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Astron.Nachr./ANxxx(xxxx)x,xxx–xxx Primordial magnetic fields and CMB anisotropies KANDASWAMY SUBRAMANIAN IUCAA,PostBag4,PuneUniversityCampus,Ganeshkhind,Pune411007,India 6 0 0 2 n a J Abstract. Possible signatures of primordial magnetic fields on the Cosmic Microwave Background (CMB) temperature andpolarizationanisotropiesarereviewed.Thesignalsthatcouldbesearchedforincludeexcesstemperatureanisotropies 5 particularlyatsmallangularscalesbelowtheSilkdampingscale,B-modepolarization,andnon-Gaussianstatistics.Afield 2 atafewnGlevelproducestemperatureanisotropiesatthe5µKlevel,andB-modepolarizationanisotropies10timessmaller, 1 andisthereforepotentiallydetectableviatheCMBanisotropies. Anevensmallerfield,withB0 < 0.1nG,couldleadto v structureformationathighredshiftz >15,andhencenaturallyexplainanearlyre-ionizationoftheUniverse. 0 7 Keywords:cosmicmicrowavebackground–cosmology:theory–magneticfields 5 1 (cid:13)c0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim 0 6 0 1. Introduction fluxfreezing,duringgalaxyand cluster formationmayease / h the problemsof the dynamo.It is then worth considering if p Magnetic fields are ubiquitous in astrophysical systems but onecandetectorconstrainsuchprimordialfields. - o theiroriginisstillamystery.Onepossibilityisthattheyarise Here we review possible probes of primordial mag- r duetothedynamoamplificationofsmallseedfields.Thedy- netic fields, which use CMB temperature and polarization t s namo paradigm has been extensively studied (cf. Branden- anisotropies.Indeedtherearealsoanumberofpuzzlingfea- a : burg&Subramanian2005forarecentreview),butpotential tures associated with current CMB observations, which are v problemsremaintobe surmounted.These involvetheques- not fully understood.These include (a) the excess power in i X tionofwhethermeanfielddynamocoefficientsforthegalac- temperatureanisotropiesdetectedbytheCosmicBackground r ticdynamoarecatastrophicallyquenchedornot,andwhether Imager(CBI)experimentonsmallangularscales(Readhead a fields generated by the fluctuation dynamo in clusters have etal.2004),(b)theobservationsbytheWilkinsonMicrowave a sufficient degree of coherence to explain the observations AnisotropyProbe(WMAP)satelliteforanunexpectedlyhigh (Subramanian,Shukurov&Haugen2006;Shukurov,Subra- redshiftofre-ionization(Kogutetal.2003),(c)thelowCMB manian&Haugen2006;Schekochihinetal.2005). quadrupole anisotropy seen compared to theoretical expec- Aninterestingalternativeisthattheobservedlarge-scale tations (cf. Spergelet al. 2003), and (d) various asymmetry magnetic fields are a relic from the early Universe, aris- andalignmenteffects(cf.deOliveira-Costaetal.2004).Such ing perhaps during inflation or some other phase transition featuresalso encourageustokeepopenpossibilitiesofnew (Turner&Widrow1988;Ratra1992;andreviewsbyWidrow physicaleffects,perhapshavingtodowithprimordialfields! 2002;Giovannini2005a).Itiswellknownthatscalar(density or potential) perturbations and gravitational waves (or tensor perturbations) can be generated during inflation. Could 2. MagneticfieldevolutionintheearlyUniverse magnetic field perturbations could also be generated? In- deedmechanismsinvolving,say,stringtheory,forthegener- Primordialmagnetogenesisscenariosgenerallyleadtofields ationofprimordialfieldshavebeenreviewedinthismeeting which are Gaussian random, characterized by a spectrum (Gasperini 2006 and references therein). These generically M(k) (see below). This spectrum is normalized by giving