The Earth Defense Force is a military force responsible for enforcing the Earth Government's orders as well as protecting Earth and its colonies. Relatively little is known about the extent and power of the E.D.F.
During the Second Aegis VII Incident, the E.D.F. sends the USM Valor to hunt down and destroy the USG Ishimura after its security breach. But, Necromorphs breach the ship and everyone on the Valor ends up dead. The ship also crashes right into the Ishimura. This is the point where Isaac Clarke goes into the Valor to get the Valor's Singularity Core. Isaac gets the core, but in doing so, the ship explodes from a catastrophic failure of fuel containment. The E.D.F.'s reaction to the loss of the vessel and what they've done afterward is unknown.
The E.D.F. may also have been involved in the First Aegis VII Incident as it is highly likely that a project as big and highly classified as the Marker research program would warrant at least some military involvement.
In Dead Space: Aftermath, members of the EDF go to investigate the damaged USG O'Bannon. They find four survivors, but one survivor kills a Marine and the Colonel orders the four survivors incapacitated. The survivors are then brought in for interrogation, but one of the survivors escapes and opens an air lock, killing himself along with several Marines.
After all the crises on Titan Station, the E.D.F. appears to have suffered great losses in the fight against the radical Unitologists and factions such as Jacob Danik's Circle.
The elements of the E.D.F. consist of the Navy, the Marine Corps, and Special Operations. Some of its known members include Sergeant John Carver and Captain Robert Norton. In Dead Space 3, John and Robert are the ones who secure Isaac Clarke at his home on the New Horizons Lunar Colony.