Many sources recommend using an inoculant on pea seeds, especially when planting in cool, wet soil. But there's no definitive answer to whether or not you need to inoculate your peas.
Peas and other legumes can fix their own nitrogen with the help of rhizobia bacteria. These bacteria are soil-based microorganisms that have a symbiotic relationship with legumes. The benefit to peas is a higher yield and stronger plants.
Rhizobia bacteria are found naturally in most garden soils, but they tend to be less active in cool, damp soil. To jumpstart their effect, you can use what is called an inoculant, a powder containing millions of rhizobia. You can either coat the seeds by shaking them in a plastic bag with the inoculant or simply mix the powder into the planting soil.
There’s no general agreement about the benefits of using inoculant, but it does seem to help in cooler soils. I've never tried it, myself. I prefer to wait until the soil warms a bit, before planting.