  When photons from distant galaxies and stars pass through our neighboring
environment, the wavelengths of the photons would be shifted by our local
gravitational potential. This local gravitational redshift effect can
potentially have an impact on the measurement of cosmological distance-redshift
relation. Using available supernovae data, Wojtak et al [1] found seemingly
large biases of cosmological parameters for some extended models (non-flat
$\Lambda$CDM, $w$CDM, etc.). Huang [2] pointed out that, however, the biases
can be reduced to a negligible level if cosmic microwave background (CMB) data
are added to break the strong degeneracy between parameters in the extended
models. In this article we forecast the cosmological bias due to local
gravitational redshifts for a future WFIRST-like supernovae survey. We find
that the local gravitational redshift effect remains negligible, provided that
CMB data or some future redshift survey data are added to break the degeneracy
between parameters.
