Takashi Torii

Recently, Cormier and Holman pointed out that fluctuations of an inflaton field $\phi$ are significantly enhanced in the model of {\it spinodal inflation} with a potential $V(\phi)$ for which the second derivative $V^{(2)}(\phi)$ changes sign. As an application of this model, we investigate particle production in the natural inflation model with a potential $V(\phi)=m^4 [1+\cos (\phi/f)]$ by making use of the Hartree approximation. For typical mass scales $f \sim m_{\rm pl} \sim 10^{19}$GeV, and $m \sim m_{\rm GUT} \sim 10^{16}$GeV, we find that growth of fluctuations relevantly occurs for the initial value of inflaton $\phi(0)<0.1 m_{\rm pl}$. Especially for $\phi(0)<10^{-6}m_{\rm pl}$, maximum fluctuations are so large that secondary inflation takes place by produced fluctuations. In this case, the achieved number of $e$-folding becomes much larger than in the case where an effect of spinodal instability is neglected.

The cosmic no hair conjecture is tested in the spherically symmetric Einstein-Maxwell-dilaton~(EMD) system with a positive cosmological constant $\Lambda$. Firstly, we analytically show that once gravitational collapse occurs in the massless dilaton case, the system of field equations breaks down inevitably in outer communicating regions or at the boundary provided that a future null infinity ${\cal I}^+$ exists. Next we find numerically the static black hole solutions in the massive dilaton case and investigate their properties for comparison with the massless case. It is shown that their Abbott-Deser~(AD) mass are infinite, which implies that a spacetime with finite AD mass does not approach a black hole solution after the gravitational collapse. These results suggest that ${\cal I}^+$ cannot appear in the EMD system once gravitational collapse occurs and hence the cosmic no hair conjecture is violated in both the massless and the massive cases, in contrast to general relativity.Comment: 9 pages, REVtex, 5 figures, to appear in Phys. Rev.

We investigate preheating of an inflaton field $\phi$ coupled nonminimally to a spacetime curvature. In the case of a self-coupling inflaton potential $V(\phi)=\lambda \phi^4/4$, the dynamics of preheating changes by the effect of the negative $\xi$. We find that the nonminimal coupling works in two ways. First, since the initial value of inflaton field for reheating becomes smaller with the increase of $|\xi|$, the evolution of the inflaton quanta is delayed for fixed $\lambda$. Second, the oscillation of the inflaton field is modified and the nonadiabatic change around $\phi=0$ occurs significantly. That makes the resonant band of the fluctuation field wider. Especially for strong coupling regimes $|\xi| \gg 1$, the growth of the inflaton flutuation is dominated by the resonance due to the nonminimal coupling, which leads to the significant enhancement of low momentum modes. Although the final variance of the inflaton fluctuation does notchange significantly compared with the minimally coupled case, we have found that the energy transfer from the homogeneous inflaton to created particles efficiently occurs for $\xi<-60$.

The cosmic no hair conjecture is tested in the spherically symmetric Einstein-Maxwell-dilaton~(EMD) system with a positive cosmological constant $\Lambda$. Firstly, we analytically show that once gravitational collapse occurs in the massless dilaton case, the system of field equations breaks down inevitably in outer communicating regions or at the boundary provided that a future null infinity ${\cal I}^+$ exists. Next we find numerically the static black hole solutions in the massive dilaton case and investigate their properties for comparison with the massless case. It is shown that their Abbott-Deser~(AD) mass are infinite, which implies that a spacetime with finite AD mass does not approach a black hole solution after the gravitational collapse. These results suggest that ${\cal I}^+$ cannot appear in the EMD system once gravitational collapse occurs and hence the cosmic no hair conjecture is violated in both the massless and the massive cases, in contrast to general relativity.

