In the tetragonal heavy fermion system CeCoIn5 the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0-1 GPa) of the basal-plane magnetic penetration depth (\lambda_a), the penetration depth anisotropy (\gamma=\lambda_c/\lambda_a) and the temperature dependence of 1/\lambda_i^2 (i=a,c) were studied in single crystals. A strong decrease of \lambda_a with pressure was observed, while \gamma and \lambda_i^2(0)/\lambda_i^2(T) are pressure independent. A linear relationship between 1/\lambda_a^2(270 mK) and Tc was also found. The large decrease of \lambda_a with pressure is the signature of an increase of the number of superconducting quasiparticles by a factor of about 2.

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