,,., Cosmic Background ExplorerCOBE, Cosmic Microwave BackgroundCMB., Wilkinson Microwave Anisotropy ProbeWMAP, CMB,. CMB,, photon 00., photon d

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1 21cm

2 ,,., Cosmic Background ExplorerCOBE, Cosmic Microwave BackgroundCMB., Wilkinson Microwave Anisotropy ProbeWMAP, CMB,. CMB,, photon 00., photon dark age,,., 21 cm 1s,, 21 cm Murchison Widefiled ArrayMWA, Square Kilometer ArraySKA. 21 cm, CMB., 21 cm CMB,, Fisher Information Analysis. Fisher Information Analysis,,., Ω b h 2, Ω dm h 2 dark matter, h, H 0 0h km sec 1 Mpc 1, τoptical depth, N ν, f ν dark matter warm dark matter, f ν Ων Ω dm, Y p mass fraction, n s spectra index, A s power spectrum, A s 9., N ν f ν, CMB 21 cm.,,, f ν, 1. 1

3 1 I 21cm cm? cm Source Term Optical Depth cm II 17 3 Matter δ 3, Free Streaming Free Streaming v T g 1, 3, photon T s , 9, H-H Collision e-h Collision p-h Collision H-H, e-h, p-h Collsion κ Collision n 0, n 1 Collision Rate Background photon Lyman 1, 12, Neutral Fraction x HI or Ionization Fraction x i T s T s T s

4 photon T γ Ionization Fraction x i cm Power Spectrum cm 16, 17, δ xhi 1 21 cm T s T γ 21 cm cm 3D Power Spectrum δ xhi 1, 21 cm 3D Power Spectrum T s T γ, 21cm 3D Power Spectrum cm 3D Power Spectrum APAlcock-Paczyński Effect 21 cm Power Spectrum III Fisher Information Analysis 21 cm 77 7 Fisher Information Analysis22, Fisher Information Matrix Fisher Information Matrix cm cm Visibility cm cm Fisher Information Matrix 20, Detector Noise Sample Variance Appendix 1 A B Conformal Newtonian Guage 3 2 B B.2 Ricci Tensor, Ricci Scalar B.3 Einstein Tensor

5 B B.5 Einstein equation C 7 D Einstein A, B 8 E T s F δ xhi 1 21 cm 111 F.1 T α T g G H χ z, d A z 116 I Alcock-Paczyński Effect 6.76, 6.77, 6.78, J 118 J J

6 I 21cm 5

7 1,,.,,,.,,,,,,.,.,, 4%, dark matter 22%, dark energy 74%,., dark dark age. dark age, CMB photon,. dark,,,., dark age,., dark age., 21 cm / 1, dark age. dark age, photon,,. or 21 cm, dark age., Reionization, 21 cm., 21 cm source,. 21 cm project, LOw Freaquency ARrayLOFAR, Murchison Widefiled ArrayMWA, Square Kilometer ArraySKA cm? 21 cm, /.,,, 1s, 2s, 2p,., L S -,., 2p. 1s 2s, 0, -. 1s, F L + S1s 0, I, F I 1 1 S S E 5.8 µev, 21 cm., / 21 cm. 6

8 1: 1.2 I, dark age 21 cm,., 1,, / 21 cm 21 cm. 2,, 21cm., 21 cm /, 2., 21 cm source. Background photoncmb photon,, 21 cm 21 cm. II, I 21 cm X x, t δ X x, t, δ X x, t X x, t X t X t X x, t X t 1 + δ X x, t 1.1., X t X x, t. 3, 21 cm baryon δ H δ b δ m, v., Boltzmann, Einstein., Matter, scale factor a.,., baryon T g.,,. photon, photon T γ,, T g a 2 scale factor 2,. 7

9 4,. 3, Collision, Background photoncmb photon, Lyman.,.,, δ Ts, δ H, δ Tg etc.... 5, Ionization Fraction x i. x i, Recombination Reionization 1., Reionization z 20?, 1 0., Reionization,. 6, 21 cm δ 21, δ H δ v., 21 cm δ H etc..., δ v., 21 cm Power Spectrum, µ. µ 4, µ 4 Matter Power Spectrum. Alcock-Paczyński, µ 6. III, Fisher Information Analysis, 21 cm +CMB,. 7, Fisher Information Analysis, -,., Fisher Information Matrix F ij, F 1 ii. 8, Fisher Information Analysis,. 21 cm, Low Frequency Array, LOFAR, MURCHISON WIDEFIELD ARRAY, MWA, Square Kilometer Array, SKA.,.,, Visibility., 21 cm Fisher Information Matrix.,,, 21 cm signal Detector Noise. 8.3, 21 cm +CMB Fisher Information Matrix,. 9. 8

10 2 21 cm 21cm 21cm,., 21 cm., 1 c d dt I ν r, t, n η ν r, t, n α ν r, t, n I ν r, t, n 2.1. I ν specific intensity,. α ν, specific extinction,., η ν, specific emissivity,. t τ ν dτ ν α ν cdt α ν ds τ ν s s 0 α ν r s, s, n s ds 2.2 di ν r, τ ν, n dτ ν I ν r, τ ν, n + η ν r, τ ν, n α ν r, τ ν, n 2.3. τ ν Optical Depth,, lower state n l r, t, upper state n u r, t , Einstein A, B, di ν hν ul 4π n uφ e ν A ul cdt di ν hν ul 4π n lφ a ν B lu I ν cdt di ν hν ul 4π n uφ e ν B ul I ν cdt 2.4a 2.4b 2.4c 1 c di ν di ν di ν + di ν di ν r, t, n dt hν ul 4π n uφ e ν A ul cdt hν ul 4π n lφ a ν B lu I ν cdt + hν ul 4π n uφ e ν B ul I ν cdt hν ul n u φ e ν A { ul 4π hν B lu ul n l 4π φ a ν n u φ e ν B } ul I ν cdt 4π hν ul n u r, t φ e ν A ul 4π hν ul { n l r, t B lu 4π φ a ν n u r, t φ e ν B ul 4π } I ν r, t, n

11 ., ν ul upper state lower state, φ e ν, φ a ν, line profile. 2.1, η ul ν r, t, n ην ul r, t hν ul n u r, t φ e ν A ul 4π { αν ul r, t, n αν ul r, t hν ul n l r, t B lu 4π φ a ν n u r, t φ e ν B ul 4π } 2.6a 2.6b., specific emissivity, specific extinction, n., Optical Depth, 2.2, τ ul ν s s 0 αν ul r s, s ds 2.7. line profile line profile φ ν φ a ν φ e ν, T s,. n u r, t n l r, t g u exp hν ul g l k B T s r, t Source Term A B, ν ul, upper state, lower state g u, g l, A ul 2hν ul 3 c 2 B ul 2.9a g u B ul g l B lu 2.9b, specific extintion2.6b, αν ul r, t hν ul 4π φ ν n l r, t B lu hν ul 4π φ ν n l r, t g u g l c 2 1 n u r, t n l r, t 2hν 3 ul c 2 g u 8πνul 2 g A ul n l r, t φ ν l B ul B lu A ul 1 g u exp hν ul g l k B T s r, t 1 exp hν ul k B T s r, t gl g u 2.a c 2 g u hν ul 8πνul 2 g A ul n l r, t φ ν l k B T s r, t 2.b

12 ., 2.3 Source Term η ul α ul ν r, t ν r, t hν ul c 2 4π A g u uln u r, t φ ν g l 2hνul 3 n u r, t g u c 2 n l r, t 1 exp 2hν3 ul 1 c 2 exp hνul k B T sr,t 1 8πνul 2 g A ul n l r, t φ ν l hν ul k B T s r, t 1 1 exp hν 1 ul k B T s r, t 2.11a 2ν2 ul c 2 k BT s r, t 2.11b., k B T s hν ul , 2.3. T b ν, Black- Body Specific Intensity I BB ν T 2hν3 1 c 2 exp hν k B T a, I ν r, t, n I BB ν T b ν; r, t, n 2.12b., Rayleigh-Jeans k B T hν 3, I ν r, t, n 2ν2 c 2 k BT b ν; r, t, n T b ν; r, t, n c2 2ν 2 k B I ν r, t, n 2.12c , 2.11b 2.12c, d 2ν 2 dτ ν c 2 k BT b ν, r τν, τ ν dt b ν, r τν, τ ν 2ν2 c 2 k BT b ν, r τν, τ ν + 2ν 2 ul c 2 k BT s r τν, τ ν νul T b ν, r τν, τ ν + dτ ν ν 2 Ts r τν, τ ν 2.13,. 2.13,. 4 T b ν, r τν, τ ν e τ ν νul 2 T b ν, r 0, 0 + Ts r 0, 0 1 e τ ν ν , hν ul k B K T s. 3,, ν ul 1.4GHz,. 4 Appendix 1 11

13 , δt b, δt b ν, r 0, 0 Tb ν, r τν, τ ν Tb ν, r 0, 0 1 e τ ν νul ν 2 Ts r 0, 0 Tb ν, r 0, , photon T b ν, r 0, 0, T b ν, r 0, 0 Tγ r 0, η z 2.16 r 0, η z CMB photon.,, r 0 η z. T s ν, r 0, τν 0 T s ν, r 0, η z 2.17 z., /, 1/1 + z redshift ν δtb obs, r 0, η z δt νul 2 b ν, r 0, η z ν Ts r 0, η z Tγ r 0, η z 1 e τ ν 1 + z 1 + z 1 + z 2.18., ν ν ul, δtb obs νul, r 0, η z δt b ν ul, r 0, η z 1 + z 1 + z. 2. T s r 0, η z Tγ r 0, η z 1 e τ νul 1 + z : 21 cm T s r 0, η z, photon Tγ r 0, η z, δt b 0, T s r 0, η z, photon T γ r 0, η z, δtb 0. 12

