New constraint on the varying fine structure constant - Univers Invisible

Since Dirac’s large number hypothesis , there have beenmany theories that allow the time variation of physicalconstants, including some unification theories such as stringtheory.In the framework of these theories, it is very natural thatmultiple constants vary simultaneously.Usually, time variation is thought to be induced by adynamical scalar field, which may be the quintessence fieldand there may be some link between varying physicalconstants and dark energy.Invisible Universe2/20

Therefore, seeking time variation of physical constantsobservationally is directly connected with testing unknownhigh ‐energy physics or investigating the origin of dark energy,so it is an important task.In this talk, we mainly focus on the fine structure constantin the case other physical constants also changein time, using CMB data .The parameter is .For simplicity, we do not consider spatial variation ofphysical constants.Invisible Universe3/20

Constraint from Oklo natural reactor (Fujii et al.,2002) Constraint from spectra of quasars(Murphy et al.,2008) Constraint from BBN(Ichikawa and Kawasaki, 2002)Constraint from CMB( )→Complementary to these observations and hasmany advantages such as “good understanding of thephysics” or “high precision data of WMAP”Invisible Universe4/20

Suggestion by Kaplinghat et al.(1999) and Hannestad (1999)⇒At MAP or PLANCK level , BOOMERanG・MAXIMA・COBE [Landau et al.(2001)]: WMAP 1‐year [Ichikawa et al.(2003)]: WMAP 5‐year [Nakashima et al.(2008)]:(Constraints are shown at 95%C.L.)Above results were obtained in the case of varying onlyCan the simultaneous variation of other physicalconstants change these results?Invisible Universe5/20

Before going into the details of the simultaneous variation,we review the relation between each physical constant andthe CMB temperature anisotropy spectrum.In this talk, we deal with three physical constants: the finestructure constant , the electron mass and the protonmass .Revealing how the time variations of these physicalconstants change the CMB spectrum tells whether or not wecan constrain the time variations of these constants from theobservational CMB data.Invisible Universe6/20

(Previous works)[ Hannestad(1999) Kaplinghat et al. (1999) Kujat et al. (2000) ]• Changing the value of and affects the CMB powerspectrum mainly through the change of the recombinationprocess.• Intuitively, their effect on the recombination process isunderstood by Saha equation ( chemical equilibrium approx.)Binding energy:We can expect that larger and results in1,the earlier recombination.2,the rapid recombination.Invisible Universe7/20

Visibility functionvisibility functionWe assume that isconstant during therecombination process.conformal timeThe larger values of andlead to1, the earlier recombination2, the narrower peaks ofthe visibility functionvisibility functionconformal timeInvisible Universe8/20

Larger Δααが大The narrower peaks of→ decrease of the small‐scalediffusion damping effectLarger ΔαThe earlier recombination →・shift of the peaksto the higher multipoles.・increase of the height of thepeaks due to ISW effect.Larger ΔmeLarger ΔmeInvisible Universe9/20

mp in the CMBThe time variation of the proton mass affects CMBmainly through thy baryon energy density parameter .Since in good approximation, we getThus, two parameters and play almostthe same roles in the CMB physics.However, the recombination process is mainly describedby the baryon number density parameterand actually CMB can discriminate these two parametersthrough .Invisible Universe10/20

mp in the CMBBecause of the last slide’s argument, we can expect that theeffect of changing and on the CMB powerspectrum are very similar.From the plot forthree different values of, we canrecognize the feature,which is well‐known inchanging , that theheight of odd peaksincreases relative to thatof even peaks.Invisible Universe11/20

Quantitative estimation for degeneracy:the Position of the First Acoustic Peakwhere.These four quantities characterize the shape of CMBangular power spectrum.Fiducial values are[Hu, Fukugita, Zaldarriaga and Tegmark (2001) ]Invisible Universe12/20

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Simultaneous Variation ofPhysical Constants In the previous works , simultaneous variation of andwere considered. [Olive et al. (1999) , Ichikawa et al. (2006)]The model : low energy effective action of a string theoryThe relation through• is a dilaton field.•Invisible Universe14/20

Simultaneous Variation ofPhysical ConstantsIn the same model, QCD energy scale can change.⇒ From , can also change!One‐loop renormalization equation suggests that⇒⇒large factorIn this model, small causes large .Invisible Universe15/20

Results‣ We use “WMAP5yr Data” ( & HST ).‣ Parameter estimations are implemented by MCMC method(using modified COSMOMC code [ Lewis and Bridle(2002) ] )‣ We assume the flat‐ΛCDM model.‣ Parameters are&Marginalized Posterior Distributionα&m e &m pα only(95% C.L.)5yr :varying only Δα[ Nakashima et al.,2008 ]Invisible Universe16/20

