The general property of dynamical quintessence field

We discuss the general dynamical behaviors of quintessence field, in particular, the general conditions for tracking and thawing solutions are discussed. We explain what the tracking solutions mean and in what sense the results depend on the initial conditions. Based on the definition of tracking solution, we give a simple explanation on the existence of a general relation between $w_\phi$ and $\Omega_\phi$ which is independent of the initial conditions for the tracking solution. A more general tracker theorem which requires large initial values of the roll parameter is then proposed. To get thawing solutions, the initial value of the roll parameter needs to be small. The power-law and pseudo-Nambu Goldstone boson potentials are used to discuss the tracking and thawing solutions. A more general $w_\phi-\Omega_\phi$ relation is derived for the thawing solutions. Based on the asymptotical behavior of the $w_\phi-\Omega_\phi$ relation, the flow parameter is used to give an upper limit on $w_\phi'$ for the thawing solutions. If we use the observational constraint $w_{\phi 0}<-0.8$ and $0.2<\Omega_{m0}<0.4$, then we require $n\lesssim 1$ for the inverse power-law potential $V(\phi)=V_0(\phi/m_{pl})^{-n}$ with tracking solutions and the initial value of the roll parameter $|\lambda_i|<1.3$ for the potentials with the thawing solutions.Comment: 11 figures, corrected some typos and presentation improved, PLB in pres

Inflationary attractors from nonminimal coupling

We show explicitly how the E model attractor is obtained from the general scalar-tensor theory of gravity with arbitrary conformal factors in the strong coupling limit. By using conformal transformations, any attractor with the observables $n_s$ and $r$ can be obtained. The existence of attractors imposes a challenge to distinguish different models.Comment: 5 pages, 1 figures, prepared for the proceedings of the International Conference on Gravitation : Joint Conference of ICGAC-XIII and IK1

Gravitational Wave Polarizations in f(R)f(R) Gravity and Scalar-Tensor Theory

The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in $f(R)$ gravity and Horndeski theory, both containing scalar modes. These theories predict that in addition to the familiar $+$ and $\times$ polarizations, there are transverse breathing and longitudinal polarizations excited by the massive scalar mode and the new polarization is a single mixed state. It would be very difficult to detect the longitudinal polarization by interferometers, while pulsar timing array may be the better tool to detect the longitudinal polarization.Comment: 10 pages, 3 figures, contribution to the proceedings of the International Conference on Gravitation : Joint Conference of ICGAC-XIII and IK1