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 $\Lambda$CDM model, the $w$CDM model, the $f(R)$ model, and two
typical interacting vacuum energy models, i.e., the I$\Lambda$CDM1 model with
$Q=\beta H\rho_{\rm c}$ and the I$\Lambda$CDM2 model with $Q=\beta
H\rho_{\Lambda}$. 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 distortion. Besides, the Planck
lensing measurement is also employed in this work. We find that, the $w$CDM
model favors a higher upper limit on the neutrino mass compared to the
$\Lambda$CDM model, while the upper limit in the $f(R)$ model is similar with
that of $\Lambda$CDM model. For the interacting vacuum energy models, the
I$\Lambda$CDM1 model favors a higher upper limit on neutrino mass, while the
I$\Lambda$CDM2 model favors an identical neutrino mass with the case of
$\Lambda$CDM.