14 Optical Depth 2.19,., 2.19 Optical Depth τ νul. Optical Depth 2.7 ν ν ul., s, 5, Specific Extinction r, cosmic time t., τ ul ν ul r, t s 0 α ul ν ul r s, s ds sα ul ν r, t s c2 g u hν ul 8πνul 2 g A ul n l r, t φ ν ul l k B T s r, t line profile φ ν ul., line profile,. r, v r, η,. 3 3: LineProfile, v r, η H z s + v p r + s, η v p r, η H z a z s + dv p dr r, η s sh z z dv p r, η H z dr η cosmic conformal time, redshift z. s, s s aη,., ν ul, ν ul v r, η ν ul sh z ν ul c c z dv p r, η H z dr

15 . line profile,, φ ν ul ν ul 1 φ ν ul 1 ν ul 0 φ ν dν c 1 sh z ν ul z dv p Hz dr c r, η sh z ν ul z dv p r, η H z dr 2.24 line profile., Hubble cosmic time t, cosmic conformal time η, τν ul ul r, η s c2 g u 8πνul 2 g A ul n l r, η l 3c 3 ha ul n l r, η 8πνul 2 k BT s r, η H z c sh z ν ul 2 Optical Depth z dv p H z dr z dv p r, η H z dr r, η hν ul k B T s r, η cm 2.19, r 0, r., Optical Depth, 1 exp τ νul τ νul. 2.19, 2.25, δt obs b νul, r, η z 1 + z. T s r, η z Tγ r, η z 1 + z 3c 3 ha ul n l r, η 8πν 2 ul k B 1 + z H z τ νul r, η z 1 T γ r, η T s r, η z dv p r, η H z dr cm., spin triplet g u 3 spin singlet g l 1. 21cm ul, 21.., A ν ul ν GHz 2.27 A ul A 21 2πα EMν 3 21 h2 3c 4 m 2 e s t, η, z, cosmic time, cosmic conformal time, redshift. 14

16 lower state, n HI r, η x HI r, η n H r, η 7, n l r, η g l n HI r, η 1 g u + g l 4 x HI r, η n H r, η , 21cm δtb obs ν z, r, η 3c3 ha 21 x HI r, η n H r, η 32πν21 2 k 1 T γ B 1 + z H z r, η T s r, η z dv p r, η H z dr , 21 cm δt b, ν 21, redshift., z 21 cm /, δt b δtb obs δt b 1+z, ν 21 ν 21 1+z redshift. 2.30, 21 cm,... I + n H 21 cm /, n H 21 cm.,, 21 cm IIMatterBaryon v p Matter 21 cm, Matter, /, line profile.., 21 cm v p, line profile φ ν III T s, 1 0 S 1/2 1 1 S 1/2 a 2, / 21 cm., 2.8, 1 0 S 1/2 n S 1/2 n cm /,. a 8 >< n : n 1, 2, 3, L : L S, P, D, J : + L 1 n F L J >: F : + 2 J L n HI, n H, x HI 8 1 : 3, lower state upper state 15

17 IVphoton T γ photon 21 cm, 2.16,, photon CMB photon, CMB photon.,, photon CMB, 21 cm δtb obs 0, photon, 21 cm δtb obs 0., 21 cm, photon CMB. VNeutral Fraction x HI I n H x HI,. 21 cm, I, Neutral Fraction x HI 21 cm. Neutral Fraction x HI, Recombination Reionization x HI. Recombination Reionizaion, x HI 1. VIHubble Parameter H z Hubble Parameter 21 cm, II, line profile φ ν, II, Hubble Parameter , 21 cm., 21 cm, 21 cm, Matter, neutral Fraction etc...., 21 cm. 2.30, x HI, 0 δtb obs 0, signal. Reionization,, x HI 0., Reionization z 6-9 z 6-, 21 cm signal., Recombinationz 00,,. x HI 0. Recombination, 21 cm., 21 cm, Reionizationz 6- Recombinationz Quasi Stellar ObjectQSO 16

18 II 17

19 3 Matter 3.1 δ 3, 4, Conformal Newtonian, ds 2 a 2 η {1 + 2ψ η, x } dη 2 { 1 2φ η, x } δ ij dx i dx j 3.1., Matter Baryon δ m v m. Matter, Baryon b, Cold Dark Matter, CDM c, ν.,. 32 Baryon, Baryon δ b + ikv b 3 φ 3.2 v b + Hv b ikψ + τ R v b + 3iΘ , baryon photon, R, τoptical depth, τ η R 3 ρ b ρ γ η0 η dη n e σ T a η 3.5., Θ 1, photon. CDM,, CDM., C.2, C.3, w c 0, δp c δρ c 0, σ c 0 3.6, δ c θ c 3 φ 3.7 θ c Hθ c + k 2 ψ 3.8. θ c ik j v cj ikv c, Cold Dark Matter δ c + ikv c 3 φ 3.9 v c + Hv c ikψ 3., Baryon photon. η 18

20 , Matter,, Cold Dark Matter. 0,., CDM, C.2, C.3, w ν 0, c 2 sν δp ν δρ ν 0, σ ν , δ ν θ ν 3 φ 3.12 θ ν Hθ ν + k 2 c 2 sνδ ν + k 2 ψ 3.13.,, k 2 c 2 sνδ ν. scale k > k νf J, scale k < k νf J, CDM., k νf J free streaming scale. CDM θ ν, v ν, δ ν + ikv ν 3 φ 3.14 v ν + Hv ν + ikc 2 sνδ ν ikψ 3.15., φ, ψ Einstein,. Appendix k 2 φ ψ 12πGa 2 a k 2 φ 4πGa 2 a 4πGa 2 a ρ a δ a + 3H ρ a δ a + 3iH k k 2 ρa + P a θa ρa + P a va 3.17 ρa + P a σa 3.16 Boltzmann Einstein, 21 cm signal O z 300,.,, baryon photon.,, photon baryon 21 cm signal 0., 3.3, photon., Baryon CDM., z z dec 300 < z eq,,,., 3.16, 3.17, ρ γ ρ m., Matter σ m., φ ψ., sub-horizaon scale ah H k, 3.17 v a.,, δ b + ikv b 3 φ v b + Hv b ikψ ikφ

21 δ c + ikv c 3 φ v c + Hv c ikψ ikφ 3.21 δ ν + ikv ν 3 φ v ν + Hv ν + ikc 2 sνδ ν ikψ ikφ 3.23 k 2 φ 4πGa 2 ρ m δ m 3.24., Hubble Parameter H H/a, 0 Einstein H 2 8πG 3 ρ 8πG 3 ρ m + ρ Λ H0 2 Ωm a 3 + Ω Λ 3.25.,, Matter ρ m, dark energyρ Λ., 3.24, k 2 φ 4πGa 2 H 2 ρ 8πG m δ m φ 3 3 ρ + ρ Λ 2 } {{ } 1 a 2 H 2 k 2 } {{ } 1 ρ m δ m δ m 3.26 ρ m + ρ } {{ Λ } O1, sub-horizon scale, φ δ m δ b, δ c, δ ν., 3.18, 3.20, 3.22, 3 φ, δ,. 0., k > k νf S, k < k νf S. free straming scale. 3.22, 3.23, 3.24, v ν, φ, δ ν 2, δ ν + H δ ν + k 2 c 2 sνδ ν 4πGa 2 ρ m δ }{{} m δ ν δ ν + H δ ν + k 2 c 2 sν 4πGa 2 ρ m δν , 3.27,,. 0 k, k 2 c 2 sν 4πGa 2 4πGa2 ρ m ρ m k k νf S c 2 sν k νf S. 6 k < k νf S,,,.,,., 3.23, ikc 2 sνδ ν, ikφ.,,, baryon CDM., k > k νf S,,., δ ν δ b, δ c. baryon CDM, Matterbaryon, CDM. 20

22 3.2 Free Streaming, free streaming scale scale k < k νf S., baryon, CDM,., δ m δ b δ c δ ν, v m v b v c v ν., δ m + ikv m v m + Hv m ikφ 3.30 k 2 φ 4πGa 2 ρ m δ m , 3.31, v m, φ, δ m 2, δ m + H δ m 4πGa 2 ρ m δ m conformal time η scale factor a., η da dη a ah a a2 H a δ m + }{{} H δ m a 2 H a ah a 2 H δ m + ah a 2 H δ m a a a 4 H 2 2 δ m a 2 + a3 H d ln H d ln a δm a , 3.25 a, 2H dh 3H Ω m da a 4 d a 3 H dh 3 1 da da 2 H2 0 Ω m a 3 a 4πG ρ m a 4πGa 2 ρ m a d da a 3 H dh da. 3.34, 3.35, 3.32, a 4 H 2 2 δ m a 2 + a3 H d ln H d ln a., a 3 H d ln H d ln a a 4 H 2 3 H 2 d ln a da } {{ } d lna3 H 2 /H d ln a δm a a d da } {{ } 8πG 3 ρm 3.35 a 3 H dh δ m da d ln H d a 3 H 2 a a 3 H dh da da da, 3.36,. { 3.36 a a 3 H 2 δ m a 2 + d a 3 H 2 } δ m da a } {{ } aa 3 H 2 δm a a 3 H dh δ m da a + d a 3 H dh } δ m da da } {{ } { 21 aa 3 H dh da δ m

