Scalar Field Model For Dark Energy

The recent measurements of type Ia Supernovae (SNe Ia) indicate that the expansion of the universe is speeding up. It is also by confirmed by the combination of result from the largescale distribution of galaxies and the most precise data on the cosmic microwave background (CMB) from the Wilkinson Microwave Anisotropy Probe (WMAP). But, the cosmological model based on the ordinary matter component denotes that the expansion of the universe would be decelerating, which is not consistent with the observation. Thus, we doubt either the validity of the cosmological model, or there be a new matter component which is not founded for the gravity source in the laboratory. There are then two ways to give rise to an accelerating expansion: (i) by supplementing the energy momentum tensor by an negative pressure, exotic form of matter which amounts to about 2/3 and permeates homogenously in all the universe and pushes the universe accelerated expansion. This kinds of component is dubbed dark energy. So far, many kinds of dark energy models have been presented, such as cosmological constant A, slow rolling scalar field Quintessence, Phantom, Quintom and Tachyon Field and so on. (ii) by modifying the geometry part in Einstein equation, corresponding to turn R into f(R) in the action. In some sense, the theoretical foundation of the cosmological model——the general relativity is modified, including Modified Gravity Theory, Braneworld Model, Brans-Dicke Theory.In the thesis, the accelerating expansion of the universe and dark energy are explored from the two above parts.At first, by using some modern mathematical methods, the modified gravity theory——the double complex symmetric gravitational theory is established and the concrete expression of the static spherically symmetric double complex metrics is derived by introducing the double complex symmetric metric tensors. Thus, the Moffat's results are extended, the hyperbolic complex symmetric gravitational theory is naturally obtained and the famous Schwarzachild solution is contained as the special case. Moreover, in the linearized weak field approximation the hyperbolic complex symmetric gravitational theory can automatically free from the potential problem of negative energy ghost states.Furthermore, the accelerating expansion of the universe is studied in the double complex symmetric gravitational theory. The universe we live in is taken as the real part of the total spacetime——the double complex space. By the two constraint conditions, the conditions of accelerating expansion are analyzed. Moreover, the equation of state for scalar field is reconstructed in the double complex symmetric gravitational theory. With the d_L(z) ansatz, the time evolution of the universe is analyzed from the observation. The results indicate that the whole spacetime, i. e. the double complex spacetime, may be either ordinary complex or hyperbolic complex. The equation of state of dark energy crosses -1 for the whole redshift range and remains close to -1 at present. And the fate of the universe would be Big Rip in the future.At last, some content of the tachyon cosmology is studied. Through the model independent equation of state of dark energy, the field function and potential of the tachyon are reconstructed. The method is applied to four known parametrization of equation of state and the evolutions of the tachyon field and potential are studied. Furthermore, the statefinder parameters are studied for the tachyon field dark energy model and the coupled tachyon field dark energy model. Not only the properties of the tachyon dark energy model are characterized, but also the difference from other dark energy model is showed.