  The high field superconducting state in CeCoIn5 has been studied by
transverse field muon spin rotation measurements with an applied field parallel
to the crystallographic c-axis close to the upper critical field Hc2 = 4.97 T.
At magnetic fields >= 4.8 T the muon Knight shift is enhanced and the
superconducting transition changes from second order towards first order as
predicted for Pauli-limited superconductors. The field and temperature
dependence of the transverse muon spin relaxation rate sigma reveal
paramagnetic spin fluctuations in the field regime from 2 T < H < 4.8 T. In the
normal state close to Hc2 correlated spin fluctuations as described by the self
consistent renormalization theory are observed. The results support the
formation of a mode-coupled superconducting and antiferromagnetically ordered
phase in CeCoIn5 for H directed parallel to the c-axis.