23 a a a 3 H 3 δm 0 a 3 H 3 δm A k δ a m a H a H H A k da a 3 H a 3 + B k a da δ m k, a A k H a a 3 H a 3 + B k H a 3.38, A k, B k, η, a a. 3.38, Growing Mode Decaying Mode. 3.25,, δ m k, a A k H 0 Ωm a 3 + Ω Λ 1 2 a da a 3 H0 3 Ωm 3 2 a 3 + Ω Λ + B k H 0 Ωm a 3 + Ω Λ dark energy Ω m a 3 Ω Λ, 3.39, 1 Ωm 2 a da δ m k, a A k H 0 a 3 a 3 H0 3 Ωm a Ωm 2 + B k H 0 a 3 2 A k 5H0 2Ω a + B k H 0 Ωm a m, Growing Mode, scale factor a, decaying mode a , Growing Mode D + a, Decaying Mode D a, D + a 5H2 0 Ω m 2 D a a da H a a 3 H a 3 5Ω m H a a 2 H 0 H 3 0 da a 3 H a H 0 Ωm H a 3.42., Ω m a 3 Ω Λ, D + a a, D a a 3 2., dark energy, Matter,.,. Matter, Matter., dark energy, 3.32 Matter dark energy, 3.32 Matter., dark energy, Matter,.., dark energy,,., Ω m, Ω Λ 1, 0, 0.3, 0.7 Growing Mode D + a, 4. 4, Ω m, Ω Λ 1, 0 Matter, Ω m, Ω Λ 0.3, 0.7 dark energy, Growing Mode. 22

24 4: Growoing Mode 3.3 Free Streaming 6, free streaming scale scale k > k νf S.,. scale, 3.27,., baryon CDM, scale. baryon CDM free streaming scale., δ ν δ b, δ c., ρ ν ρ b, ρ c, ρ ν ρ b δ b, ρ c δ c., 3.31, ρ m δ m ρ b δ b + ρ c δ c + ρ ν δ ν ρ b δ b + ρ c δ c baryon CDM,, δ b δ c δ m.,, ρ m δ m ρ b + ρ c δ m ρ m ρ ν δ m ρ m 1 f ν δ m 3.44., Matter f ν ρ ν ρ m Ω ν Ω m., k > k νf S, Ω ν Ω b + Ω c + Ω ν 3.45 δ m + ikv m v m + Hv m ikφ 3.47 k 2 φ 4πGa 2 ρ m 1 f ν δ m

25 . k < k νf S, 3.48,., k < k νf S, δ m, δ m + H δ m 4πGa 2 ρ m 1 f ν δ m , dark energy. 3.25, H 2 8πG 3 ρ m H0 3 Ω m a , H a 3 2. η a, 3.34, 3.49, a 4 H 2 2 δ m a 2 + a3 H d ln H d ln a } {{ } δ m a 3 2 a2 H 2 1 f ν δ m 0 2 δ m a δ m 2a a 3 2a 2 1 f ν δ m , δ m a p, p. δ m a p 3.51, p p p f ν 0 p p f ν , p p ± 1 2 ± f ν 1 ± f ν f ν 1, p f ν f ν 3.54 p f ν f ν Growing Mode D + a Decaying Mode D a, D + a a p + a f ν 3.56 D a a p a f ν f ν 0, k < k νf S Ω m a 3 Ω Λ., k < k νf S, Growing Mode a vs a fν.,. 24

26 3.4 v 18 baryonmatter v b v c v m. 3.29, 3.46, v m i k δ m i k a2 H δ m a i k a2 H a iah a dd + k D + da D + δ m D + δ m iah k f a δ m Growing Mode δ m D +, Decaying Mode., f a a dd + D + da d ln D+ d ln a 3.59, f a., f a O 1., Matter, D + a, f a 1., 3 v m, v m k k v m ikah k 2 f a δ m ,, v m x, a d 3 k eik x 2π 3 v m k, a iah a f a d 3 k 2π 3 eik x k k 2 δ m k, a 3.61., 21 cm 2.30, v p. 11, 3.61, 2.30 dv p dr., 3.61, ˆx,., v m v m x, a ˆx iah a f a iah a f a µ k ˆx k d 3 k 2π 3 eik x k ˆx k 2 δ m k, a d 3 k 2π 3 eik x µ k δ m k, a , k ˆx µ., 3.62 r x., x, x rˆx, r, k x, k x k x + k x x krµ 3.64 } {{ }. 5, 11 2, Peculiar Velocity, v p. 25

27 5: dv m dr x, a iah a f a., ah a f a d 3 k d 2π 3 eik x dr } {{ } ikµe ik x µ k δ m k, a d 3 k 2π 3 µ2 δ m k, a 3.65 dv m dr k, a ah a f a µ2 δ m k, a 3.66,, gradient,., 21 cm, δ v k, a 1 dv m ah a dr k, a f a µ2 δ m k, a 3.67., δ v, µ,,. 26

28 3.5 T g 1, 3, 11, T g.,,., x δv g phys, conformal time dη, d Q x, η. 6: v x, η. n g x, η, δv g phys x, η, δn g x, η n g x, η δv g phys x, η δn g. T g x, η, 1, 3 2 k BT g x, η., δu g x, η, δu g x, η 3 2 δn g x, η k B T g x, η 3.69., p g x, η, p g x, η n g x, η k B T g x, η dη d δu g x, η, d x, η,, δv phys g d Q x, η d δu g x, η + p g x, η d δv phys g x, η

29 ., η x dη, x + v x, η dη, d δu g x, η δu g x + v x, η dη, η + dη δu g x, η 3 2 δn g x + v x, η dη, η + dη k B T g x + v x, η dη, η + dη 3 2 δn g x, η k B T g x, η 3 2 δn g x, η k B T g x + v x, η dη, η + dη T g x, η 3 2 n g x, η δv g phys x, η v x, η T g x, η + T g η x, η dη 3.72., δn g, δn g x, η δn g x + v x, η dη, η + dη., d Q x, η ϵ x, η δv phys g x, η dη 3.73 δv g phys, dη. 3.70, 3.72, 3.73, 3.71, ϵ x, η δv g phys x, η dη 3 2 n g x, η δv g phys x, η v x, η T g x, η + T g η x, η dη +n g x, η k B T g x, η d δv g phys x, η T g η x, η + v x, η T g x, η d δv g phys x, η 2ϵ x, η 3 δv g phys T g x, η x, η dη 3n g x, η k B H g x, η 1 δv phys g x, η d δv phys g dη x, η 3.75,.. { } 3.1, dx i, a η 1 φ x, η dx i., δv com g δv phys, δv phys g, 3δV g x, η a 3 com η 1 φ x, η g x, η a 3 η 1 3φ x, η δv g com x, η φ. δv g com x, η,, v x, η., δv g com x + v x, η dη, η + dη 1 + v x, η dη δv g com x, η 3.77., η + dη, 28

30 δv phys g x + v x, η dη, η + dη a 3 η + dη 1 3φ x + v x, η dη, η + dη δv g com a 3 η x + v x, η dη, η + dη da η a η dη dη 1 3 φ x, η + dη v x, η φ x, η } {{ } v x, η dη δv g com x, η a 3 η 1 3φ x, η δv g com x, η } {{ } δv g phys x,η 3 φx,η +dη φ η x, η 1 + 3H η dη 1 3 φ x, η dη 1 3φ x, η 1 + v x, η dη } {{ } { δv g phys x, η 1 + dη 3H η 3 φ } x, η + v x, η 3.78, η δv g phys x, η, H, φ, v. 12, φ v, , 3.75, 3H g x, η 1 δv phys g x, η δv phys g x + v x, η dη, η + dη δv phys g x, η dη 3H η 3 φ x, η + v x, η 3H η 1 1 { φ x, η 1 } H η 3 v x, η { }. 0, H η.,, { }.,, 3.74., T g x, η, T g x, η T g η 1 + δ Tg x, η 3.80, 3.74, v x, η T g x, η v x, η Tg η 1 + δ Tg x, η T g η v x, η δ Tg x, η , 3.74, 12 η. 29

31 T g x, η + 2H η 1 1 { φ x, η 1 } H η 3 v x, η T g x, η 2ϵ x, η 3n g x, η k B T g x, η., photon etc...., 0, photon , 0, T g, T g x, η + 2H η 1 1 { φ x, η 1 } H η 3 v x, η T g x, η Background0, T g η + 2H η T g η Tg a 2 η a η 2 η η 0 T g η a η z η , 0, T g η, scale factor a η 2..,,, p, p a 1 scale factor., 3 2 k BT g p2 2m., scale factor ,, Tg η 1 + δ Tg x, η + 2H η 1 1 { φ x, η 1 } η H η 3 v x, η T g η 1 + δ Tg x, η 0 Tg η + 2H η T g η 1 + δtg x, η + T g η δ Tg x, η 2 φ x, η 1 } {{ } 3 v x, η T g η , T g η, δ Tg x, η 2 φ x, η 1 3 v x, η δ Tg., φ source. 30

32 3.5.2 photon , photon baryon., photon,, couple,., dt g dt 8σ T ρ γ n e T γ T g 3.87 compton 3m e cn tot. 3, 5, m e, c, σ T σ T 8π 3 e πϵ 0 c m 2 ec cm ρ γ photon, photon T γ 4. photon monopole δ Tγ T γ x, η T η 1 + δ Tγ x, η 3.89, photon,, ρ γ x, η ρ γ η 1 + δ ργ x, η ρ γ η 1 + 4δ Tγ x, η n e photon, n tot, n tot n H + n He + n e n H 1 + f He + x i 3.91, photon, +., f He n He /n H., +, Ionization Fraction x i n e /n H., 3.87, n e n tot n e n H + n He + n e x i 1 + f He + x i dt, 3.82, dη. 3.1,, dt a η 1 + ψ x, η dη 3.93., dt g x, η dη dt compton dη dt g dt x, η a η 1 + ψ x, η dt g x, η compton dt 3.94 compton, , 3.94, dt g x, η dη 8σ T a η 1 + ψ x, η ρ γ x, η x i x, η T γ x, η T g x, η compton 3m e c 1 + f He + x i x, η

