Dark energy must be taken into account to estimate more reliably the amount of dark matter and how it is distributed in the local universe .
For systems several Mpc across like the Local Group , we introduce three self-consistent independent mass estimators .
These account for the antigravity effect of dark energy treated as Einstein ’ s cosmological constant \Lambda .
The first is a modified Kahn-Woltjer model which gives a value of the Local Group mass via the particular motions of the two largest members , the Milky Way and M31 .
Inclusion of dark energy in this model increases the minimum mass estimate by a factor of three compared to the “classical estimate” .
The increase is less but still significant for different ways of using the timing argument .
The second estimator is a modified virial theorem which also demonstrates how dark energy can ” hide ” from detection a part of the gravitating mass of the system .
The third is a new zero-gravity method which gives an upper limit to the group mass which we calculate with high precision HST observations .
In combination , the estimators lead to a robust and rather narrow range for a group ’ s mass , M. For the Local Group , 3.2 < M < 3.7 \times 10 ^ { 12 } M _ { \odot } .
Our result agrees well with the Millennium Simulation based on the \Lambda CDM cosmology .