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For two types of quintessence models having thawing and tracking properties, there exist analytic solutions for the dark energy equation of state w expressed in terms of several free parameters. We put observational bounds on the parameters in such scenarios by using the recent data of Supernovae type Ia, Cosmic Microwave Background, and Baryon Acoustic Oscillations. The observational constraints are quite different depending on whether or not the recent BAO data from BOSS are taken into account. With the BOSS data the upper bounds of today's values of w (=w_0) in thawing models is very close to -1, whereas without this data the values of w_0 away from -1 can be still allowed. The tracker equation of state w_{(0)} during the matter era is constrained to be w_{(0)}<-0.949 at 95 % confidence level even without the BOSS data, so that the tracker models with w away from -1 are severely disfavored. We also study observational constraints on scaling models in which w starts to evolve from 0 in the deep matter era and show that the transition to the equation of state close to w=-1 needs to occur at an early cosmological epoch. In the three classes of quintessence models studied in this paper, the past evolution of the Hubble parameters in the best-fit models shows only less than the 2.5 % difference compared to the LCDM., Comment: 12 pages, 10 figures

The current observational and experimental bounds on the time variation of the constants of nature (the fine structure constant $\alpha$, the gravitational constant $G$ and the proton-electron mass ratio $\mu=m_p/m_e$) are reviewed., Comment: 27 pages, 2 figures, to be published in Prog.Theor.Phys, ref. added

We compute the shadows of colliding black holes using the Kastor-Traschen cosmological multiblack hole solution that is an exact solution describing the collision of maximally charged black holes with a positive cosmological constant. We find that in addition to the shadow of each black hole, an eyebrowlike structure appears as the black holes come close to each other. These features can be used as probes to find the multiblack hole system at the final stage of its merger process., Comment: 5 pages, 1 figure, accepted for publication in PRD

Recently spatial as well as temporal variations of the fine structure constant alpha have been reported. We show that a "runaway domain wall", which arises for the scalar field potential without minima, can account for such variations simultaneously. The time variation is induced by a runaway potential and the spatial variation is induced by the formation of a domain wall. The model is consistent with the current cosmological data and can be tested by the future experiments to test the equivalence principle., Comment: 10 pages, 2 figures, published version

We study time evolution of the $Q$ ball in thermal logarithmic potential using lattice simulations. As the temperature decreases due to the cosmic expansion, the thermal logarithmic term in the potential is eventually overcome by a mass term, and we confirm that the $Q$ ball transforms from the thick-wall type to the thin-wall type for a positive coefficient of radiative corrections to the mass term, as recently suggested. Moreover, we find that the $Q$ ball finally "melts down" when the $Q$-ball solution disappears. We also discuss the effects of this phenomenon on the detectability of gravitational waves from the $Q$-ball formation., Comment: 10 pages, 7 figures, Ver.2, published version

We study the detectability of the gravitational waves (GWs) from the Q-ball formation associated with the Affleck-Dine (AD) mechanism, taking into account both of the dilution effect due to Q-ball domination and of finite temperature effects. The AD mechanism predicts the formation of non-topological solitons, Q-balls, from which GWs are generated. Q-balls with large conserved charge $Q$ can produce a large amount of GWs. On the other hand, the decay rate of such Q-balls is so small that they may dominate the energy density of the universe, which implies that GWs are significantly diluted and that their frequencies are redshifted during Q-ball dominated era. Thus, the detectability of the GWs associated with the formation of Q-balls is determined by these two competing effects. We find that there is a finite but small parameter region where such GWs may be detected by future detectors such as DECIGO or BBO, only in the case when the thermal logarithmic potential dominates the potential of the AD field. Otherwise GWs from Q-balls would not be detectable even by these futuristic detectors: $\Omega_{\rm GW}^0<10^{-21}$. Unfortunately, for such parameter region the present baryon asymmetry of the universe can hardly be explained unless one fine-tunes A-terms in the potential. However the detection of such a GW background may give us an information about the early universe, for example, it may suggest that the flat directions with $B-L=0$ are favored., Comment: V.2, 46 pages, 12 figures, references added, published version

We derive the equation of state of tracker fields, which are typical examples of freezing quintessence (quintessence with the equation of state approaching toward -1), taking into account of the late-time departure from the tracker solution due to the nonzero density parameter of dark energy $\Omp$. We calculate the equation of state as a function of $\Omp$ for constant $\Gamma=VV"/(V')^2$ (during matter era) models. The derived equation of state contains a single parameter, $w_{(0)}$, which parametrizes the equation of state during the matter-dominated epoch. We derive observational constraints on $w_{(0)}$ and find that observational data are consistent with the cosmological constant: $-1.11< \wzero< -0.96 (1 \sigma)$., Comment: 5 pages, 2 figures

We derive slow-roll conditions for thawing k-essence with a separable Lagrangian $p(X,\phi)=F(X)V(\phi)$. We examine the evolution of the equation of state parameter, $w$, as a function of the scale factor $a$, for the case where $w$ is close to -1. We find two distinct cases, corresponding to $X \approx 0$ and $F_X \approx 0$, respectively. For the case where $X\approx0$ the evolution of $\phi$ and hence $w$ is described by only two parameters, and $w(a)$ is model-independent and coincides with similar behavior seen in thawing quintessence models. This result also extends to non-separable Lagrangians where $X\approx0$. For the case $F_X \approx 0$, an expression is derived for $w(a)$, but this expression depends on the potential $V(\phi)$, so there is no model-independent limiting behavior. For the $X \approx 0$ case, we derive observational constraints on the two parameters of the model, $w_0$ (the present-day value of $w$), and the $K$, which parametrizes the curvature of the potential. We find that the observations sharply constrain $w_0$ to be close to -1, but provide very poor constraints on $K$., Comment: 7 pages and 5 figures, typos corrected