33 . ρ γ, x i, T γ, T g δ ργ δ Tγ, δ xi, δ Tγ, δ Tg, 3.94, dt g 8σ T a η 1 + ψ x, η ρ γ η 1 + 4δ Tγ x, η x i η 1 + δ xi x, η x, η dη { } compton 3m e c 1 + f He + x i η 1 + δ xi x, η Tγ 1 + δtγ x, η T g 1 + δtg x, η 8σ T a η ρ γ η x i η Tγ η 3m e c 1 + f He + x i η T g η 1 + ψ x, η 1 + 4δ Tγ x, η 1 + δ xi x, η 1 x i η δ xi x, η 1 + T γ η δ Tγ x, η T g η δ Tg x, η 1 + f He + x i η T γ η T g η 8σ T a η ρ γ η x i η Tγ η 3m e c 1 + f He + x i η T g η 1 + ψ x, η + 4δ Tγ x, η 1 + f He f He + x i η δ x i x, η + T γ η δ Tγ x, η T γ η T g η T g η δ Tg x, η T γ η T 3.96 g η., 3.82, T g x, η + 2H η 1 1 { φ x, η 1 } H η 3 v x, η T g x, η Tg η 1 + δ Tg x, η + 2H η 1 1 { φ x, η 1 } η H η 3 v x, η T g η 1 + δ Tg x, η Tg η + 2H η T 1 g η + δtg x, η + T g η δ Tg x, η 2 φ x, η 1 3 v x, η T g η. 3.96, 3.97, 3.82,, Tg η + 2H η T 1 g η + δtg x, η + T g η δ Tg x, η 2 φ x, η 1 3 v x, η T g η σ T a η ρ γ η x i η Tγ η 3m e c 1 + f He + x i η T g η 1 + ψ x, η + 4δ Tγ x, η f He 1 + f He + x i η δ x i x, η + T γ η δ Tγ x, η T γ η T g η T g η δ Tg x, η T γ η T g η photon,. Background0, T g η + 2H η T g η 8σ T a η ρ γ η x i η Tγ η 3m e c 1 + f He + x i η T g η photon T g > T γ Tg < T γ,, photon photon., z 300, baryon photon, T γ T g. z 300, 3.85 scale factor 2,. photon scale factor,, T g < T γ. 32

34 . 3.98, δ Tg, T g η δ Tg x, η 2 φ x, η 1 3 v x, η T g η 8σ T a η ρ γ η x i η Tγ η 3m e c 1 + f He + x i η T g η 1 + ψ x, η + 4δ Tγ x, η f He 1 + f He + x i η δ x i x, η + T γ η δ Tγ x, η T γ η T g η T g η δ Tg x, η T γ η T g η 1 + δ Tg x, η 8σ T a η ρ γ η x i η Tγ η 3m e c 1 + f He + x i η T g η ψ x, η + 4δ Tγ x, η 1 + f He f He + x i η δ T γ η x i x, η + T γ η T δ Tγ x, η δ Tg x, η g η. T g, δ Tg x, η 2 φ x, η 1 3 v x, η 8σ T a η ρ γ η x i η Tγ η 3m e c 1 + f He + x i η T g η 1 ψ x, η + 4δ Tγ x, η f He 1 + f He + x i η δ x i x, η + T γ η δ Tγ x, η δ Tg x, η T g η φ, ψ, v, photon monopole δ Tγ, Ionization Fraction δ xi, source. photon 0,

35 4 T s 1, 1, n u g u exp hν ul n l g l k B T s 4.1., T s., n u, n l.,, n u n 1, n l n 0 g u g 1 3, g l g 0 1 ν ul ν GHz. T s,. - H-H Collision, - e-h Collision spin flip Background photon, Lyman, Neutral Fraction x HI, Ionization Fraction x i.,., τ g , 9,,., 1 H-H Collision 2 e-h Collision 3 p-h Collision., z 00,,, H-H Collision,.,,, H-H Collision, e-h Collision p-h Collision., κ eh κph κhh..,,,. κ,, κ e-h Collision. 34

36 4.1.1 H-H Collision, 7. 7:, 4 13, F z m. 1 0 S 1/2 a : F, m 0, b : F, m 1, S 1/2 c : F, m 1, d : F, m 1, 1, a, b, c, d. 2 H A + H B H A + H B, 14, m A + m B m A + m B 4.4.,, m X H X z., 4.4,, F. 2, F 2, 1, 0. F 2,, cc aa. F 2 De-Excitaion S 1/2 F 0 spin singlet, 1 1 S 1/2 F 1 spin triplet 4 14,,,..,, dipolar interaction,., dipolar interaction,. 35

37 σ + de., F 1 De-Excitaion σ de, F 0 σ0. F 2, 1, De-Excitaion, Excitaion σ e +, σe, Detailed Balance, De-Excitaion σ + de, σ de. σ., T, V, A, B n A, n B, v rel, σv rel n A n B V T 4.5. σ. V T σv rel n A n B 4.6. σv rel De- Excitation α, Excitaion β., F 0 De-Excitaion Excitaion, α, β., α + σ + de v rel, β + σ e + v rel α σ de v rel, β σe v rel α 0 σ 0 v rel β 0.. σv rel,. E, A B E 1 2 µ AB v rel µ H v rel µ AB m A m B m H µ H. m H m A m H, m B m H. σ E, v rel, σ E, σ v rel. v rel Maxwell 3 µh 2 P v rel exp µ H v rel 2 2πk B T g 2k B T g µh 2πk B T g 3 2 exp µ Hvrel 2 2k B T g 4.12., 4.7, 4.8, 4.9,, α σv rel, 36

38 α σ v rel v rel 2π 4π 0 µh d 3 v rel σ v rel v rel P v rel π dφ vrel dθ vrel sin θ vrel dv rel vrel 2 σ v µh rel v rel 0 0 2πk B T g de 2E 2 σ E exp E 2πk B T g 0 2µH E µ H k B T g deeσ E exp E k B T g 8k B T g πµ H 1 k B T g exp µ Hvrel 2 2k B T g 4.13., , v rel E. σ E, σ v rel, 4.13, α +, β +, α, β, α 0 β 0., Schrödinger,,. 1, 7, 8 H-H Collision, + 2, Hamiltonian H, H H NR + H spin H NR 1 2 P 2 i + 1 2m p 2m e H spin α2 EM R 3 i1 2 p 2 i + e2 1 4πϵ 0 x 1 x 2 + e2 1 4πϵ 0 X 1 X 2 e2 4πϵ 0 i1 2 i,j x i X j 4.15 S 1 S 2 3 S 1 R S 2 R R 2 + etc , X i, P i 2, x i, p i 2. S i R 2. H NR,,,,. H spin,,. 4.16,,. H spin, α EM , H NR, H spin. 4.4, H NR, H spin, 4.4., H NR 4.4,. H-H Collision F, 1. a, b, c, d, a, b, c, d. n a, n b, n c, n d.,,, ±,. 37

39 1. F a b c d F 2 cc α+ aa ± β + F 2 bd α+ aa ± β + F 2 db α+ aa ± F 1 F 1 F 1 F 1 F 1 F 1 F 1 F 1 F 1 F 1 F 1 F 1 F 0 F 0 β + ac ±1 1 ±1 1 bd α β ca ±1 1 ±1 1 bd α β ac ±1 1 ±1 1 db α β ca ±1 1 ±1 1 db α β ad ± cd α β da ± cd α β ad ± dc α β da ± dc α β ab ± bc α β ba ± bc α β ab ± cb α β ba ± cb α β bd α0 cc 0 1 ±2 1 β 0 db α0 cc 0 1 ±2 1 β 0 1, a, b, c, d n a, n b, n c, n d. 4.6, A + B α C + D, A n A β, n A αn A n B + βn C n D ,, 15 BA, n A 2αn A n B + 2βn C n D. 38

40 n a HH n b HH 2α + n 2 c 2β + n 2 a + 2 2α + n b n d 2β + n 2 a F α n b n d β n a n c + 4 α n c n d β n a n d + 4 α n b n c β n a n b F F 0 6β + n 2 a 4β n a n b + n c + n d + 4α n b n c + 4 α + + α n b n d + 2α + n 2 c + 4α n c n d 2 α + n b n d + β + n 2 a F α n b n d + β n a n c F α 0 n b n d + β 0 n 2 c F β + n 2 a + 4β n a n c 2α + + 4α + 2α 0 n b n d + 2β 0 n 2 c 4.19 n c 2α + n 2 c + 2β + n 2 a HH F α n b n d β n a n c + 4 α n c n d + β n a n d + 4 α n b n c + β n a n b F α 0 n b n d 2β 0 n 2 c F 0 2β + n 2 a + 4β n a n b n c + n d 4α n b n c + 4α + 4α 0 n b n d 2α + + 4β 0 n 2 c 4α n c n d 4.20 n d 2 α + n b n d + β + n 2 a HH F α n b n d + β n a n c F α 0 n b n d + β 0 n 2 c F 0 2β + n 2 a + 4β n a n c 2α + + 4α + 2α 0 n b n d + 2β 0 n 2 c F 2,1,0, 1 F 2, 1, 0. F 2,1,0, 1. 16, Detailed Balance. Detailed Balance,,,.,, F 2,1 0. Detailed Balance, De-Excitation Rate Excitation Rate, α + β +, α β. F 2. F 2 0, EQ, 16, bd α+ β + aa db α + β + aa 2. 39

41 α + n EQ c α + n EQ b n EQ d 2 β + n EQ 2 a 0 β + α + n EQ c n EQ a β + n EQ 2 a 0 β + α + neq b n EQ a n EQ d n EQ a ,.,, n EQ b n EQ a neq c n EQ a neq d n EQ a exp hν 21 exp T k B T g T g , β + α + exp 2T T g 4.25, α + β +. F 1, F 1 0, α n EQ b n EQ d α n EQ c n EQ d α n EQ b n EQ c β n EQ a n EQ β n EQ a n EQ β n EQ a n EQ c 0 β α neq b n EQ a d 0 β α neq c n EQ a b 0 β α neq c, 4.24, β α exp T T g n EQ a n EQ d n EQ c α β., , T g 2, 1, F 2, 1. a, b, c, d,, n 0 n a n 1 n b + n c + n d.,, 1, H-H Collision, a, b, c, d, n HI n a + n b + n c + n d n 0 + n 1., n HI n a HH + n b HH + n c HH + n d HH n 0 HH + n 1 HH HH 40