involvethebreakingoftheconformalinvarianceoftheelec- thefieldstrengthB0,atsomefiducialscaleandasmeasured tromagnetic action, and the predicted amplitudes are rather atthepresentepoch,assumingitdecreaseswithexpansionas modeldependent.Nevertheless,ifaprimordialmagneticfield B = B0/a2(t), wherea(t)is theexpansionfactor.We take withapresent-daystrengthofB ∼ 10−9 Gandcoherenton B0 to be a free parametersince the predictionsforits value Mpcscalesisgenerated,itcanstronglyinfluenceGalaxyfor- from magnetogenesistheories are highly modeland param- mation. An even weaker field, sheared and amplified due to eter sensitive. Note that the magnetic and radiation energy 3 CMBSIGNALSFROMTANGLEDMAGNETICFIELDS densitiesbothscalewithexpansionas1/a4.Sowecanchar- theCMBleadtothe’primary’anisotropiesintheCMBtem- acterizethemagneticfieldeffectbytheratioB02/(8πργ0) ∼ peratureasseenatpresentepoch.Furthermore,variationsin 10−7B−29whereργ0isthepresent-dayenergydensityinradi- interveninggravitationaland scattering effects, which influ- ation,andB−9 =B0/(10−9G).Magneticstressesarethere- encetheCMBphotonsastheycometousfromthelastscat- fore small comparedto the radiation pressure for nG fields. teringsurface,can leadto additionalsecondaryanisotropies The scalar, vector and tensor parts of the perturbed stress (cf.Subramanian2005forareview).TheCMBtemperature tensor associated with magnetic fields lead to correspond- anisotropies∆T(θ,φ)/T areexpandedinsphericalharmon- ingmetricperturbations.Furtherthecompressiblepartofthe ics, Lorentzforceleadstocompressible(scalar)fluidvelocityand ∆T (θ,φ)= a Y (θ,φ); a∗ =(−1)ma , (1) associateddensityperturbations,whileitsvorticalpartleads T lm lm lm l−m to vortical(vector)fluidvelocityperturbation.Themagneti- Xlm and expressed in terms of their angular power spectrum C callyinducedcompressiblefluidperturbations,fornGfields, l are highly subdominantcompared to those due to the infla- wherethe ensemble averagehalma∗l′m′i = Clδll′δmm′. The meansquaretemperaturefractionalanisotropyisgivenby tionaryscalarmodes.Moreimportantin ourcontextwillbe the Alfveń mode driven by the rotational componentof the h(∆T)2i 2l+1 l(l+1)C l = C ≈ dlnl Lorentzforce,especiallysincetheydecaywithoutsuchmag- T2 l 4π Z 2π Xl netic driving.We recall below some featuresof their evolu- with the last approximate equality valid for large l. So tion(Jedamzik,Katalinic&Olinto1998(JKO);Subramanian (l(l + 1)C)/2π measures the power in the temperature &Barrow1998(SB98a)). l anisotropies per logarithmic interval in l space. (This com- TheAlfveńmodeoscillatesnegligiblyonMpcScalesby bination is used because scale-invariant potential perturba- recombination,withthephaseofitsoscillationχ=kV η ∼ A tions generate anisotropies, which at large scales (small l) 10−2B−9(k/0.2hMpc−1)(η/η∗). Here the Alfveń velocity have a nearly constant l(l + 1)C). A convenient charac- is VA ∼ 3.8×10−4cB−9, k the comovingwavenumber,η terization of the scale-dependent tlemperature anisotropy is theconformaltimewithη itsvalueatrecombination.Unlike ∗ ∆T(l) = T[l(l+1)C )/2π]1/2.ThisisplottedinFigure1, thecompressionalmode,whichgetsstronglydampedbelow l asadashed-triple-dottedlineforastandardΛCDMmodel. the Silk scale L due to radiative viscosity (Silk 1967), the S Primordialmagneticfieldsinduceavarietyofadditional Alfveń mode behaves like an over-damped oscillator. Note signals on the CMB. An uniform field would for exam- thatforanover-dampedoscillatorthereisonenormalmode ple select out a special direction, lead to anisotropic expan- which isstronglydampedandanotheronewherethe veloc- sion around this direction, hence leading