IS THE VACUUM STABLE

The experimental data, as well as theoretical considerations allow (an d, in some cases, require) the Universe at present to rest in a false vacuum, whose approximate stability imposes constraints on the model p arameters. Under very general and mild conditions, the Universe would have ended up in the standard vacuum even if the potential has deeper minima, provided there was a period in which the temperature was great er than or similar to 1 TeV. In many cases, the zero temperature tunne ling rate is much smaller than the inverse age of the Universe. Future experiments may reveal that the physical vacuum is not entirely stabl e. Implications for the cosmological constant are discussed.