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CMB: Theory and History Leonardo Senatore (Physics Dept. and SLAC) CMB: theory and history The Cosmic Microwave Background The Cosmic Microwave Background • It is a remarkable aspect of the theory of the Big Bang • It is also an extremely accurately predicted observable • allows us to learn about the fundamental constituents of the universe at early times • allows us to map the reconstruct the very initial conditions of the universe • This lecture is largely based on a review by: Challinor and Peiris 0903.5158 but see also for example Hu 0802.3688 and the most-complete book Modern Cosmology by Dodelson Thermal History • The universe starts very hot. Indeed, it starts so hot that there are no nuclei. As the expansion progress and slows down, nuclear reaction fall out of equilibrium and nuclei form and their abundances freeze (Big Bang Nucleosynthesis (BBN)). The overall abundance of nuclei depends on how many photons are there, as they break the newly formed nuclei. In fact, nuclei form at a much lower temperature than their binding energy. • Therefore, observation of current abundance of nuclei implies a prediction for a bath of thermal radiation at a certain temperature. This was the first prediction of the Cosmic Microwave Background (CMB), by Gamov (1948), Alper & Herman (1948), but it was largely unnoticed. By observed homogeneity of the universe, it was expected to be homogenous. • After BBN the universe cools down: reactions that changes number of photons fall out of equilibrium very early on, and the distribution of photons remains in kinetic equilibrium for a long time due to Thomson scattering with electron. • At some later time (when universe is 4000K (again, delay due to large number of photons per baryon)), hydrogen starts to recombine. Thermal History • Quickly, photons, whose energy is typically T 0 . 1eV , much lower than the energy for exciting ⇠ Hydrogen, begin to travel freely: their mean freeE patch becomes of order Hubble distance (the (1) !1 1 k 0.45 h Mpc− (2) maximum distance). In other words, the probability⇠ for a photon that we get in our eyes to have last (3) scattered at some time, it is highly peaked at )a distance of order 300 kyr, and then they travelled δ⌫ (4) quite freely for 13 Gyr. δdm (5) • This time is called the Last Scattering Surfaceq (6) δ(q) (7) 2 Pcounter,slow ⌫0s = f⌫, slowcsP11(k) (8) • Therefore, there should be a quite homogenouskfs radiation& kNL of a few Kelvins coming to us from all (9) 1 k directions. fs (10) k 2 k NL ✓ NL ◆ δ(1) 0 (11) di↵ ' δ(1) δ(1) (12) • This was serendipitously discovered in 1964 bydi↵ Penzias' dm and Wilson k . kfs (13) 14f P (14) − ⌫ dm, dm 8f P (15) ⇠ ⌫ dm, dm k & kfs (16) (1 f ) (17) − ⌫ (1) 1+f⌫ δdm(a) D D(a) (1 + f⌫ log(a)) (18) (1) / ⇠ · δdm (19) (1) f⌫ δdi↵ (20) log(a ) 8 (21) equality ⇠ cs (22) δdm@iδdm (23) v /v 1 (24) NL ⌧ δ(qi) > 1forqi >kNL (25) [δ(~x ,t )δ(~x ,t )] = δ(3)(~x ~x ) f (everything,...,@ @ Φ(x) ...) 1 1 2 2 C D 1 − 2 very complicated i j |past light cone =atlongwavelengthswecanTaylorexpand= Φ (26) Φ(1) (27) q ,q k (28) 1 2 (29) Discovery Nobel Prize 1978: Penzias and Wilson • This was serendipitously discovered in 1964 by Penzias and Wilson • Princeton physicists • were looking for that, • and told them how to interpret • their discovery • There was a problem • with pigeons Thermal History Credit Hu and White 2004 The hunt for Inhomogeneities • This was a spectacular confirmation of the Big Bang picture: the universe was homogenous at very early times, with great precision. • The numbers matched the ones roughly predicted from BBN. • Cosmology was transforming in a highly quantitative discipline • A natural picture for the formation of structures in the universe emerged: – the universe started very homogenous – starts, galaxies, and clusters (large-scale structure) formed out of gravitational growth of small inhomogeneities. • There had to be inhomogeneities in the CMB! k⌘ 1 φ(k⌘) constant ⌧ ) ⇠ ) 1 k⌘ 1 φ(k⌘) 0 (1) ) ⇠ (k⌘)2 ! C2(~k)=0 (2) 1 δ (k, ⌘) C (~k) cos kr (⌘)+C (~k) (3) γ ' 1 (1 + R)1/4 s 2 ✓ ⇣ ⌘◆ δγ (4) R (5) !1 vb = ikˆvb (6) f = ⇥0 + (7) lm (8) { } (1 + cos(✓)2) (9) σT =ThomsonCross-section (10) ⇥ (11) d @ = + e =derivativealongflow (12) d⌘ @⌘ · r ˙= @/@⌘ (13) Df @f dx @f d✏ @f de @f = + + + (14) d⌘ @⌘ d⌘ · @x d⌘ @✏ d⌘ · @e Df = C[f] (15) d⌘ 1 f ✏ (16) ' e aT¯[1+⇥(⌘,x,e)] 1 e = e ,e ,e − (17) { 1 2 3} The hunt for Inhomogeneities (18) )• There had to be inhomogeneities in the CMB! ∆• Some✓ numbers:2⇡/l the CMB has now a temperature of 2.72K. Since when it was emitted the (19) ⇠ 3 temperature