My eyes could be failing me, but that doesn't look like Asparagus to me, but rather, 'Plumosa Fern.' It's not really a fern, more closely related to Asparagus the vegetable, if I remember correctly, but it's a houseplant really (although, some do grow these outdoors in more mild climates). It also goes by the name 'Asparagus Fern.' It's new growth looks like tiny asparagus, hence the monkier (there are other asparagus ferns that do the same), but I don't believe it's edible.
