We discuss the important role played during inflation by one of the soft supersymmetry breaking terms in the inflationary potential of supersymmetric hybrid inflation models .
With minimal Kähler potential , the inclusion of this term allows the prediction for the scalar spectral index to agree with the value n _ { s } = 0.963 ^ { +0.014 } _ { -0.015 } found by WMAP5 .
In the absence of this soft term , and by taking into account only radiative and supergravity corrections , it is well known that n _ { s } \geq 0.985 .
This same soft term has previously been shown to play a key role in resolving the MSSM \mu problem .
The tensor to scalar ratio r is quite small in these models , taking on values r \leq 10 ^ { -5 } in the WMAP5 2 \sigma range of n _ { s } .