Factory-girl create that bypasses my model validation

This isn't very specific to FactoryGirl, but you can always bypass validations when saving models via save(validate: false):

describe ".current" do
  let!(:current_group) { FactoryGirl.create(:group) }

  let!(:old_group) do
    g = FactoryGirl.build(:group, expiry: Time.now - 3.days)
    g.save(validate: false)
    g
 end
      
 specify { Group.current.should == [current_group] }
end

I prefer this solution from https://github.com/thoughtbot/factory_girl/issues/578.

Inside the factory:

trait :without_validations do
  to_create { |instance| instance.save(validate: false) }
end

It's a bad idea to skip validations by default in factory. Some hair will be pulled out finding that.

The nicest way, I think:

trait :skip_validate do
  to_create {|instance| instance.save(validate: false)}
end

Then in your test:

create(:group, :skip_validate, expiry: Time.now + 1.week)

foo = build(:foo).tap { |u| u.save(validate: false) }

For this specific date-baesd validation case, you could also use the timecop gem to temporarily alter time to simulate the old record being created in the past.