Observing Loop Quantum Cosmology through ... - Univers Invisible

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Observing Loop Quantum Cosmology through ... - Univers Invisible

ObservingLoopQuantumGravitythroughcosmologicalperturba8ons?‐J.Grain(IAS,Orsay)‐‐A.Barrau,A.Gorecki&T.Cailleteau(LPSC,Grenoble)‐HowtounifyGeneralRela8vityandQuantumMechanics?TheoreHcalquesHonNeedshighenergeHcphenomenaInfla8onaryparadigmintheveryearlyUniverseHighenergeHcphenomenonObservaHonalconsequencesAbridgebetweententa8vetheoryandobserva8onsJulienGrain InvisibleUniverse20091


ArapidsketchofLoopQuantumGravity(LQG)€« Can we construct a quantum theory of spacetime based only on theexperimentally well confirmed principles of general relativity and quantummechanics ? » L. Smolin, hep-th/0408048GRclassicallyre‐wriHenwithAshtekarvariables:densiHzedtriad E a i≡ det(e b j) −1 ae iiAshtekarconnecHon A a= Γ i ia+ γK aQuan8za8onbyuseofholonomiesandfluxes(backgroundindependence)€F(E) ∝ ∫ τ i E a in ad 2 sS€⎛h(A) ∝exp⎜∫⎝C⎞τ iA i au a dλ⎟⎠- The area, volume and length operators have a discrete,finite spectra.€- The horizon entropy is completely explained.- Singularities are eliminated.- The hawking radiation is recovered.- Ultraviolet divergences of QFT are not present.- Loop quantum cosmology is on the way….JulienGrain InvisibleUniverse2009 2


LQGinthecosmologicalframework:BackgroundFLRW‐reducedformulaHonofLQG:LoopQuantumCosmology(LQC)ds 2 = a 2 (η) dη 2 −δ ijdx i dx j( )Backgroundequa8on:classicalresults€H 2 = 8πG3 ρΦ ˙ + 3HΦ ˙ + δVδΦ = 0Seeworksof:Ashtekar,Bojowald,Lewandowski,Pawlowski,Singh,Corichi…Forareview,see:Calcagni&Hossain,Adv.Sci.Le].2,184(2009)Backgroundequa8on:quantumcorrectedresultsH 2 = 8πG3 ρ × ⎡S(a) − ρ ⎤⎢ ⎥⎣ ρ c ⎦⎛Φ ˙ D+ 3H − ˙ (a) ⎞⎜ ⎟ Φ ˙ + D(a) δV⎝ D(a) ⎠ δΦ = 0bouncingcosmology{quantumphase+inflaHon}JulienGrain InvisibleUniverse2009 3


LQGinthecosmologicalframework:GravitywavesPerturbedFLRWmetricds 2 = a 2 (η) dη 2 − ( δ ij+ h ij )dx i dx j( )Gravitywavesequa8on:classicalresults€d 2 φ kdη + ⎛k 2 − a ′ ⎞⎜ ⎟ φ = 02 ⎝ a ⎠(k )with φ k≡ a(η)h ijGravitywavesequa8on:quantumcorrectedresultsd 2 φ kdη + ⎛k 2 − a ′ 2 a −V (a,γ) ⎞⎜holo ⎟ φ⎝⎠k= 0 with φ k≡ a(η)h ijd 2 ψ kdη + ⎛S 2 k 2 − a ′ 2 a −V ⎞⎜I −V(a,S,γ) ⎟ ψ k= 0 with ψ k≡ a(η)h ij⎝⎠S(k)(k )• Modifiedbackground• Modified«Dispersionrela8on»Bojowald&Hossain,Phys.Rev.D77023508(2008)JulienGrain InvisibleUniverse2009 4


Slow‐rollinfla8on:Holonomycorrec8onsClassicalinfla8onarybackgrounda(η) ∝ η −1−ε!"#$%#&'(!(&)$*#$+,*-.**/ !0$%$+'(*1$('#&2"""5*67'%#7,*0+'2*8"++$8#$9€a ′ a = 2 + 3εη 2V holo∝− E infM Pl1€k 2η 2−2ε !Time:"%;"+,'( #&,$J.Grain&A.Barrau,Phys.Rev.Le].102081301(2009)JulienGrain InvisibleUniverse2009 5


