We study Brans-Dicke cosmology with an inverse power-law effective potential. By using dynamical analyses, we search for fixed points corresponding to the radiationlike matter and dark energy-dominated era of our Universe, and the stability of fixed points is also investigated. We find phase space trajectories which are attracted to the stable point of the dark energy-dominated era from unstable fixed points like matter-dominated era of the Universe. The dark energy comes from effective potentials of the Brans-Dicke field, whose variation (related to the time-variation of the gravitational coupling constant) is shown to be in good agreement with observational data.

In this paper, we suggest an [Formula: see text] gravity model for the dark energy, which can also be applied for a kind of galactic dark matter. Constructing the [Formula: see text] gravitational Lagrangians by Legendre transform from scalar-tensor theories, we study a future behavior of the late-time accelerating Universe as well as a subsequent behavior of an inflation model. Moreover, we discuss possible relations to the galactic dark matter, with a spherically symmetric solution for the static metric in our [Formula: see text] model.

There have been vigorous research attempts to test various modified gravity theories by using physics of the cosmic microwave background (CMB) anisotropy. In this article, with the CMB we try to distinguish two different scenarios of spontaneous symmetry breaking (SSB) in primordial era of the universe. The first scenario is a broken symmetric theory of gravity, which was suggested by A. Zee in 1979. The second scenario is an application of Palatini formalism to Zee's model and it combines the idea of SSB with Weyl scalar-tensor geometry.Since our new model based on Palatini formalism has geometrical feature, the scalar field coupled with gravity affects an evolution of Hubble parameter whereas Zee's model gives additional contributions to the energy-momentum tensor. Furthermore, it turns out that our model has different (from Zee's) sensitivity of CMB anisotropy power spectra with the scalar field mass. This fact enables us to verify distinct kinds of primordial symmetry breaking.

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