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Grishchuk has shown that the stochastic background of gravitational wavesproduced by an inflationary phase in the early Universe has an unusualproperty: it is not a stationary Gaussian random process. Due to squeezing, thephases of the different waves are correlated in a deterministic way, arisingfrom the process of parametric amplification that created them. The resultingrandom process is Gaussian but non-stationary. This provides a unique signaturethat could in principle distinguish a background created by inflation fromstationary stochastic backgrounds created by other types of processes. Weaddress the question: could this signature be observed with a gravitationalwave detector? Sadly, the answer appears to be "no": an experiment which coulddistinguish the non-stationary behavior would have to last approximately theage of the Universe at the time of measurement. This rules out direct detectionby ground and space based gravitational wave detectors, but not indirectdetections via the electromagnetic Cosmic Microwave Background Radiation(CMBR).Comment: 17 pages, 4 Postscript figures, uses revtex, psfig, to be submitted  to PRD, minor revisions - appendix B clarified, corrected typos, added  reference

Is the squeezing of relic gravitational waves produced by inflation detectable?