Slow‐rollinfla8on:Holonomycorrec8ons⎛(IRP ) T= C 1 ⎜⎝E infM Pl⎞⎟⎠−3 εk 3⎛(UVP ) (GRT= P ) T= C 2 ⎜⎝E infM Pl⎞⎟⎠2k −2ε€Largescales(IRregim,k→0)Smallscales(UVregim,k→∞)J.Grain&A.Barrau,Phys.Rev.Le].102081301(2009)JulienGrain InvisibleUniverse2009 6


Slow‐rollinfla8on:Inverse‐volumecorrec8onsV I −V= − a ′a′ SS + 3 4⎛⎜⎝′ SS⎛S =1+ cste ×L ⎞Pl⎜ ⎟⎝ a(η) ⎠κ⎞⎟⎠2− S ′ 2Sanaly&callysolvedbymeansofκ(1+ ε) = 2Kummerfunc&ons €⎛ ⎛(IRP ) T(k) = cste × k 3 exp cste × E ⎞ ⎞inf⎜ ⎜ ⎟ k −1⎟⎝ ⎝ M Pl ⎠ ⎠⎡ ⎛(UVP ) (GRT(k) = P ) T(k) × 1+ cste × E ⎞⎢inf⎜ ⎟⎣ ⎢ ⎝ M Pl ⎠2k −2⎤⎥⎦ ⎥3/455$*%".6(7&8"'$.&%8$9:.+,&;1212021?1>121=12112=12


Gravitywaves:Cumula8ngtheeffectsGravitywavesequa8on:quantumcorrectedresultsd 2 ψ kdη + ⎛S 2 k 2 − a ′ 2 a −V (a,S,γ) − ˜ ⎞⎜I −VV holo(D,S,a,γ) ⎟ ψ⎝⎠k= 0 with ψ k≡ a(η)h ijS(k)analy&callysolvedbymeansκ = 2 and ε = 0ofKummerfunc&ons⎛ ⎛(IRP ) T(k) = cste × k 3 exp cste × E ⎞ ⎞inf⎜ ⎜ ⎟ k −1⎟⎝ ⎝ M Pl ⎠ ⎠(UVP ) (GRT(k) = P ) T(k) × k −4 E 2inf2/ 3M Pl⎡ ⎛× ⎢ 1+ cste × E inf⎜⎣ ⎢ ⎝ M Pl⎞⎟⎠2k −2⎤⎥⎦ ⎥inverse‐volumedominant{holonomy+inverse‐volume}T.Cailleteau,J.Grain,A.Barrau&A.Gorecki,inprep.JulienGrain InvisibleUniverse2009 8


Whatistheanswer?Whatisdone:Holonomy&Inverse‐volumecorrecHonimplementedinstandardinfla&onforgravitywaves• Qualita8velyholonomybluespectrumintheIRinverse‐volumeveryredspectrumintheIR,strongHlt&runnninginverse‐volume>>holonomy• Quan8ta8vely:propagatesthosespectrauptoB‐modeHolonomyunobservableNeedstobedoneforinverse‐volumeWhatneedstobedone:• Holonomy&Inverse‐volumecorrecHonimplementedinacompletequantumbackgroundCopeland,Mulryne,Nunes,Shaeri,Phys.Rev.D77023510(2009)&Phys.Rev.D79023508(2009)Mielczarek&Szydlowski,Phys.Le].B65720(2007)&arXiv:0710.2742Mielczarek,JCAP811011(2008)&arXiv:0902.2490• ScalarperturbaHons(observedintheTandE‐polarizaHon)Bojowald,Hossain,Kagan,Shankaranarayanan,Phys.Rev.D79043505(2009)JulienGrain InvisibleUniverse2009 9


ToconcludeCosmologyisnowintheplaygroundofprecisionscience.Quantumgravity(generallyspeaking)isintheplaygroundofcosmology…JulienGrain InvisibleUniverse2009 10

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