Based only on the assumption that the Universe is homogenous and isotropic on large scales, cosmography is an ideal tool to investigate the cosmic expansion history in an almost model-independent way. Fitting the data on the luminosity distance and baryon acoustic oscillations allows to determine the confidence ranges for the cosmographic parameters hence giving some quantitative constraints that at whatever theory has to fulfill. As an application, we consider here the case of teleparallel gravity also referred to as f(T) gravity. To this end, we first work out analytical expressions to express the present day values of f(T) derivatives as a function of the cosmographic parameters, which hold under quite general and physically motivated conditions. We then use the constraints coming from cosmography to find out the confidence ranges for f(T) derivatives up to the fifth order and show how these can be used to check the viability of given teleparallel gravity models without the need to explicitly solve the second order dynamic equations.

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 propose a new model of intermediate inflation in the framework of brane cosmology in the presence of tachyonic field. We derive the expressions for the model parameters and estimate the observable parameters in the model numerically. We finally conclude that these parameters fit well with the observational data.

Scalar-field dark energy models for tachyon fields are often regarded as an effective description of an underlying theory of dark energy. In this Letter, we propose the agegraphic dark energy model in tachyon cosmology by interaction between the components of the dark sectors. In the formalism, the interaction term emerges from the tachyon field nonminimally coupled to the matter Lagrangian in the model rather than being inserted into the formalism as an external source. The model is constrained by the observational data. Based on the best fitted parameters in both original and new agegraphic dark energy scenarios, the model is tested by Sne Ia data. The tachyon potential and tachyon field are reconstructed and coincidence problem is revisited.

A logamediate inflationary model in the presence of the tachyon scalar field will be studied. Considering slow-roll inflation, the equations of motion of the Universe and the tachyon field will be derived. In the context of perturbation theory, some important perturbation parameters will be obtained and using numerical calculations, the consistency of our model with observational data will be illustrated.DOI: http://dx.doi.org/10.1103/PhysRevD.89.063504Published 5 March 2014Received 31 August 2013© 2014 American Physical Society