Ultra-light axions ( ULAs ) with mass less than 10 ^ { -20 } eV have interesting behaviors that may contribute to either dark energy or dark matter at different epochs of the Universe .
Its properties can be explored by cosmological observations , such as expansion history of the Universe , cosmic large-scale structure , cosmic microwave background , etc .
In this work , we study the ULAs with a mass around 10 ^ { -33 } eV , that means the ULA field still rolls slowly at present with the equation of state w = -1 as dark energy .
In order to investigate the mass and other properties of this kind of ULA field , we adopt the measurements of Type Ia supernova ( SN Ia ) , baryon acoustic oscillation ( BAO ) , and Hubble parameter H ( z ) .
The Markov Chain Monte Carlo ( MCMC ) technique is employed to perform the constraints on the parameters .
Finally , by exploring four cases of the model , we find that the mass of this ULA field is about 3 \times 10 ^ { -33 } eV if assuming the initial axion field \phi _ { i } = M _ { pl } .
We also investigate a general case by assuming \phi _ { i } \leq M _ { pl } , and find that the fitting results of \phi _ { i } / M _ { pl } are consistent with or close to 1 for the datasets we use .