Dark energy versus modified gravity: Impacts on measuring neutrino mass

In this paper, we make a comparison for the impacts of smooth dynamical dark energy, modified gravity, and interacting dark energy on the cosmological constraints on the total mass of active neutrinos. For definiteness, we consider the ΛCDM model, the wCDM model, the f(R) model, and two typical interacting vacuum energy models, i.e., the IΛCDM1 model with Q = βHρc and the IΛCDM2 model with Q = βHρΛ. In the cosmological fits, we use the Planck 2015 temperature and polarization data, in combination with other low-redshift observations including the baryon acoustic oscillations, the type Ia supernovae, the Hubble constant measurement, and the large-scale structure observations, such as the weak lensing as well as the redshift-space distortions. Besides, the Planck lensing measurement is also employed in this work. We find that, the wCDM model favors a higher upper limit on the neutrino mass compared to the ΛCDM model, while the upper limit in the f(R) model is similar with that in the ΛCDM model. For the interacting vacuum energy models, the IΛCDM1 model favors a higher upper limit on neutrino mass, while the IΛCDM2 model favors an identical neutrino mass with the case of ΛCDM.