In higher-curvature inflation models $(R+{\alpha }_n{R}^n),$ we study a parametric preheating of a scalar field $\chi$ coupled nonminimally to a spacetime curvature $R\left(\xi R{\chi }^2\right).\mathrm{}$ In the case of the $R^2$-inflation model, efficient preheating becomes possible for rather small values of $\xi ,$ i.e., $|\xi |\lesssim$ several. Although the maximal fluctuation ${\sqrt{〈{\chi }^2〉}}_{\max }\approx 2\times {10}^{17}\mathrm{GeV}$ for $\xi \approx -4$ is almost the same as the chaotic inflation model with a nonminimally coupled $\chi$ field, the growth rate of the fluctuation becomes much larger and efficient preheating is realized. We also investigate preheating for the $R^4$ model and find that the maximal fluctuation is ${\sqrt{〈{\chi }^2〉}}_{\max }\approx 8\times {10}^{16}\mathrm{GeV}$ for $\xi \approx -35.$

We investigate the resonant particle production of a scalar field $\chi$ coupled nonminimally to a spacetime curvature $R$ $\left(\xi R{\chi }^2\right)$ as well as to an inflaton field φ ${(g}^2{\phi }^2{\chi }^2).\mathrm{}$ In the case of $g\lesssim 3\times {10}^{-4},$ the ξ effect assists g resonance in certain parameter regimes. However, for $g\gtrsim 3\times {10}^{-4},$ $g$ resonance is not enhanced by the $\xi$ effect because of the $\xi$ suppression effect as well as a back reaction effect. If $\xi \approx -4,$ the maximal fluctuation of produced $\chi$ particles is ${\sqrt{〈{\chi }^2〉}}_{\mathrm{}\max }\approx 2\times {10}^{17}\hspace{0.5em}\mathrm{GeV}$ for $g\lesssim 1\times {10}^{-5},$ which is larger than the minimally coupled case with $g\approx 1\times {10}^{-3}.$

We calculate how much a first-quantized string is excited after crossing the inner horizon of charged Vaidya solutions, as a simple model of generic black holes. To quantize a string suitably, we first show that the metric is approximated by a {\it plane-wave} metric near the inner horizon when the surface gravity of the horizon $\kappa_I$ is small enough. Next, it is analytically shown that the string crossing the inner horizon is excited infinitely in an asymptotically flat spacetime, while it is finite in an asymptotically de Sitter spacetime and the string can pass across the inner horizon when $\kappa_I<2\kappa:= 2 {min}\{\kappa_B,\kappa_C \}$, where $\kappa_B$~($\kappa_C$) is the surface gravity of the black hole~(cosmological) event horizon. This implies that the strong cosmic censorship holds in an asymptotically flat spacetime, while it is violated in an asymptotically de Sitter spacetime from the point of view of string theory.

In higher-curvature inflation models ($R+\alpha_n R^n$), we study a parametric preheating of a scalar field $\chi$ coupled non-minimally to a spacetime curvature $R$ ($\xi R \chi^2$). In the case of $R^2$-inflation model, efficient preheating becomes possible for rather small values of $\xi$, i.e. $|\xi|< several. Although the maximal fluctuation $\sqrt{< \chi^2 >}_{max} \approx 2 \times10^{17}$ GeV for $\xi \approx -4$ is almost the same as the chaotic inflation model with a non-minimally coupled $\chi$ field, the growth rate of the fluctuation becomes much larger and efficient preheating is realized. We also investigate preheating for $R^4$ model and find that the maximal fluctuation is $\sqrt{< \chi^2 >}_{max} \approx 8 \times 10^{16}$ GeV for $\xi \approx -35$.

We investigate a resonant particle production of a scalar field $\chi$ coupled non-minimally to a spacetime curvature $R$ ($\xi R \chi^2$) as well as to an inflaton field $\phi$ ($g^2\phi^2\chi^2$). In the case of $g < 3 \times 10^{-4}$, $\xi$ effect assists $g$-resonance in certain parameter regimes. However, for $g > 3 \times 10^{-4}$, $g$-resonance is not enhanced by $\xi$ effect because of $\xi$ suppression effect as well as a back reaction effect. If $\xi \approx -4$, the maximal fluctuation of produced $\chi$-particle is $\sqrt{< \chi^2 >}_{max} \approx 2 \times 10^{17}$ GeV for $g < 1 \times 10^{-5}$, which is larger than the minimally coupled case with $g \approx 1 \times 10^{-3}$.