We apply the holographic principle to Brans-Dicke cosmology. We analyze the holographic bound in both the Jordan and Einstein frames. The holographic bound is satisfied for both the kϭ0 and kϭϪ1 universes, but it is violated for the kϭ1 matter-dominated universe.PACS number͑s͒: 04.50.ϩh, 98.80.Hw

Intermediate/Extreme mass ratio inspiral (I/EMRI) system provides a good tool to test the nature of gravity in strong field. Based on the method of osculating orbits, we compute the orbital evolutions of I/EMRIs on quasi-elliptic orbits in both Einstein's general relativity and Brans-Dicke theory. The extra monopolar and dipolar channels in Brans-Dicke theory accelerate the orbital decay, so it is important to consider the effects of monopolar and dipolar emissions on the waveform. With the help of accurate orbital motion, we generate waveform templates which include both monopolar and dipolar contributions for I/EMRIs on eccentric orbits in Brans-Dicke theory. With a two-year observation of gravitational waves emitted from I/EMRIs by LISA, we get the most stringent constraint on the Brans-Dicke coupling parameter ω 0 > 106.

In the derivation of Lorentz transformation, linear transformation between inertial frames is one of the most important steps. In teaching special relativity, we usually use the homogeneity and isotropy of spacetime to argue that the transformation must be linear transformation without providing any rigorous detail. We provide a mathematical proof of linear transformation based on the two postulates of special relativity and the homogeneity and isotropy of spacetime.

The generalized Brans-Dicke cosmology is studied. We find that the difference in the evolution of the universe is significant between the generalized Brans-Dicke cosmology and the standard cosmology during the radiation-dominated era and the inflationary era, though the difference is negligible during the matter-dominated era. The consequences arising from the differences remain to be studied in detail.