42 ., n 0, n 1, n 0 n a HH n 1 HH 6β + n 2 a 4β n a n b + n c + n d + 4α n b n c + 4 α + + α n b n d + 2α + n 2 c + 4α n c n d 6α + ñ 2 a 4α ñ a n b + n c + n d + 4α n b n c + 4 α + + α n b n d + 2α + n 2 c + 4α n c n d n 0 HH HH 6β + n 2 a + 4β n a n b + n c + n d 4α n b n c 4 α + + α n b n d 2α + n 2 c 4α n c n d 6α + ñ 2 a + 4α ñ a n b + n c + n d 4α n b n c 4 α + + α n b n d 2α + n 2 c 4α n c n d , 4.25, 4.29 β +, β α +, α., ñ a exp T T g n a. 17,,.,. F 1 3 a Statistical Equilibrium. n b n c n d 1 3 n 1. n 1 3n 0 exp T T g 3ñ 0 a, b, c, d., dipolar interaction. 4.31, n b n c n d 1 3 n 1, n 0 6α + ñ 2 0 4β ñ a n 1 + 4α n α + + α n α + n α n 1 2 HH α + ñ 2 0 4α ñ 0 n α + + 2α n , { α + α 2 + γ α α 2 γ, α +, α, α, γ, 4.33, { α α + + α γ 1 2 α+ α 4.34 n 0 6 HH α α 2 + γ ñ γ ñ 0 n { α α } γ γ n 2 1 α 3ñ ñ 0 n 1 n γ 9ñ 2 0 6ñ 0 n 1 + n 2 1 α 3ñ 0 n 1 ñ 0 + n γ 3ñ 0 n β + n 2 a α + exp 2T «n 2 a α + ñ 2 a T g β n a α exp T «n a α ñ a T g 41

43 ., n 1 3ñ 0,,., n 0 α 3ñ 0 n 1 ñ 0 + n HH, T g, ñ 0 n 0 exp T g n 0., n 0 α 3ñ 0 n 1 n 0 + n 1 α 3ñ 0 n 1 ñ 0 n HH,., n HI n 0 + n 1, n 0 α 3ñ 0 n 1 n 0 + n 1 HH 3α exp T g n HI n 0 + αn HI n , κ HH 01 3α exp T 3 α + + α exp T 4.39 T g T g κ HH α α + + α 4.40 κ HH 01, κhh., 4.13, α ±, T g, κ HH 01, κhh, T g., C HH 01 κ HH 01 n HI κ HH 01 x HI n H 4.41 C HH κ HH n HI κ HH x HI n H 4.42, C01 HH, CHH n HI x HI n H., n 0 n , 4.32, n 0 n 1 C01 HH n 0 + C HH n HH n 0 HH C01 HH n 0 C HH n HH., Statistical Equilibrium, Statistical Equilibrium, spin-spin H spin., spin-spin, b c, d c. 42

44 4.1.2 e-h Collision H-H Collision, Collisione-H Collision.,, H NR 1 2m e 2 i1 p 2 i + 1 P 2 + e2 1 2m p 4πϵ 0 x 1 x 2 e2 1 4πϵ 0 x 1 X e2 1 4πϵ 0 x 2 X X, P, x i, p i.,. e-h Collision,,. 9 H-H Collision, κ HH 01, κhh, e-h Collision κ eh 01, κeh, n 0, n 1,., n 0 n 1, C eh 01, CeH. C01 eh n 0 + C eh n eh n 0 eh C01 eh n 0 C eh n eh C eh 01 κ eh 01 n e κ eh 01 1 x HI n H 4.48 C eh κ eh n e κ eh 1 x HI n H p-h Collision, Collisionp-H Collision.,, H NR 1 2m e p m p 2 P 2 i + e2 1 4πϵ 0 X 1 X 2 e2 1 4πϵ 0 x X 1 e2 1 4πϵ 0 x X 2 i1 4.50, H 2 +. X i, P i, x, p. H-H Collision, e-h Collision, κ ph 01, κph, C ph 01 κph 01 n p κ ph 01 1 x HI n H 4.51 C ph κph n p κ eh 1 x HI n H 4.52, C ph 01, CpH, n 0, n 1,. n 0 n 1 C ph 01 n 0 + C ph n ph n 0 ph C ph 01 n 0 C ph n ph 43

45 4.1.4 H-H, e-h, p-h Collsion κ 3 CollisionH-H, e-h, p-h κ 8. 8: H-H, e-h, p-h Collision κ S. R. Furlanetto and M. R. Furlanetto2007, e-h Collision κ eh.,,., x HI 1 x i 0, H-H Collision. n e n p 1 x HI n HI n HI Collision n 0, n 1 Collision Rate, H-H Collision, e-h Collision, p-h Collision, Collision n 0, n 1, n 1 n 1 collision + n 1 HH + n 1 eh C 01 n 0 C n ph n 0 n 0 collision + n 0 HH + n 0 eh C 01 n 0 + C n ph 44

46 ., C 01 C01 HH + C01 eh + C ph 01 κ HH 01 T g x HI n H + κ eh 01 T g 1 x HI n H + κ ph 01 T g 1 x HI n H 4.57 C C HH + C eh + C ph κ HH T g x HI n H + κ eh T g 1 x HI n H + κ ph T g 1 x HI n H 4.58, C 01, C., Collision Rate C, T s., κ T g. 4.58, x HI, n H, T g., f x 1 + δ x f x + xδ x df x d x f x 1 + x f x, C HH, C HH κ HH Tg 1 + δtg xhi 1 + δ xhi n H 1 + δ H κ HH HH C Tg xhi n H δ H + δ xhi + d ln κhh d ln T g Tg Tg d ln κhh d ln T δ Tg + g df x f x 1 + d x 1 + δ xhi 1 + δ H d ln f x d ln x δ x { } d ln κhh Tg δ xhi δ H + d ln T δ xhi δ Tg g , CHH κ HH Tg xhi n H., 4.60 { }, 2, Neutral Fraction δ xhi O 1 18,., δ xhi., C eh, CpH, i e, p, C ih κ ih Tg 1 + δtg {1 xhi 1 + δ xhi } n H 1 + δ H Tg κ ih d ln κhh Tg 1 xhi n H 1 + d ln T g ih C 1 x HI δ xhi 1 + δ H 1 x HI 1 + δ H x HI d ln κih δ xhi + Tg 1 x HI d ln T δ Tg g { + x HI δ xhi δ H x HI d ln κ ih } Tg 1 x HI 1 x HI d ln T δ xhi δ Tg g C ih κih Tg 1 xhi n H, i e, p. C HH 4.61 { }, δ xhi O , 4.61, C C HH + C eh + CpH, 18, Reionization. 45

47 C CHH + + C eh + C HH d ln κ HH d ln T g { + C HH x HI { { ph C 1 + δ H + C HH x HI CeH 1 x HI Tg Tg + eh d ln κ C eh d ln T g + } ph C δ δ xhi H + + ph d ln κ C ph d ln T g } ph C δ xhi CeH 1 x HI + C HH d ln κ HH Tg d ln T x HI C eh d ln κ eh Tg g 1 x HI d ln T ph d ln κ + C ph } Tg g d ln T δ xhi δ Tg g C C 1 HH + δ H + x HI C ih C 1 x HI C ie,p δ x HI + C ih d ln κ ih Tg C ih,e,p d ln T δ Tg g C HH + x HI C ih C 1 x HI C ie,p δ x HI δ H C HH d ln κ HH Tg + C d ln T x HI C ih d ln κ ih Tg g 1 x HI C d ln T g δ x HI δ Tg ie,h Tg δ Tg 4.62., C ih,e,p C ih. 2, 3, δ x HI,. C δ C, C C 1 + δ C, 4.62, C HH δ C δ H + x HI C ih C 1 x HI C ie,p δ x HI + C ih d ln κ ih Tg C ih,e,p d ln T δ Tg g C HH + x HI C ih C 1 x HI C ie,p δ x HI δ H C HH d ln κ HH Tg + C d ln T x HI C ih d ln κ ih Tg g 1 x HI C d ln T g δ x HI δ Tg ie,h 4.63., T s δ Ts. 4.7 T s 46

48 4.2 Background photon 11, Background photon,. Background photon, CMB photon. 19 n 1, n 0, Einstein A, B, n 1 n 0 n 0 B 01 Iν CMB 21 BGphoton n 0 B 01 Iν CMB 21 BGphoton n 1 A + B Iν CMB 21 + n 1 A + B Iν CMB n 0 B 01 Iν CMB 21 Background photoncmb photon n 1, n 1 A n 1, n 1 B Iν CMB 21 n 1., 4.65, 4.65 n 0 B 01 Iν CMB 21 Background photoncmb photon n 0, n 1 A n 0, n 1 B Iν CMB 21 n : Background photon,, 2 n HI n 0 + n 1., , n HI n 1 BGphoton + n 0 BGphoton BGphoton, n HI , Background photon, CMB photon+21cm photon,, CMB photon. 47

49 4.3 Lyman 1, 12, 13 Lyman,, Lyman photon, 1s 2p, 1s, F.,, 1 0 S 1, Lyman photon, 2 1 P 1, 2 2., 1 1 S S , 1 1 S 1 2, 2 0 P 1 2, 2 1 P 1 2, 2 1 P 3, 2 2 P 3, 0, 1, 2, 3, 4, Lyman photon /, F 0, 1, F 0 F 0.,, 0 3, 0 4, 1 2, 1 3, 1 4, , F 0 F 0, 0 5, F 2., 0 1, , 1 0, 1 3 0, , 3 4. : Lyman, n 0, n 1, P 01, P, n 1 P 01 n 0 P n Lymanα n 0 P 01 n 0 + P n Lymanα. P 01, , 0 1, P,