was about 3000K, it means that the redshift of about z 10 ECMB =photonenergyinCMBrestframe LSS ⇠ (20) ¯ T 0.1eV (1) TCMB = T =isotropictemperature ⇠ (21) δ•TNow, the evolution of small inhomogeneities in the universe tells usE that, if the universe is (2) 5 !1 1 dominated3 10by dark− matter, we have k 0.45 h Mpc− (22) (3) T ⇠ · ⇠ a 3 (4) δdm(a)=δdm(ain) if δdm(a0) 1 ) δdm(aLSS) 10− (23) ain ) ⇠ δ)⌫ ⇠ (5) 3 z 10 δdm δT 5 (24) (6) LSS– there are various detailed corrections that tells us that the correct prediction is 3 10− ⇠ q T ⇠ · (7) T 0.1eV a (25) 3 ⇠ δ(q) δdm(a)=δdm(ain) if δdm(a0) 1 δdm(aLSS) 10− (1) (8) aain ) ⇠ ) ⇠ • of course this disagreement matters a lot if you are an experimentalist!! 32 (26) Pcounter,slow ⌫ s =z f⌫, slow10c P11(k) (2) (9) 0 LSS ⇠ s k k T 0.1eV (3)(10) fs & NL ⇠ 1 k (4) fs (11) k 2 k NL ✓ NL ◆ δ(1) 0 (12) di↵ ' δ(1) δ(1) (13) di↵ ' dm k . kfs (14) 14f P (15) − ⌫ dm, dm 8f P (16) ⇠ ⌫ dm, dm k & kfs (17) (1 f ) (18) − ⌫ (1) 1+f⌫ δdm(a) D D(a) (1 + f⌫ log(a)) (19) (1) / ⇠ · δdm (20) (1) f⌫ δdi↵ (21) log(a ) 8 (22) equality ⇠ cs (23) δdm@iδdm (24) v /v 1 (25) NL ⌧ δ(qi) > 1forqi >kNL (26) [δ(~x ,t )δ(~x ,t )] = δ(3)(~x ~x ) f (everything,...,@ @ Φ(x) ...) 1 1 2 2 C D 1 − 2 very complicated i j |past light cone =atlongwavelengthswecanTaylorexpand= Φ (27) Φ(1) (28) q ,q k (29) 1 2 (30) The Discovery of Inhomogeneities • In 1971 a large dipole pattern was detected (see R. Muller Scientific American 1978 for an overview) – This is interpreted as the dipole induced by the relative motion of our galaxy wrt the intergalactic medium (~600km/sec) • After many experiments falling short of the target, δT 5 – Intrinsic anisotropies were detected by COBE in 1992: 3 10− T ⇠ · a 3 δdm(a)=δdm(ain) if δdm(a0) 1 δdm(aLSS) 10− (1) aain ) ⇠ ) ⇠ z 103 (2) LSS ⇠ T 0.1eV (3) ⇠ Nobel Prize 2006: Mather and Smooth (4) • We understood how structure get formed! How structures gets formed http://lambda.gsfc.nasa.gov/ Actual distribution of structures in our Universe Movie del viaggio nelle galassie http://astro.uchicago.edu/cosmus/projects/sloanmovie/ Measuring the Inhomogeneities • COBE discovery not only explained us the basic picture of how structure got formed, it also opened up a series of extraordinary questions. • In fact, there was the need to characterize the spectrum: – they appeared to be highly gaussian – and what was the wavelength distribution of the power in anisotropies? • This questions needed to be answered by making measurements. δT 5 • Furthermore, since 3 10 − , it became pretty clear that it should be possible to make T ⇠ · extremely accurate predictions, by expandinga in the smallness of the inhomogeneities. 3 δdm(a)=δdm(ain) if δdm(a0) 1 δdm(aLSS) 10− (1) – The CMB was to become the instrumentaain to turn) cosmology into a⇠ high-precision) science ⇠ z 103 (2) LSS ⇠ T 0.1eV (3) ⇠ (4) Measuring the Spectrum Inhomogeneities • QMAP, Boomerang, Maxima begun to first measure the spectrum of the inhomogeneities. • They found a very tantalizing peak structure Measuring the Spectrum Inhomogeneities • Since then, many improvements Interpreting the measurements • The peak structure is very tantalizing. Can we understand it? • Let us begin to study the theory of the inhomogeneities. • Let us expand in the smallness of the perturbations. • At zeroth order, we have that the one-particle distribution (number of photons per proper phase- space volume) is a Black Body: – where ECMB =photonenergyinCMBrestframe TCMB = T¯ =isotropictemperature (1) • Due to our motion wrt the CMB, we have δT 5 3 10− (2) T ⇠ · • This is a angle-dependent black body a 3 δdm(a)=δdm(ain) if δdm(a0) 1 δdm(aLSS) 10− (3) aain ) ⇠ ) ⇠ • with z 103 (4) LSS ⇠ • This is our distributionT if0 the.1eV universe were homogeneous. We are interested in the inhomogeneities. (5) ⇠ (6) CMB observables • It is useful to decompose the perturbation in spherical harmonics: – each multipole encodes information on a scale ∆✓ 2⇡/l ⇠ • We can make predictions only on the statistical properties ofE CMBthe fluctuations=photonenergyinCMBrestframe (we do not have a (1) ¯ theory that predicts the amplitude of each ). So, we computeTCMB directly= T =isotropictemperature correlation functions of (2) δT 5 – the statistical properties of the fluctuations should be compatible3 with10− the background space, (3) T ⇠ · which for FRW is rotation and translation. Since under rotation transforms under a a 3 δdm(a)=δdm(ain) if δdm(a0) 1 δdm(aLSS) 10− (4) Wigner rotation matrix as , rotation invariance of atheain perturbations) ⇠ ) ⇠ implies z 103 (5) LSS ⇠ ».
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