Can they travel outside the US before the approval of the 1130 application?

They will need an I-131 advance parole application filed and approved before they can travel, assuming the I-130 AND I-485 were filed at the same time. If only the I-130 was filed there may be some problems.

You do not want to do anything that could jeopardize a case. With that being said you should have an experienced Immigration Attorney look over everything to guide you in the right direction. The money spent for a consultation, whether in person or via telephone, is usually well worth it if it helps or prevents a negative consequence.

If you only filed the I-130 and not the I-485 along with that, they can travel back to their home country but they may not be allowed to come back in as visitors now that there is a pending I-130 petition. They may have to stay there until they can consular process for their immigrant visas (9-12 months from filing). If they want to travel and it is not urgent, you can file for I-485 and with that they will get interim travel documents. They usually arrive within 90 days of filing. That way they can travel internationally and return to continue with their permanent residence processing. Also, if you want both your parents to get green cards, you need to make sure you filed two separate I-130 petitions as there are no derivatives allowed on immediate relative petitions.

In addition to filing the I-130's, your parents should also apply for adjustment of status on form I-485 and advance parole on form I-131. The advance parole will allow them to travel and return from abroad while their applications for adjustment of status are being processed. After filing for adjustment of status, they should not travel until they have received the advance parole or USCIS may terminate their applications.

If you filed an I-130 application, did you consult with an attorney? If so, ask them. If not, please check the USCIS website for guidance or employ an immigration attorney for the answer to this question. Too many unknowns to answer your question as posed.