50 P, P 01, Lyman photon I ν Jν 1 4π dωiν., J ν, P 01, P.,, 0 3. τ g photon Specific Intensity I ν x, τ g, n. 0 3, Intesnsity, di ν r, τ g, n 0 3 hν 4π n 0 r, τ g φ 03 ν B 03 I ν r, τ g, n cdτ g B 03, 0 3 B, φ 03 ν 0 3 Line Profile. photon n dωn, J ν x, τ g 1 4π dω ni ν x, τ g, n, dj ν r, τ g 0 3 hν 4π n 0 r, τ g φ 03 ν B 03 J ν r, τ g cdτ g 4.70., photon u ν n ν, J ν hνn ν u ν 4π c J ν,, dn ν r, τ g 0 3 n 0 r, τ g φ 03 ν B 03 J ν r, τ g dτ g dn ν r, τ g dτ g n 0 r, τ g φ 03 ν B 03 J ν r, τ g photon n γ, n ν nγ 0 dνn ν, ν, dn γ r, τ g dτ g n 0 r, τ g B 03 φ 03 ν J ν r, τ g , 0 3 photon 0 3., photon 3, , 3 1 photon,,, A 30, A 31 B 30, B 31. dn γ r, τ g dτ g n 3 r, τ g A 30 + B 30 φ 30 ν J ν r, τ g dn γ r, τ g dτ g n 3 r, τ g A 31 + B 31 φ 31 ν J ν r, τ g n 3 3. φ 30 ν, φ 31 ν, 3 0, 3 1 Line Profile. 3 1, decay 1 decay D 31, 0 0 D 31 dn γ r,τ g 3 1 dτ g 3 1 dn γ r,τ g 3 0 dτ g + dn γr,τ g dτ g n 3 r, τ g A 31 + B 31 0 φ 31 ν J ν r, τ g n 3 r, τ g A 30 + B 30 0 φ 30 ν J ν r, τ g + n 3 r, τ g A 31 + B 31 0 φ 31 ν J ν r, τ g A c2 2hν φ 31 ν J ν r, τ g A c hν φ 30 ν J ν r, τ g + A c2 2hν φ 31 ν J ν r, τ g 49

51 . Einstein A B D.7., ν 30, ν , 3 1.,,., hν 31 hν 30 hν α.2 ev. hν α.2 ev 1s 2p. Line Profile, φ 31 φ 30, D 31, D 31 A 31 A 30 + A , D 31, 1 0 1, 1 D 31, 0, 0 3 1, 1 0,, n 1 n 0 dn γ dτ g D n 0 B 03 0 dn γ dτ g D n 0 B 03 0 φ 03 ν J ν A 31 A 30 + A φ 03 ν J ν A 31 A 30 + A r, τ g., 0 4 1, 1 3 0, 1 4 0, n 1 A 41 n 0 B 04 φ 04 ν J ν A 40 + A 41 n 0 A 41 n 0 B 04 φ 04 ν J ν A 40 + A 41 n 1 n 0 n 1 n 0 n 1 B n 1 B n 1 B n 1 B φ 13 ν J ν A 30 A 30 + A φ 13 ν J ν A 30 A 30 + A φ 14 ν J ν A 40 A 40 + A φ 14 ν J ν A 40 A 40 + A , Lyman n 1, n 0, 50

52 n 1 n 1 Lymanα + n n n A 31 A 41 n 0 B 03 φ 03 ν J ν + B 04 φ 04 ν J ν 0 A 30 + A 31 0 A 40 + A 41 A 30 A 40 n 1 B 13 φ 13 ν J ν + B 14 φ 14 ν J ν 0 A 30 + A 31 0 A 40 + A 41 n 0 n 0 Lymanα + n n n A 31 A 41 n 0 B 03 φ 03 ν J ν + B 04 φ 04 ν J ν 0 A 30 + A 31 0 A 40 + A 41 A 30 A 40 +n 1 B 13 φ 13 ν J ν + B 14 φ 14 ν J ν A 30 + A 31 A 40 + A , 4.68, P 01, P, A 31 P 01 B 03 φ 03 ν J ν + B 04 A 30 + A 31 0 P B φ 13 ν J ν A 30 A 30 + A 31 + B φ 04 ν J ν A 41 A 40 + A φ 14 ν J ν A 40 A 40 + A Lyman, 0 1. Lyman, 1s 2p.,, 0, 1 1s, 2, 3, 4, 5 2p., Lyman, 0 3, 0 4, 1 2, 1 3, 1 4, 1 5. Lyman, photon,, n γ n 1s B 1s 2p φ α ν J ν n 1s P α 4.89 α 0. n 1s 1s, B 1s 2p, 1s 2p B., Lyman P α, P α B 1s 2p φ α ν J ν P α Lyman rate, 1s 1. P α P., P B A 13 0 φ 13 ν J 30 A ν A 30 +A 31 + B 14 0 φ 14 ν J 40 ν A 40 +A 41 P α B 1s 2p 0 φ α ν J ν c 2 A A 2hν φ 13 ν J 30 ν 0 A 30 +A c 2 A 2hνα 3 1s 2p 0 φ α ν J ν c2 A A 2hν φ 14 ν J 40 ν A 40 +A 41 A 30 A 31 A 30 +A 31 + A 40A 41 A 40 +A 41 3A 2p 1s

53 ., Einstein A B 21, ν α ν 30 ν 31, φ α φ 13 φ p 1s A 2p 1s, 3 0, 3 1, 4 0, 4 1 A 30, A 31, A 40, A 41 sum rule.13, 14 sum rule, nf J n J F, m F 2F ,, n 2, F 2, J 3 n 1, F 1, J P 3 2 2, 1 11 S S 1 n 1, F 0, J decay Intensity, 2F sum rule, I ij i j Intensity, I 51 + I 50 I 51 I 41 + I 40 I 41 + I 40 5, 3 5 1, 0 4 1, I 40 + I 41 I 30 + I 31 1, 4 1, 0 3 1, I 31 + I 30 I 31 + I 30 I 21 + I 20 I 21 3, 3 1, 0 2 1, I 40 + I 50 I 40 I 41 + I 51 I 41 + I 51 1, 3 0 4, 5 1 4, I 20 + I 30 I 30 I 21 + I 31 I 21 + I 31 1, 3 0 2, 3 1 2, , I 21, I 30, I 31, I 40, I 41, I I 51, 1 5 I 51, 2 5 I 51, 2 5 I 51, 1 5 I 51, I I 21 : I 30 : I 31 : I 40 : I 41 : I 51 1 : 1 : 2 : 2 : 1 : Intensity A, I ij g i A ij I α 4.99 g 2p A 2p 1s. g i, i, i n F L J, g i 2F +1., g 2 1, g 3 3, g 4 3, g 5 5., g 2p, 2p, g 2p g 2 + g 3 + g 4 + g 5 12, 24 I α total Lyman Intensity, I α I 21 + I 30 + I 31 + I 40 + I 41 + I I 51., 4.99, , A ij A 2p 1s 5I ij g i I D.7, D.8, g 1s 2 2 4, g 2p , g 1 g 3 g ν α.2 ev, ν 13, ν 14, 23 n, F, J. 24 2p, 6. g 2p 12,, 2. 52

54 A 51 A 2p 1s 5I 51 g 5 I 51 A 2p 1s 4.1 A 41 A 2p 1s 5I 41 g 4 I A 2p 1s 4.2 A 40 A 2p 1s 5I 40 g 4 I A 2p 1s 4.3 A 31 A 2p 1s 5I 31 g 3 I A 2p 1s 4.4 A 30 A 2p 1s 5I 30 g 3 I A 2p 1s 4.5 A 21 A 2p 1s 5I 21 g 2 I 51 A 2p 1s 4.6 A, 2p 1s., 4.91, P P α 1 3 A 2p 1s 2 3 A 2p 1s 1 3 A 2p 1s+ 2 3 A 2p 1s A 2p 1s 1 3 A 2p 1s 2 3 A 2p 1s+ 1 3 A 2p 1s 3A 2p 1s , Lyman, Neutral Fraction x HI or Ionization Fraction x i 11, Neutral Fraction x HI, Ionization Fraction x i. 3, n HI n 0 + n 1,.,, n HI n 0 + n 1, 3.,. 3,, F 0 F 1,,,,. n HI, n H Neutral Fraction x HI, Ionization Fraction x i, n HI x HI n H 1 x i n H 4.8., x HI, x i n HI, n HI x HI n H, or n HI NF x i n H 4.9 IF., n 1, n 0., n HI n 0 + n g 0 1, g 1 3, n 0 n 1 1:3, n 1 g 1 x i n H 3 1 x i n 0 + n IF g 0 + g x i n 0 g 0 x i n H 1 1 x i n 0 + n IF g 0 + g x i 53

55 . 4.5 T s, n 1 n 0,. n 1 n 1 + n 1 Collision + n 1 BGphoton + n 1 Lymanα IF C 01 n 0 C n 1 + n 0 B 01 Iν CMB 21 n 1 A + B Iν CMB 21 + P01 n 0 P n x i n 0 + n x i C 01 + B 01 Iν CMB 21 + P 01 n0 C + A + B Iν CMB 21 + P n1 3 1 x i n 0 + n x i n 0 n 0 + n 0 Collision + n 0 BGphoton + n 0 Lymanα IF C 01 n 0 + C n 1 n 0 B 01 Iν CMB 21 + n 1 A + B Iν CMB 21 P01 n 0 + P n x i n 0 + n x i C 01 + B 01 Iν CMB 21 + P 01 n0 + C + A + B Iν CMB 21 + P n1 1 1 x i n 0 + n x i,., n 1 3 exp hν 21 3 exp T ln 3 ln n 1 + ln n 0 n 0 k B T s T s T s T 1 n 0 1 n T s n 0 n 1 T s n 1, n 0., hν 21 k B K ν , 4.114,, T s, 1 1 x i 1 4 C T s 1 x i T s 1Tg 1Ts 1 + P 1 { T γ 1 + A 1 } T α T s T γ T s Appendix, T g Lyman α Color TemperatureT α, C 01 3 exp hν 21 3 exp T C k B T g T g P 01 3 exp hν 21 3 exp T P k B T α T α., Background photon CMB I CMB ν I BB ν 2hν3 c 2 1 exp hν k B T γ

