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We study in this paper chameleon cosmology applied to Friedmann-Robertson-walker space, which gives rise to the equation of state (EoS) parameter larger than −1 in the past and less than −1 today, satisfying current observations. We also study cosmological constraints on the model using the time evolution of the cosmological redshift of distant sources which directly probes the expansion history of the universe. Due to the evolution of the universes expansion rate, the model independent Cosmological Redshift Drift (CRD)test is expected to experience a small, systematic drift as a function of time. The model is supported by the observational data obtained from the test.

We study general properties of attractors for tachyonic potential chameleon scalar-field model which possess cosmological scaling solutions. An analytic formulation is given to obtain fixed points with a discussion on their stability. The model predicts a dynamical equation of state parameter with phantom crossing behavior for an accelerating universe. We constrain the parameters of the model by best fitting with the recent data-sets from supernovae and simulated data points for redshift drift experiment generated by Monte Carlo simulations.

We investigate chameleonic Brans-Dicke model applied to the FRW universes. A framework to study stability and attractor solutions in the phase space is developed for the model. We show that depending on the matter field and stability conditions, it is possible to realize phantomlike behavior without introducing phantom filed in the model while the stability is fulfilled and phantom crossing occurs. The statefinder parameters to the model for different kinds of matter interacting with the chameleon scalar field are studied. We also compare our model with present day observations.

We study longstanding problem of cosmological clock in the context of BransDicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogeneous cosmological models. Then, we show that formulation of the Brans-Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the FriedmannRobertson-Walker cosmological models.