LETTERSAnupperlimitonthestochasticgravitational-wavebackgroundofcosmologicaloriginTheLIGOScientificCollaboration*&TheVirgoCollaboration*Astochasticbackgroundofgravitationalwavesisexpectedtoarisefromasuperpositionofalargenumberofunresolvedgravitational-wavesourcesofastrophysicalandcosmologicalorigin.ItshouldcarryuniquesignaturesfromtheearliestepochsintheevolutionoftheUniverse,inaccessibletostandardastrophysicalobserva-tions1.DirectmeasurementsoftheamplitudeofthisbackgroundarethereforeoffundamentalimportanceforunderstandingtheevolutionoftheUniversewhenitwasyoungerthanoneminute.Herewereportlimitsontheamplitudeofthestochasticgravitational-wavebackgroundusingthedatafromatwo-yearsci-encerunoftheLaserInterferometerGravitational-waveObser-vatory2(LIGO).Ourresultconstrainstheenergydensityofthestochasticgravitational-wavebackgroundnormalizedbythecriticalenergydensityoftheUniverse,inthefrequencybandaround100Hz,tobe,6.931026at95%confidence.ThedataruleoutmodelsofearlyUniverseevolutionwithrelativelylargeequation-of-stateparameter3,aswellascosmic(super)stringmodelswithrelativelysmallstringtension4thatarefavouredinsomestringtheorymodels5.ThissearchforthestochasticbackgroundimprovesontheindirectlimitsfromBigBangnucleosynthesis1,6andcosmicmicrowavebackground7at100Hz.Accordingtothegeneraltheoryofrelativity,gravitationalwavesareproducedbyacceleratingmassdistributionswithaquadrupole(orhigher)moment.Moreover,intheearlyphasesoftheevolutionoftheUniverse,theycanbeproducedbythemechanismofamplifica-tionofvacuumfluctuations.Onceproduced,gravitationalwavestravelthroughspace-timeatthespeedoflight,andareessentiallyunaffectedbythemattertheyencounter.Asaresult,gravitationalwavesemittedshortlyaftertheBigBang(andobservedtoday)wouldcarryunalteredinformationaboutthephysicalprocessesthatgeneratedthem.Thesewavesareexpectedtobegeneratedbyalargenumberofunresolvedsources,formingastochasticgravitational-wa