to a quadrupole ity starts from zero and freezes at the terminal velocity till anisotropy.ThedegreeofisotropyoftheCMBthenimplies the damping becomes weak at a latter epoch. The net re- alimitofseveralnGonsuchafield(Barrow,Ferreira&Silk sultisthattheAlfveńmodesurvivesSilkdampingforscales 1997).Comparablelimitsmayobtain,atleastfortheuniform bigger than L ∼ (V /c)L ≪ L , the canonical Silk A A S S component,fromupperlimitstotheIGMFaradayrotationof damping scale (JKO; SB98a). The resulting baryon veloc- high redshift quasars (cf. Blasi et al. 1999). For inhomoge- ity is potentiallydetectable,since dueto the Dopplereffect, neous,tangledprimordialfields,thespatialinhomogeneities CMBtemperatureanisotropies∆T/T ∼V/c∼f χV /c∼ d A aroundthesurfaceoflastscattering,duetomagneticallyin- 10−3fdχ(B−9/3) are induced. Here fd < 1 takes into ac- duced perturbations(scalar, vector and tensor), lead to both countpossible dampingeffectsdue the thickness of the last largeand small angularscale anisotropiesin the CMB tem- scattering surface. One sees that for nG fields, significant peratureandpolarization. temperature anisotropies with ∆T/T ∼ 10−6 can result, For magneticallyinducedscalar perturbations,the ques- even for f χ ∼ 10−3. Detailed computations bear out this d tionoftheinitialconditionshasonlybeenanalyzedinsome simpleestimateandshowthatthesignalpeaksonarcminute detailrecentlyinapaperbyGiovannini(2004),anddetailed scales,l ∼103(correspondingtotheanglesubtendedbythe predictionsoftheCMBanisotropies,forgeneralinitialcondi- Silkscaleatrecombination),andbecauseL ≪ L ,itis A Silk tions,areyettobeworkedout.(Forsomeapproximatetreat- significantevenbelowtheSilkscale. ments of the magnetosonic scalar modes see Adams et al. Afterrecombination,whenradiationdecouplesfromthe 1996; Koh & Lee 2000; Yamazaki, Ichiki & Kajino 2005). baryons, the cosmic pressure drops by a large factor of or- Further, scalar modes are dominated by the standard infla- der the photon to baryon ratio, n /n ≫ 1. The surviving γ b tionaryscalar perturbationandarealsodampedbyradiative tangled magnetic fields can now drive strong compressible viscositybelowtheSilkscale. motions and seed density fluctuations (Wassermann 1978; Much more work has been done on the vector modes SB98a; Sethi 2003), which could well be very important (Subramanian & Barrow 1998 (SB98b), 2002 (SB02); Se- in forming the first structures and leading to an early re- shadri & Subramanian 2001 (SS01); Mack, Kahniashvilli ionizationoftheUniverse(Sethi&Subramanian2005). & Kosowsky 2002; Subramanian, Seshadri & Barrow 2003 (SSB03);Lewis2004).Theytypicallylead toa temperature 3. CMBsignalsfrom tangled magneticfields anisotropy∆T ∼5µK(B−9/3)2atl ∼1000andabove(see below). A comparable signal arises at large angular scales, CMBanisotropiesingeneralarise intwoways.Firstly,spa- l < 100, due to gravitational wave perturbations (tensors). tial inhomogeneitiesaroundthe surface of last scattering of All modes lead to much smaller polarization signals. The 3.1 Vectormodes 3 CMBSIGNALSFROMTANGLEDMAGNETICFIELDS tensor and vector components in particular also lead to B- Here v(k,η) is the magnitude of the rotational component type polarization,which can help distinguishmagnetic field of the fluid velocity vi in Fourier space, and η0 the present inducedsignalsfromthoseduetoinflationaryscalarmodes. value of η. The ’visibility function’ g(η0,η) determines the In addition, the presence of tangled magnetic fields in probability that a photon reaches us at epoch η0 if it was the intergalactic medium can cause Faraday