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1、TheHubbleDiagramofTypeIaSupernovaeinNon-UniformPressureUniversesMariuszP.D¸abrowski1,21AstronomyCentre,UniversityofSussex,Falmer,BrightonBN19QH,UK2InstituteofPhysics,UniversityofSzczecin,Wielkopolska15,70-451Szczecin,PolandMartinA.Hendry,2,31AstronomyCentre,UniversityofSussex,Falmer,BrightonBN19QH
2、,UK3DeptofPhysicsandAstronomy,UniversityofGlasgow,GlasgowG128QQ,UKReceived;acceptedarXiv:astro-ph/9704123v218Nov1997–2–ABSTRACTWeusetheredshift-magnituderelation,asderivedbyD¸abrowski(1995),forthetwoexactnon-uniformpressuresphericallysymmetricStephaniuniverseswiththeobserverpositionedatthecenterof
3、symmetry,totesttheagreementofthesemodelswithrecentobservationsofhighredshifttypeIasupernovae(SNIa),asreportedinPerlmutteretal.(1997).Byaparticularchoiceofmodelparameters,weshowthatthesemodelscangiveanexcellentfittotheobservedredshiftsand(corrected)BbandapparentmagnitudesofthePerlmutteretal.data,but
4、foranageoftheUniversewhichistypicallyabouttwoGyr–andmaybemorethanthreeGyr–greaterthaninthecorrespondingFriedmannmodel,forwhichnon-negativevaluesofthedecelerationparameterappeartobefavouredbythedata.Weshowthatthisageincreaseisobtainedforawiderangeofthenon-uniformpressureparametersoftheStephanimodel
5、s.Weclaimthispaperisthefirstattempttocompareinhomogeneousmodelsoftheuniversewithrealastronomicaldata.SeveralrecentcalibrationsoftheHubbleparameter,fromtheHubblediagramofSNIaandotherdistanceindicators,indicateavalueofH0≃65,andaHubbletimeof∼15Gyr.BasedonthisvalueforH0andassumingΛ≥0,theP97datawouldimp
6、lyaFriedmannageofatmost13Gyrandinfactabest-fit(forq0=0.5)ageofonly10Gyr.OurStephanimodels,ontheotherhand,cangiveagoodfittotheP97datawithanageofupto15Gyr.TheStephanimodelsconsideredherecould,therefore,significantlyalleviatetheconflictbetweenrecentcosmologicalandastrophysicalagepredictions.Thechoiceofmo
7、delparametersisquiterobust:inordertoobtainagoodfittothecurrentP97data,–3–onerequiresonlythatthenon-uniformpressureparameter,a,inoneofthemodelsisnegativeandsatisfies
8、a
9、<2s−2Mpc−1.Thislimit∼3kmgivesavaluefortheaccele
