function. We also derive fixed points for such a scaling Lagrangian with a GB coupling $f(\phi) \propto e^{\mu \phi}$ and clarify the conditions under which the scaling matter era is followed by a de-Sitter solution which can appear in the presence of the GB coupling. Among scaling models proposed in the current literature, we find that the models which allow such a cosmological evolution are an ordinary scalar field with an exponential potential and a tachyon field with an inverse square potential, although the latter requires a coupling between dark energy and dark matter.Comment: 18 pages, 4 figures, version to appear in JCA

A new twist to preheating

Metric perturbations typically strengthen field resonances during preheating. In contrast we present a model in which the super-Hubble field resonances are completely {\em suppressed} when metric perturbations are included. The model is the nonminimal Fakir-Unruh scenario which is exactly solvable in the long-wavelength limit when metric perturbations are included, but exhibits exponential growth of super-Hubble modes in their absence. This gravitationally enhanced integrability is exceptional, both for its rarity and for the power with which it illustrates the importance of including metric perturbations in consistent studies of preheating. We conjecture a no-go result - there exists no {\em single-field} model with growth of cosmologically-relevant metric perturbations during preheating.Comment: 6 pages, 3 figures, Version to appear in Physical Review