Comparing 1-D Marginalized Distributionsα&m e &m p α&m eα onlyConstraint on is improved ,however that on made worse.Invisible Universe17/20

Comparing 1-D Marginalized Distributionsvaryingonly m pvaryingα&m e &m pTwo marginalized plots of are very similar , whichimplies that the dominant factor in constraining the variationof physical constants is .Invisible Universe18/20

2D analysis on the parameter valuesat the recombination epochIn order to check our analysis, we use the fact that CMB issensitive to the parameters’ values at the recombination epoch.Thus, we expect that the limits on are the same orderfor two cases.case.1Varying only( Plotted isactually itself )case.2Varying all the physicalconstants( Plotted is actually)Invisible Universe19/20

Conclusion• We have obtained the <strong>constraint</strong> on the variation of the finestructure constant considering simultaneous time variation ofother physical constant: the electron mass and the protonmass , which is based on the specific model including thevariation of .• Resultant <strong>constraint</strong> on at 95%C.L.-0.0083 < Δα/α < 0.0018Δα only : -0.028 < Δα/α < 0.026Δα & Δmeonly : -0.025 < Δα/α < 0.019•This <strong>constraint</strong> is very stringent and it is expected that futuredata such as PLANCK may provide the non‐null variation result.Invisible Universe20/20

Additional Limits from our analysis: the proton‐to‐electron mass ratio →: the dilaton field variation→These <strong>constraint</strong>s are not so stringent compared with thosefrom other observations, but are very meaningful because theprevious works could not have limited in the CMB epoch.July 2, 2009 Invisible Universe21/20

Conclusion• We have updated the <strong>constraint</strong> on the time variation of αusing WMAP 5‐year data.• Resultant <strong>constraint</strong>s are, at 95%C.L,With HST : -0.028 < Δα/α < 0.026Without HST (WMAP only) : -0.050 < Δα/α < 0.042• Refined CMB‐Polarization data will give more stringent limit→ WMAP 8‐year or PLANCK data will fit this purpose !Future Forecast (CMB only)[ Rocha et al.(2003) ]・PLANCK : |Δα/α| < 0.0031 at 68%C.L.・Cosmic Variance Limited : |Δα/α| < 0.0010 at 68%C.L.The 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)22/13

Time variation of fundamental physical constant is the longstandingissue.e.g.) Dirac’s Large Number Hypothesis(1937) Recent theoretical progress motivates the possibility.・Model from Superstring Theorye.g.)Heterotic string theory ‐ tree level effective actionThe 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)23/13

Among various physical constants, we feature fine structureconstant . We do not consider about specific models of time variationof α. We just give the <strong>constraint</strong> on the time variation of α ata given time from observation (especially, Cosmic MicrowaveBackground). Parameter is We do not consider spatial variation of physical constantThe 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)24/13

BBNRelation between Helium mass fraction and fine structureconstant α is model‐dependent.Detailed calculation of BBN needs strong or weak gaugecoupling constants, and we must include these time variationsbesides that of α ,which results in larger uncertainties.CMBCMB is almost independent of the other gauge couplings.Physics of CMB is fully understood, and the effect of α is alsovery clear.There are plentiful of high precision data ( WMAP!).The 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)25/13

[ Hannested(1999) Kaplinghat et al. (1999) ]baryon‐photonliquid● obsfreestreaminglast scatteringsurface (LSS) ~Recombination ~z~1100Effect of variation of αon the CMBtemperature anisotropy: Visibility FunctionThe 18th Workshop on General Relativity and Gravitation in Japan (JGRG18): Optical Depth26/13

Recombination & visibility functionRecombination process is mainly described by+α[Seager, Sasselov and Scott (1999)] Numerical calculation is implemented by modified RECFASTcode. During recombination, we assume that the value of isconstant = →The 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)27/13

Ionization fractionredshift zredshift z &ionization fractionThe larger α causes・the earlierrecombination・the narrower widthofvisibility functionconformal timeconformal time &visibility functionThe 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)28/13

Earlier recombination →・Shift of peaks to higher multipole・Enhanced Early ISW effectαが 大Larger ΔαNarrower width of →αが 大Weakend Silk Damping effectLarger ΔαThe 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)29/13

Marginalized DistributionsWith and without HSTWith HSTWithout HSTWith HSTWithout HSTWithout HST:The 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)30/13

1-D Marginalized DistributionsWMAP3yr vs WMAP5yrWMAP 5yrWMAP 3yrBelow:[ Dunkley et al.,2008 ]The 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)31/15

1-D Marginalized Distributionsw=‐1 vsw≠‐1w≠‐1 with Δαw=‐1 with ΔαThe 18th Workshop on General Relativity and Gravitation in Japan (JGRG18)32/15