56 T s > 0.. T g > T s T g < T s, C 1 T g 1 T s < 0 C 1 T g 1 T s > 0, Collision, 1 T s. 1 T s T s 1 T s T s.,, Collision. n 1 n 0 3 exp T s,, Collision n 1, n 0 Collision n 1, n 0.,, Collision, Collision,. T α > T s T α < T s,, Lyman, , T s. T γ > T s T γ < T s, Background photon photon, T s. x i > 0 xi 1 x < 0, i 1 1 x i T s > 0 1 x i 1 1 x i T s < 0, 1 T s.. x i Ionization Fraction, Ionization Fraction,,. 4.6 T s 4.117,, 0,., Recombinationz 00 Reionizationz Ionizaton Fraction x i 0, 21 cm Recombination Reionization, , Recombination Reionization, Ionization Fraction., 25,., spin flip 3 Collision, BGphoton /, Lymanα.,., T s C 1Tg 1Ts 1 + P 1 { T γ 1 + A 1 } T α T s T γ T s A T γ + C + P A 1 + C 1 T g + P 1 T α T γ + C A T g T g + P A T α T α 1 + C A T g + P A T α y c C A T g y α P A T α Collision BGphoton, 55

57 y c, y α 26,, T s T γ + y c T g + y α T α 1 + y c + y α , photon T γ, T g, Background Lyman T α 1 : y c : y α., y c, T s T g, y α T s T α, y c, y α 1, T s T γ., Lyman, T s, photon T γ, T g 11. Collision κ ih n i 1, i H, e, p Background photon T / A T γ. 11: Temperature HistoryA. Lewis and A. Challinor c α collision c Lyman α α. 56

58 z 300, photon baryon, T γ T g. Lyman 27, T s T γ T g., 30 z 300, photon baryon, baryon T g T g 1 + z 2. T g < T γ., κ ih 1 n i < T / A T γ, Background photon, Collision., T s T g < T γ,. z 0, Collision., Collision κ T g T g,., κ ih n i 1 > T / A T γ, Background photon Collision., T s photon T γ.,, Lyman,, T g T γ., T s, T s T g T γ.,, Lyman,,. 4.7 T s δ Ts., 4.117,, 4.124,. T s, T γ, T g, T α, C, P, T s,. T γ, T g, T α, C, P, 1.1, 4.124, δ Ts T s T s T s T s T s 1 A + C T g + P T α A Tγ + C + P A + C T g + P T α A Tγ + C + P 1 + Tγ A 1 + δtγ + C 1 + δ C + P 1 + δ P T g1+δ T g + P 1 1+δ P T α 1+δ T α A Tγ A + C 1+δ C + C + P + A + C T g + P T α C T g Tγ A δ Tγ + C δ C + P δ P { } δc 1 δtg δtg + P δ T P δ Tα α A Tγ + C + P 1 A Tγ δ Tγ + C δ C + P δ P 1 + A + C T g + P T α 1 C T g { δc 1 δtg δtg } + P T α δ P δ Tα δ Ts., δ Tγ, δ Tg, δ Tα, δ P,., δ C, Neutral Fraction x HI x HI 1 + δ xhi δ xhi, Reioniation, x HI, δ xhi O 1, δ C O 1.,, 21 cm,, neutral Fraction, δ xhi,., Lyman, z

59 δ C, δ Ts 1 + Tγ A + T C + P 1 A Tγ 1 Tγ A δ Tγ + T C δ C + P δ P A + C + P 1 C P δc δ Tg + δ P δ Tα 1 T g T α T g T α A Tγ + C + P δ Tγ + C + Tγ A + C + P P + Tγ A + C + P A A + C + P δ Tγ + T γ T γ { C A 1 Tγ 1 Tg + + C T g A + C T g + P C T g A + C T g + P T α P T α A + C T g + P T α C T g δ Tg + T α δ C A + C T g + P T α δ Tg + + P T γ 1 Tα 1 Tg } δ P A + C + P A T γ T γ + C + P δ C T g T α { } P A 1 Tγ 1 Tα + C T γ 1 Tg 1 Tα P T α A + C T g + P T α δ Tα P T α A + C T g + P T α δ Tα A + C T γ + P T γ A + C T g + P T α δ P 4.126,., 4.63, Collision Rate δ C, Baryon δ H δ b, δ Tg, Neutral Fraction δ xhi 28,, δ Ts A A + C + P δ Tγ + T γ T γ { C A 1 Tγ 1 Tg + A + C + P T γ δ H + T γ A C HH C x HI 1 x HI C T g A + C T g + P T α δ Tg + + P T γ 1 Tα 1 Tg } + C + P T g ie,p { } P A 1 Tγ 1 Tα + C T γ 1 Tg 1 Tα + A + C + P A T γ T γ + C + P δ P T g T α P T α A + C T g + P T α δ Tα T α C ih C δ x HI + ih,e,p C ih d ln κ ih Tg C d ln T δ Tg g 28`, δ xhi, 4.63 δ xhi δ H, δ xhi δ Tg. 58

60 A A + C + P T γ + C T g T γ δ Tγ + A + C + P + T g T α P T α A + C T g + P T α δ Tα { C A 1 Tγ 1 Tg A + C + P A T γ T γ + C + P T g T α { } P A 1 Tγ 1 Tα + C T γ 1 Tg 1 Tα + A + C + P A T γ T γ + C + P δ P + T g T α { } C A 1 Tγ 1 Tg + P T γ 1 Tα 1 Tg + A + C + P A T γ T γ + C + P T g T α C ih d ln κ ih Tg C ih,e,p d ln T δ Tg g { } C A 1 Tγ 1 Tg + P T γ 1 Tα 1 Tg A + C + P A T γ T γ + C + P δ H T g T α + P T γ 1 Tα 1 Tg } C HH C x HI 1 x HI ie,p C ih C δ x HI 4.127, δ Tγ, δ Tg, δ Tα, δ H, δ xhi, δ P , 4.124, Neutral Fraction δ xhi., 21 cm δ 21 δt b δt b. δt b 59

61 5 5.1 photon T γ Background photon T γ, 11, scale factor a. T γ T γ0 a T γ0 1 + z 5.1 T γ0 2.7 K CMB. photon baryon z z dec 300, photon T γ T g., T g,, T g scale factor 2, scale factor photon, T g < T γ. 11 photon baryon, z z dec 300, T dec, T dec T γ0 1 + z dec 5.2. Tg z 1 + z 2, photon z < z dec, baryon,. T g z T dec 1 + z z dec 2 T γ0 1 + z dec 1 + z z 1 + z dec } {{ } <1 T γ z Ionization Fraction x i Ionization Fraction x i,., Recombination z z rec 00,, x i 1.,, z z rec 00,, x i, 1 0,. 21 cm signal,. z 6-,,,, Reionization., x i 0 1,, 21 cm. 21 cm 2.30 x HI 1 x i 0., 21 cm,, Neutral Fraction x HI δ xhi.,, Reionization, Neutral Fraction δ xhi Ionization Fraction δ xi. 60

62 6 21cm Power Spectrum , 21 cm., δt obs δt obs b δ T obs b δ T obs b δ , δ 21, δ H, δ xhi, δ Tγ, δ Ts, gradient. dv p dr b cm 16, 17, cm δ 21 δ δt obs b δ 21 x, η; z δ δt obs b x, η; z. δ, 2.30, δ δtb obs ν21 T obs b T obs b, 1+z, x, η δ δ T obs b T obs ν21 b 1+z, η ν21 1+z, η δtb obs ν21 δ T obs b 1+z, x, η ν21 1+z, η z, 3c 3 ha 21 x HI n H 32πν21 2 k 1 T γ B 1 + z H z T s. 21 cm mk. 6.2 δ v 1 + z dv p H z dr. 21 cm, 1.1, δtb obs 3c3 ha 21 x HI 1 + δ xhi n H 1 + δ H 1 32πν21 2 k T γ 1 + δtγ 1 δ v B 1 + z H z T s 1 + δ Ts 1 T γ 1 + δ xhi 1 + δ H T s 3c 3 ha 21 x HI n H 32πν 2 21 k B 1 + z H z δ δ Ts obs 1 T b 1 + δ H + δ xhi δ Ts { + δ xhi δ H + δ xhi δ v T s δ Ts T γ δ Tγ T s T 1 δ v γ T s T s T γ δ Ts T s T s T γ δ xhi δ Ts T s T s T γ δ H δ Ts T γ T s T γ δ Tγ δ v T γ T s T γ δ xhi δ Tγ } T s T s T δ v δ Ts γ , δ H, CMB photon δ Tγ, Matter δ v,, δ H δ Tγ., Neutral Fraction x HI, Reionization, O 1,., 4.125, δ Ts δ C, δ xhi, O { }, δ xhi O 1, δ Ts O 1 61