rotation of the last scattered at the epoch η. So it weighs the contribu- polarizedcomponentofthe CMB, leadingto the generation tion at any conformaltime η by the probabilityof last scat- of new B-type signals from the inflationary E-mode signal. tering from that epoch. We have shown as a solid line in Theirdampinginthepre-recombinationeracanleadtospec- Fig. 3 the visibility function for a standard ΛCDM model. tral distortions of the CMB (Jedamzik, Katalinic & Olinto The spherical Bessel function of order l, the jl(z) term, 2000),whiletheirdampinginthepost-recombinationeracan projectsvariationsin space, at the conformaltime η around changetheionizationandthermalhistoryoftheUniverse.A the last scattering epoch, to angular (or l) anisotropies at potentially important consequence which we discuss below thepresentepoch.ThesesphericalBesselfunctionsgenerally isthemagneticfieldinducedstructureformation,whichmay peakaroundk(η0−η)≈l.Themultipoleslarethenprobing be relevantto explain the early re-ionizationimplied by the generallyspatialscaleswithwavenumberk ∼ l/(η0−η)at WMAPdata.Wediscusssomeoftheseeffectsfurtherbelow, aroundlastscattering. focusing in more detail on vector modes and post recombi- Weassumethatb0isaGaussianrandomfield.ItsFourier nation effects, where we have been directly involved in the components satisfy < bi(k)b∗j(q) >= δk,qPij(k)M(k), computationofthemagneticsignals. where the magnetic power spectrum is normalized using a top hat filter in k-space, and taking k3M(k)/(2π2) = (B2/2)(n+3)(k/k )3+n withn > −3.We generallynor- 0 G 3.1. Vectormodes malizethefieldatk = 1hMpc−1.Thespectrumiscut-off G atk ,determinedbydissipativeprocesses. On galactic scales and above, the induced velocity due to c An analytic estimate of the temperature anisotropy, for the Lorentz forces is generally so small that it does not lead to any appreciable distortion of the initial field (JKO; kLS <1isthen(SB98b;SB02) SB98a). Hence, the magnetic field simply redshiftsaway as B−9 2 l l B(x,t) = b0(x)/a2. TheLorentzforceassociatedwith the ∆TB(l)≈5.8µK(cid:18) 3 (cid:19) (cid:18)500(cid:19)I(R ), (4) ∗ tangled field FL = F/(4πa5), with F = (∇×b0)×b0, whereasforscalessmallerthanSilkscaleswithkL >1, pushes the fluid to create rotational velocity perturbations. S 2 −3/2 ThesecanbeestimatedbyusingtheNavier-Stokesequation ∆T (l)≈13.0µK B−9 l I( l ). (5) forthebaryon-photonfluidintheexpandingUniverse, B (cid:18) 3 (cid:19) (cid:18)2000(cid:19) R ∗ 4 ∂v ρ da k2η P Fˆ HereI(k)isamodecouplingintegral ρ +ρ i + b + v = ij j. (2) (cid:18)3 γ b(cid:19) ∂t (cid:20) a dt a2 (cid:21) i 4πa5 I2(k) = 8(n+3)( k )6+2n; n<−3/2 3 k Here, ρ is the photon density, ρ the baryon density, and G γ b 28(n+3)2 k k η = (4/15)ργlγ the shear viscosity coefficient associated = ( )3( c )3+2n; n>−3/2. withthedampingduetophotons,wherelγisthephotonmean 15(3+2n) kG kG free path. The projection tensor, P (k) = [δ −k k /k2] Note that for n < −3/2, I is independent of k . For a ij ij i j c projects Fˆ, the Fourier component of F onto its transverse nearlyscale-invariantspectrum,say with n = −2.9,we get componentsperpendiculartok. ∆T(l) ∼ 4.7µK(l/1000)1.1 for scales larger than the Silk One can solve Eq. 2 in two asymptotic limits, which al- scale, and ∆T(l) ∼ 5.6µK(l/2000)−1.4 for scales smaller lowssemi-analyticestimatesofthesignals.Forscaleslarger than LS but largerthan Lγ. Largersignals will be expected thantheSilkscale,kL < 1,theradiativeviscousdamping forsteeperspectra,n>−2.9atthehigherlend. S can be neglected to get vi = 3PijFˆjD(η)/(16πρ0), where One can also do a