Can Social Security benefits be received retroactively?

The answer is contingent upon reaching full retirement age - retroactive benefits can not be claimed if they are taken before FRA.

The answer is contingent upon reaching full retirement age (FRA). "Retroactive" benefits can not be claimed if benefits are taken before FRA. Having reached FRA and you apply one to five months after that date, retroactive benefits can be paid in a lump sum. For any filing at six months or greater, a lump sum totaling six months can be paid. 

Keep in mind that a retroactive lump sum payment will sacrifice the Delayed Retirement Credits (DRCs) earned for that time frame, ultimately affecting the benefit amount going forward. Given that DRCs accrue at 8% per year, the adjustment would reduce the benefit amount by 0.67% for each back-paid month.  For example, a six-month retroactive payment would have a 4% impact on the benefit amount.