63 . Neutral Fraction δ xhi, { } , 21 cm δ 21, δ δ Ts 1 + δ H + δ xhi + { + δ xhi δ H + δ xhi δ v + T s T s T γ δ Ts T s T s T γ δ xhi δ Ts T s T s T γ δ H δ Ts T γ T s T γ δ Tγ δ v T γ T s T γ δ xhi δ Tγ } T s T s T δ v δ Ts 1 γ 6.5., δ Ts δ H, δ xhi, δ Tg, δ Tγ, δ Tα, δ P 29, 21 cm,, δ H, Neutral Fraction δ xhi, CMB photon δ Tγ, δ Tg, Lyman photon δ Tα, Lyman photon P δ P, gradient δ v.,. δ 21, , ,,, 2. 1 δ xhi δ 21 δ. 2 T s T γ T γ T s δ xhi 1 21 cm Recombination Reionization, Ionization Fraction Neutral Fraction,. δ 21, 6.5, δδ, δ 21 1 δ Ts δ H + δ xhi δ H + δ xhi + T γ T s T γ δ Ts T s T s T γ δ Ts T γ T s T δ Tγ δ v 1 γ T γ T s T γ δ Tγ δ v 6.6., δ 21 δ., 4.124, δ xhi, 4.127, Appendix,, δ 21 q H δ H + q xhi δ xhi + q Tγ δ Tγ + q Tg δ Tg + q Tα δ Tα + q P δ P + q v δ v ,,., x, η; z.,, , 4.117, T s, δ Ts. 62

64 k, η; z. q, { } C A 1 Tγ 1 Tg + P T γ 1 Tα 1 Tg q H 1 + C 1 Tγ 1 Tg + P 1 Tγ 1 Tα A + C + P 6.8 T γ T γ { } C A 1 Tγ 1 Tg + P T γ 1 Tα 1 Tg q xhi 1 + C 1 Tγ 1 Tg + P 1 Tγ 1 Tα A + P T γ T γ q Tγ q Tg q Tα q P A + C + P T g T α C 1 Tγ 1 Tg + P 1 1 Tγ 1 Tα + C C HH C x HI 1 x HI A A + C T γ + P T γ C T g C 1 Tγ 1 Tg + P 1 Tγ 1 Tα { } C A 1 Tγ 1 Tg + P T γ 1 Tα 1 Tg + C 1 Tγ 1 Tg + P 1 Tγ 1 Tα A + C + P T γ T γ ie,p C ih C ih,e,p C ih d ln κ ih Tg C d ln T g 6.11 P T α C 1 Tγ 1 Tg + P Tγ 1 Tα { } P A 1 Tγ 1 Tα + C T γ 1 Tg 1 Tα C 1 Tγ 1 Tg + P 1 Tγ 1 Tα A + C + P 6.13 T γ T γ q v δ H, δ xhi, δ Tγ, 2.30, 2.30 T s. q,,,., δ Tα, δ Tg, δ P, 21 cm. δ v, 2.30, 21 cm. δ H, δ xhi, δ Tγ, δ Tg, δ Tα, δ P,, gradient δ v. δ v,., 21 cm Power Spectrum Matter Power Spectrum ,,. δ iso 21 q H δ H + q xhi δ xhi + q Tγ δ Tγ + q Tg δ Tg + q Tα δ Tα + q P δ P cosµ, µ 4 Matter Power Spectrum. 63

65 δ xhi 1, T g T α., Lyman photon Color Temperature T α T g.,. 1, S. A. Wouthuysen, Lyman photon T g,, Lyman photon,, photon, Lyman, T g. T α T g., δ 21 q. q, 6.7,. q, δ 21 Tα T g q H δ H + q xhi δ xhi + q Tγ δ Tγ + q Tg δ Tg + q P δ P + q v δ v 6.16 q H 1 + q xhi 1 + C C + P C C + P A A + C + P A A + C + P T γ 6.17 T γ C HH x HI 6.18 C 1 x HI ie,p C ih C q Tγ q Tg T g T g T γ T γ T g T γ + A + C + P T g A + C + P 6.19 T γ A C C + P C ih d ln κ ih Tg C d ln T 6.20 g A + C + P T γ ih,e,p q P P C + P A A + C + P T γ 6.21 q v , 6.15,, δ21 iso. Apenndix Tα T g q H δ H + q xhi δ xhi + q Tγ δ Tγ + q Tg δ Tg + q P δ P T s T γ 21 cm,, T g CMB photon T γ. T s, CMB photon T γ.,., Tγ T s 1, T s CMB photon T γ., 6.5, δ Ts, δ Tγ,. δ 21, δ δ H + δ xhi δ v + {δ xhi δ H δ xhi δ v } 1 δ H + δ xhi δ v + {δ xhi δ H δ xhi δ v }

66 ., δ 1, δ H + δ xhi., 1 δ v,., Power Spectrum, δ xhi δ v, µ k., k. F.12,., A x B x, ÃB k à k B k, ÃB k d 3 k à k B k k., δ 21 k, η; z δ H k, η; z + δ xhi k, η; z δ { } v k, η; z + δ xhi δ H k, η; z δ xhi δ v k, η; z 2π 3 δ H k, η; z + δ xhi k, η; z δ v k, η; z d 3 k + { δxhi k 2π 3, η; z δh k k, η; z δ xhi k, η; z δ v k k, η; z } 6.25., 21 cm, δ H, δ xhi, δ v 3., z z eq 31,, δ v µ 2 fδ b, 21 cm, Ionization Fraction δ xhi δ b δ H. T s T γ δ xhi 1, 6.24, 6.25, { },,. δ 21 δ H + δ xhi δ v cm 3D Power Spectrum 16, 21 cm 3 3DPower Spectrum. 3 Power Spectrum P 21, δ21 k δ21 k 2π 3 δ D k k P 21 k δ, Dirac delta δ D. notation, à k A x d 3 xa x e ik x 6.28 d 3 k 2π 3 à k eik x 6.29.,., δ x,, δ x δ x, δ k δ k., 6.27, δ21 k δ 21 k 2π 3 δ D k + k P 21 k z eq, ρ m ρ r. 65

67 . 6.1, δ xhi 1, T s T γ δ xhi 1, 21 cm 3D Power Spectrum, δ 21, 6.7, 6.27, 21 cm Power Spectrum P ,,, 2π 3 δ D k k δiso δiso P 21 k 21 k δ v k 21 k δ v k δiso iso 21 k δ 21 k δiso 21 k δ v k iso δ v k δ 21 k + δ v k δ v k 2π 3 δ D k k P δ iso 21 δiso 21 k + P δ iso 21 δ v k +P δ v δ21 iso k + P δ v δ v k P 21 k P δ iso k P 21 δiso 21 δ21 isoδ k P v δ v δ21 iso k + P δ v δ v k 6.31, 21 cm Power Spectrum., δ A, δ B, δa k δb k 2π 3 δ D k k P δa δ B k 6.32, P δa δ B., P {δa δ B } k 1 2 P δa δ B k + P δb δ A k 6.33, 6.31, P 21 k P δ iso 21 δiso 21 k 2P {δ iso 21 δ v} k + P δ v δ v k , 6.34, k, δ21 iso, P δ iso 21 δiso, k k k.,, δ v µ 2 fδ 21 H, µ k k, P 21 k k k µ k k., P 21 k, P 21 k, µ., 6.34, P 21 k, µ P δ iso 21 δiso 21 k 2fµ2 P {δ iso 21 δ H} k + f 2 µ 4 P δh δ H k P µ 0 k + µ 2 P µ 2 k + µ 4 P µ 4 k 6.35., µ. 6.35, P 21, µ, µ 4 Matter Baryon Power Spectrum., Matter, Neutral Fraction,, 21 cm Power Spectrum Matter Power Spectrum. 7 66

68 , µ P µ 0, P µ 2, P µ 4,. P µ 0 k P δ iso 21 δiso 21 k q 2 HP δh δ H k + q 2 x HI P δxhi δ xhi k + q 2 T γ P δtγ δ Tγ k +q 2 T g P δtg δ Tg k + q 2 T α P δtα δ Tα k + q 2 P P δp δ P k +2q H q xhi P {δh δ xhi } k + 2q Hq Tγ P {δh δ T γ } k + 2q Hq Tg P {δh δ T g} k +2q H q Tα P {δh δ T α } k + 2q H q P P {δh δ P } k + 2q x HI q Tγ P {δxhi δ T γ } k +2q xhi q Tg P {δxhi δ T g} k + 2q x HI q Tα P {δxhi δ T α} k + 2q x HI q P P {δxhi δ P } k +2q Tγ q Tg P {δt γ δ Tg} k + 2q T γ q Tα P {δt γ δ Tα} k + 2q T γ q P P {δt γ δ P } k +2q Tg q Tα P {δt g δ Tα} k + 2q T g q P P {δt g δ P } k + 2q T α q P P {δt α δ P } k 6.36 P µ 2 k 2fP {δ iso 21 δ H} k 2f q H P δh δ H k + q xhi P {δxhi δ H} k + q T γ P {δt γ δ H} k + q Tg P {δtg δ H} k + q T α P {δtα δ H } k + q P P {δt δ H} k 6.37 P µ 4 k f 2 P δh δ H k 6.38 q, F.5, F.6, F.7, F.8, F.9, F.. 21 cm Power Spectrum, Power Spectrum,., µ, Physical Matter Power Spectrum P δh δ H Astrophysical P δxhi δ xhi. Power Spectrum,, δ xhi, δ Tg, δ Tα, δ P.., δ xhi, Ionization historyreionization,. T g, X-ray hetaing, Lyman hetaing,., δ Tα, δ P, Lyman photon., 21 cm Power Spectrum., T s T γ, 4, δ Tg, δ Tα, δ P, Ionization history, 21 cm Power Spectrum., T α T g, 21 cm, F.12, Power Spectrum, 6.35 δ21 iso δiso 21 Tα T g., P 21 k, µ P δ iso 21 T αtg δiso 21 k 2fµ 2 P j ff k + f 2 µ 4 P δh T αtg δ21 iso δ δ H k T H αtg P T αt g µ 0 k + µ 2 P T αt g µ 2 k + µ 4 P T αt g µ 4 k µ P T αt g µ 0, P T αt g µ 2, P T αt g µ 4,, 67