similar calculation for the expected D(η) = η/(1+R ). Since |Fˆ | ∼ kV2, we get for large CMB polarizationanisotropy (SS01;SSB03). Note that po- ∗ ij A larizationoftheCMBarisesduetoThomsonscatteringofra- scales v/c ∼ χV /c, as in our earlier simple estimate. For A diationfromfreeelectronsandissourcedbythequadrupole scales smaller than the Silk scale, kL > 1, one assumes a S componentoftheCMBanisotropy.Forvectorperturbations, terminalvelocityapproximationtobalanceviscousdamping theB-typecontributiondominatesthepolarizationanisotropy with thedrivingduetotheLorentzforce.Thisthenleadsto D(η) ∼ 5/ck2L , and v/c ∼ (5/kL )V2/c2, where L is (HW97), unlike for inflationary scalar modes. Further, as γ γ A γ mentioned earlier, the vector mode signals can also be im- theco-movingphotonmeanfreepath. portantbelowtheSilkdampingscale(l≥103). TheangularpowerspectrumC ofCMBanisotropiesdue l We show in Figs. 1 and 2 the temperatureand polariza- torotationalvelocityperturbationsisgivenby(Hu&White tionanisotropyforthe magneticfield inducedvectormodes 1997(HW97)) obtained by evaluating the η and k integrals in Eq. (3) nu- ∞ k2dk l(l+1) merically.WeretaintheanalyticapproximationstoI(k)and C = 4π l Z0 2π2 2 vi(k). These curves show the build up of power in temper- × <|Z0η0dηg(η0,η)v(k,η)jl(kk((ηη00−−ηη)))|2 > (3) afrtoumretaanndgleBd-tmypaegnpeotliacrfiizealtdiosnwdhuicehtsourvvoirvteicSalilkpedratumrbpaintigonast 3 CMBSIGNALSFROMTANGLEDMAGNETICFIELDS 3.2 Tensormodes Fig.1. ∆T versus l predictions for different cosmological Fig.2. ∆TBB versus l predictions for different cosmologi- P models and M(k) ∝ kn, for B−9 = 3. The bold solid line cal models and magnetic power spectrum M(k) ∝ kn, for is for a canonicalflat, Λ-dominatedmodel,with ΩΛ = 0.7, B−9 = 3. The bold solid line is for a standard flat, Λ- Ωm =0.3,Ωbh2 =0.02,h=0.7andalmostscale-invariant dominated model, with ΩΛ = 0.73, Ωm = 0.27, Ωbh2 = spectrumn=−2.9.Thedottedcurve(....)obtainswhenone 0.0224,h = 0.71 and almost scale invariantspectrum n = changes to Ωm = 1 and ΩΛ = 0 model. The dashed line −2.9. The dashed curve obtains when one changes to n = is for the Λ-dominated model with a larger baryon density −2.5. The dotted curve gives results for a Ω = 1 and m Ωbh2 = 0.03, and a larger n = −2.5. We also show for ΩΛ = 0 model, with n = −2.9. We also show for qualita- qualitativecomparison(dashed-tripledottedcurve),thetem- tive comparison (dashed-dottedcurve), the B-type polariza- peratureanisotropyina’standard’ΛCDMmodel,computed tionanisotropyduetogravitationallensing,inthecanonical using CMBFAST (Seljak & Zaldarriaga 1996) with cosmo- ΛCDM model, computed using CMBFAST (Seljak & Zal- logical parameters as for the first model described above. darriaga1996).Thesignalduetomagnetictanglesdominate (AdaptedfromSB02andSSB03) forllargerthanabout1000.Finally,thethinsolidlinegives the expected galactic foreground contribution estimated by Prunetetal.(1998),whichisalsosmallerthanthepredicted highl∼1000−3000.Theeventualslowdeclineisduetothe signals.(AdaptedfromSSB03) dampingbyphotonviscosity,whichisonlyamilddeclineas the magneticallysourced vortical mode is over damped.By contrast, in the absence of magnetic tanglesthere is a sharp 3.2. Tensormodes cut-off due to Silk damping.Our numericalresults are con- Tangled magnetic fields also produce anisotropies on large sistent analytic estimates givenin Eqs. (4) and (5). A scale- angular scales, or small l, dominated by tensor metric per- invariant spectrum of tangled fields with B0 = 3 × 10−9 turbations induced by anisotropic magnetic stresses (Dur- Gauss,producesreducestemperatureanisotropiesatthe5µK rer, Ferreira & Kahniashvili 2000; Mack, Kahniashvili & level and B-type polarization anisotropies ∆T ∼ 0.3 − B Kosowsky2002;Caprini&Durrer2002;Giovannini2005b). 