| The cosmological constant problem, which combining the Standard Model of particlephysics and the latest achievement of modern cosmological observation, is a great crisisfacing theoretical physics. Its related problem of vacuum energy is the focus of severalcontradictions concerning fundamental physics concepts. In this thesis, I will extend thediscussion along two important problems in modern cosmology: the one is the problemof vacuum energy, and the other is the baryon asymmetry in the universe. In addition,the arising dark energy di?culty is also taken into the consideration of the problem ofvacuum energy.Recent cosmological observation has indicated that the upper limit of vacuum energydensity in the universe is tens of magnitudes less than its predicted value from theparticle standard model. To release this severe contradiction, the dynamical propertyof the vacuum energy in the higher dimensional model with compactified extra space isfirstly discussed. Secondly, I will present a new model of Higgs mechanism based on thecomplex scalar gravity theory, which I will show is theoretically natural and provides arunning density of vacuum energy with a survival running speed of mass scale.Thirdly, I will propose a model which connects the gravitational origin of thebaryo/leptogenesis to the spontaneous breaking of gravitational scalar. In this classof models, the baryon asymmetry in the universe is generated along the ideas of sym-metry breaking—CPT violation—spontaneous baryo/leptogenesis. On this basis, weintroduce the spontaneous baryo/leptogenesis into Brans-Dicke cosmology, where thegravitational scalar of Brans-Dicke theory is assumed to be coupled with the current ofbaryon (or lepton). We find that a su?cient baryon asymmetry in the early universecan be obtained in such model.
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