Abstract:
In order to examine the gravitational waves emitted from the neutron stars in the tensor-vector-scalar (TeVeS) theory, we derive the perturbation equations for relativistic stars, where for simplicity we omit the perturbations of vector field. That is, we consider the perturbations of scalar and tensor fields. With this assumption, we find that the axial gravitational waves, which are corresponding to the oscillations of spacetime ($w$ modes), are independent from the perturbations of scalar field and the effects of scalar field can be mounted only via the background properties. Using two different equations of state, we calculate the complex eigenfrequencies of axial $w$ modes and find that the dependences of frequencies on the stellar compactness are almost independent from the adopted equation of state and the parameter in TeVeS. Additionally, these dependences of frequencies of axial $w$ modes in TeVeS is obviously different from those expected in the general relativity. Thus the direct observations of gravitational waves could reveal the gravitational theory in the strong-field regime.

Abstract:
The Wheeler-DeWitt equation is solved for the Bergmann-Wagoner scalar-tensor gravitational theory in the case of Friedmann-Robertson- Walker cosmological model. We present solutions for several cosmological functions: i) \lambda(\phi)=0, ii) \lambda(\phi)=3\Lambda_0\phi and iii) a more complex \lambda(\phi), that depends on the choice of the coupling function, considering closed, flat and hyperbolic Friedmann universes (k=1, 0, -1). In the first two cases we show particular quantum wormhole solutions. Also, classical solutions are considered for some scalar-tensor theories, and we study the third quantization of some minisuperspace models.

Abstract:
Unlike general relativity, the scalar gravitational waves can be excited due to the radial oscillations in scalar-tensor gravity. To examine the scalar gravitational waves in scalar-tensor gravity, we derive the evolution equations of the radial oscillations of neutron stars and determine the specific oscillation frequencies of the matter oscillations and scalar gravitational waves, where we adopt two different numerical approaches, i.e., the mode analysis and direct time evolution. As a result, we observe the spontaneous scalarization even in the radial oscillations. Depending on the background scalar field and coupling constant, the total energy radiated by the scalar gravitational waves dramatically changes, where the specific oscillation frequencies are completely same as the matter oscillations. That is, via the direct observations of scalar gravitational waves, one can not only reveal the gravitational theory, but also extract the radial oscillations of neutron stars.

Abstract:
The scalar background field and its consequences are discussed for the Friedmann type cosmological solutions of the scalar-tensor theory of gravity with the Higgs field of the Standard Model as the scalar gravitational field.

Abstract:
We derive the perturbation equations for relativistic stars in scalar-tensor theories of gravity and study the corresponding oscillation spectrum. We show that the frequency of the emitted gravitational waves is shifted proportionally to the scalar field strength. Scalar waves which might be produced from such oscillations can be a unique probe for the theory, but their detectability is questionable if the radiated energy is small. However we show that there is no need for a direct observation of scalar waves: the shift in the gravitational wave spectrum could unambiguously signal the presence of a scalar field.

Abstract:
Unlike general relativity, scalar-tensor theories of gravity predict scalar gravitational waves even from a spherically symmetric gravitational collapse. We solve numerically the generation and propagation of the scalar gravitational wave from a spherically symmetric and homogeneous dust collapse under the approximation that we can neglect the back reaction of the scalar wave on the space-time, and examine how the amplitude, characteristic frequency and wave form of the observed scalar gravitational wave depend on the initial radius and mass of the dust and parameters contained in the theory. In the Brans-Dicke theory, through the observation of the scalar gravitational wave, it is possible to determine the initial radius and mass and a parameter contained in the theory. In the scalar-tensor theories, it would be possible to get the information of the first derivative of the coupling function contained in the theory because the wave form of the scalar gravitational wave greatly depends on it.

Abstract:
We calculated the evolution of the Newton gravitational in a scalar tensor theory, using parameters that holds for the present Universe. We analised the evolution from one billion of years ago.

Abstract:
The low-momentum structure of the gravitational polarization tensor of an ultrarelativistic plasma of scalar particles with $\lambda\phi^4$ interactions is evaluated in a two-loop calculation up to and including order $\lambda^{3/2}$. This turns out to require an improved perturbation theory which resums a local thermal mass term as well as nonlocal hard-thermal-loop vertices of scalar and gravitational fields.

Abstract:
The cosmological behavior of modified gravity theories with additional degrees of freedom (DOFs) is typically complex and can give rise to non-intuitive results. A possible way of exploring such theories is to consider appropriate parameterizations of these new DOFs. Here I suggest using the algebraic structure of trivial identities, which typically occur at the level of the perturbed field equations, for defining such parameterizations. Choosing the example of Bekenstein's tensor-vector-scalar theory (TeVeS) and considering perturbations in the conformal Newtonian gauge, this parameterization is then used to study several aspects of the cosmological evolution in an Einstein-de Sitter universe. As a main result, I conclude that perturbations of the scalar field take a key role in generating enhanced growth if this enhancement is primarily associated with a gravitational slip. From this point of view, the previously found modified growth in TeVeS is truly a result of the complex interplay between both the scalar and the vector field. Since the occurrence of trivial identities of the above kind appears as a generic feature of modified gravity theories with extra DOFs, these parameterizations should generally prove useful to investigate the cosmological properties of other proposed modifications. As such parameterizations capture the full nature of modifications by construction, they also provide a suitable framework for developing semi-analytic models of cosmologically interesting quantities like, for instance, the growth factor, leading to various applications. Supplementary to numerical analysis, parameterizations based on trivial identities are thus an interesting tool to approach modified gravity theories with extra DOFs.

Abstract:
A covariant scalar-tensor-vector gravity theory is developed which allows the gravitational constant $G$, a vector field coupling $\omega$ and the vector field mass $\mu$ to vary with space and time. The equations of motion for a test particle lead to a modified gravitational acceleration law that can fit galaxy rotation curves and cluster data without non-baryonic dark matter. The theory is consistent with solar system observational tests. The linear evolutions of the metric, vector field and scalar field perturbations and their consequences for the observations of the cosmic microwave background are investigated.