0.4µK between l ∼ 1000−3000. Larger signals result for Thetensormetricperturbationh obeystheequation steeperspectrawithn>−3.Notethattheanisotropiesinhot ij orcoldspotscouldbeseveraltimeslarger,becausethenon- h′′ +2Hh′ −∇2h =−16πGa2δTTT ij ij ij ij linear dependence of C on M(k) will imply non-Gaussian l where H = a′/a, a prime denotes derivative with respect statisticsfortheanisotropies. tothe conformaltime,andδTTT isthetransverse,traceless ij Thesemagneticallyinducedsignalscouldthereforecon- componentoftheenergymomentumtensor(duetothemag- tribute to the excess power detected by the CBI experi- neticfield).TheresultingCMBanisotropyisthencomputed ment.Adistinguishingfeature,comparedtosaytheSunyaev- using Zeldovich (SZ) effect (Zeldovich & Sunyaev 1969) canoni- 1 η0 callyinvokedtoexplaintheCBIexcess,willbeprovidedby (∆T/T)=− h′ ninjdη theB-typepolarizationsignals.Notethatiftheobservedex- 2Zηi ij cesspowerintheCBI experimentarisesfromtheSZeffect, where ni is a unit vector along the line of sight, and prime thisisnotexpectedtobestronglypolarized.Thespectralde- denotes a conformal time derivative. Using the formalism pendence of the SZ signal could also help to distinguish it describedin these papers, we estimate a tensor contribution from any magnetically induced signals, which are expected at small l < 100 of ∆T ∼ 7(B−9/3)2(l/100)0.1µK, for tobefrequencyindependent,atleastathighfrequencies. n = −2.9. (One has to account for neutrino anisotropic Recently, Lewis (2004) has done a detailed numerical stresscompensation(Lewis2004)afterneutrinodecoupling). computationofthevectormodesignalandfindsqualitatively Since we have to add this powerto the standardpowerpro- similarresultstothesemi-analyticalestimatesgivenabove. duced by inflationary scalar perturbations in quadrature, a 5 CONCLUSIONS tangled field with B−9 ∼ 3 will produce of order a few to 10 percent perturbation to the power in the standard CMB anisotropy at large angular scales. So if they are indeed de- tectedatlargel,belowtheSilkdampingscale,onewillalso havetoconsidertheireffectsseriouslyatlargeangularscales, especiallyin cosmologicalparameterestimation.Thetensor mode also contributes to the B-type polarization anisotropy atlargeangularscales(l < 100orso),with∆T < 0.1µK B forB−9 <3.Theproductionofgravitationalwaveshasbeen usedinanindirectmannerbyCaprini&Durrer(2002)toset strongupperlimitsonB0forspectrawithn>−2.5orso. 3.3. Faradayrotationduetoprimordialfields Another interesting effect of primordial fields is the the Faraday rotation it induces on the polarization of the CMB Fig.3.Visibilityfunctionfordifferentmodels.Thesolidand (Kosowsky&Loeb1996;Kosowskyetal.2005;Campanelli the dotted curves are for the standard recombination and a etal.2005).Therotationangleisabout model in which the Universe re-ionizes at z = 17, respectively. The dashed curve corresponds to a decaying turbu- η0 ∆Φ = λ20 (3/e) dη′g(η0,η′)n·B0[n(η′−η0)] lence modelwith B0 = 3×10−9G. The dot-dashedcurve Z0 correspondstotheambipolardiffusioncase with B0 = 3× ≈ 1.6oB−9(ν/30GHz)−2 10−9Gandn=−2.8.