On the E1–term of the gravity spectral sequence

The author constructed a spectral sequence strongly converging to h∗(ΩΣX) for any homology theory in [13]. In this note, we prove that the E1 –term of the spectral sequence is isomorphic to the cobar construction, and hence the spectral sequence is isomorphic to the classical cobar-type Eilenberg–Moore spectral sequence based on the geometric cobar construction from the E1 –term. Similar arguments can be also applied to its variants constructed in [14].