(AdaptedfromSS05) where λ0 is the wavelength of observation.So this effect is important only at low frequencies, and here it can lead to powerspectra,ascomputedbySS05.WhenRisnormalized thegenerationofB-modepolarizationfromtheFaradayrota- to the magnetic Jeans scale, λ , it turns out that σ depends tionoftheinflationaryE-mode.FromtheworkofKosowsky J onlyonthe ratioR/λ andnotexplicitlyonthe strengthof et al. (2005) one can estimate a B-mode signal ∆T ∼ J B thefield.Thisinterestingfeaturearisesbecausedensityfluc- 0.4(B−9/3)(ν/30GHz)−2µK,forn = −2,atl ∼ 104.The tuations are generated by the divergence of F and so are signalsaresmalleratsmallern.TheFaradayrotationsignal L canbedistinguishedfromtheB-modepolarizationgenerated ∝ k2B02. Since the magnetic Jeans scale λJ ∝ kJ−1 ∝ B0, the magneticfield dependencecancelsoutin σ whenscales bysayvectormodes,orgravitationallensing,becauseoftheir frequencydependence(ν−2). areexpressedintermsofR/λJ (seeSS05fordetails).Struc- turescollapsewhenσ >1(forthethesphericaltophatmodel whenσ =1.68).Forthenearlyscale-freepowerlawmodels, 4. Postrecombination blues eventypicalstructuresatthemagneticJeansscalecollapseat highredshiftsintherangebetween10to20. AfterrecombinationtheUniversebecamemostlyneutral,re- The mass of these objects does depend on the magnetic sulting also in a sharp drop in the radiative viscosity. Pri- fieldstrengthsmoothedtotheJeansscale,andlieintherange mordial magnetic fields can then dissipate their energy into 109M⊙ to 3 × 1010M⊙ for B0 ∼ 10−9G to B0 ∼ 3 × theintergalacticmedium(IGM)viaambipolardiffusionand, 10−9G. An even smaller field could have a major impact, forsmallenoughscales,bygeneratingdecayingMHDturbu- providedthecollapsingstructureshaveamasslargerthanthe lence. These processes can significantly modifythe thermal thermal Jeans mass. For example, a field as small as B = and ionization history of the post-recombination Universe. 0.1nGcaninducea106M dwarfgalaxycollapseathighz ⊙ WeshowinFig.3themodifiedvisibilityfunctionduetothe (z >15),causingearlyenoughre-ionizationtoexplaintheT- gradual re-ionization by ambipolar damping and turbulence EcrosscorrelationpeakobservedbyWMAP.Moredetailed decayfromtheworkofSethi&Subramanian(2005). workonthisaspectisunderway. These dissipative processes, for B−9 ∼ 3, can give rise to Thomsonscatteringopticaldepthsτ >∼ 0.1,althoughnot intherangeofredshiftsneededtoexplaintherecentWMAP 5. Conclusions polarization observations (the T-E cross correlation seen at lowl).However,futureCMBprobeslikePLANCK canpo- We briefly reviewed some of the possible ways one could tentially detect the modified CMB anisotropy signal from detect/constrain primordial magnetic fields using the CMB such partial re-ionization(Kaplinghatet al. 2003).This can anisotropies and polarization. This endeavor would be even be used to detector furtherconstrainsmall-scale primordial morefruitfulif there were a compellingmechanismforpri- fields. mordialmagnetognesis,whichalso producedstrongenough Potentially more exciting is the possibility that primor- (B−9 ∼ 1) and coherent enough (ordered on Mpc scales) dial fields could induce the formation of subgalactic struc- fields.Atthisjuncture,theoreticalpredictionsarehighlypa- tures for z >∼ 15. We show in Fig. 4 the mass dispersion rameter dependent,and so we have taken a more pragmatic σ(R,z)fortwomodelswithnearlyscale-freemagneticfield approachofassumingthatsuchafieldcouldbegeneratedin References References canpotentiallyleadtotheearlyre-ionizationindicatedbythe presentWMAPpolarizationdatainaverynaturalmanner. Acknowledgements. Much of the work reviewed here are in joint papers with John Barrow, T. R. Seshadri and Shiv Sethi. I thank themforveryenjoyablecollaborations, DmitriSokoloff foruseful comments,andtheSKAProjectOfficeforpartialsupport. 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