## Cosmological Physics Errata

A comprehensive introduction to modern cosmology, at the advanced undergraduate / beginning postgraduate level.

Comments and corrections are most welcome. Please contact me at jap@roe.ac.uk

## Errors corrected in the first reprint (July 1999):

- p11 Equation (1.22) dg/dx -> partial g / partial x
- p25 Second para: rho^2 -> rho c^2
- p172 Equation (6.77) z^2 -> w^2 on rhs
- p256 Line 6: eV should be in roman, not italic
- p333 d ln a / d ln tau = X -> d ln a / d tau = X
- p333 X^2 = (W + Y'^2/2)/W_i -> X^2 = (W + Y'^2/2)/(W_i+Y_i'^2/2)
- p333 y -> Y in (11.28)
- p358 X-ray background discovered early 1960s, not 1970s
- p389 Wavelength of H alpha is 6563, not 5653
- p414 B=19.3 -> I=19.3
- p468 partial (dot a)^2/ partial K = 1 -> ( partial (dot a)^2/ partial K )_a = 1
- p473 exp( +- i integral ) in (15.60)
- p515 3 lines after (16.77), beta=1 -> beta=0
- p515 (16.79) applies for an exponential one-point distribution, so the pairwise distribution is not exponential. For an exponential pairwise distribution, (16.79) should be delta_k -> delta_k (1+k^2mu^2sigma^2)^(-1/2) and the bottom factor on the rhs of (16.80) should be (1+k^2mu^2sigma^2).
- p516 As printed, top line of p516 is consistent with p515. For consistency with exponential pairwise distribution, P_s/P_r = pi/(2 k sigma).
- p553 1/r -> 1/r^2 in (17.1)
- p556 [1 + 4M_B/ etc.]^(1/2) -> 1 + [1 + 4M_B/ etc.]^(1/2)
- p574 Line 8: 100 L_sun -> 100 L_*
- p575 6 lines before 17.4: did did -> did
- p595 Equation (18.35) should have a factor 2 on the rhs
- p627 Last displayed equation: g^(mu nu) -> g^mu_nu
- p640 Solution 15.4, lines 12 & 13; exp( +- i integral ), as for (15.60)
- p654 Hamilton (1993b) reference: ApJ 417, 19
- p664 Natural units for time: J -> s

## Errors corrected in the 3rd reprint (October 2000, but dated 2001):

- p9 Section 1.2, line 5: Greek indices run from 0 to 3
- p19 Equation (1.60): derivatives should be partial devivatives
- p20 Equation (1.63): the three small d's should be partial derivative symbols
- p23 Equation (1.76): Replace dg_{mu nu}/dx^lambda by partial g_{mu nu}/partial x^lambda |_{parallel}, i.e. the change in g caused by parallel transport. Also, replace g_{beta nu} by g_{beta mu}
- p23 Equation (1.77): covariant derivative should be with respect to lambda, not nu
- p36 Line 2: "downpour really stars" -> "downpour really starts"
- p76 3 lines before equation (3.40): aspect -> aspects
- p77 Equation (3.42): k(Omega-1) -> k / (Omega-1)
- p79 Equation (3.47): spurious G on lhs
- p125 Line 12: Mpc -> kpc
- p127 Equation (5.2): Last term in root should be z(2+z) Omega_v, not 2(2+z) Omega_v.
- p129 11 lines from the bottom: "Gyr; The main source of ...". The -> the
- p144 6 lines from the bottom: "see Press et al. 1992, Pelt et al. 1996" , -> ;
- p166 Equation (6.58) mis-defines the Majorana gamma matrices. The rhs should be (gamma^0_dirac gamma^2_dirac, gamma^2_dirac gamma^1_dirac, -gamma^2_dirac, gamma^2_dirac gamma^3_dirac)
- p166 Before Equation (6.59), Lorentz invariance of bar{psi} psi -> bar{psi} gamma^mu psi to be a 4-vector
- p172 Line 6: a tensors -> at tensors
- p192 Equation (7.59): Lower limit of second integral should be -infinity, not infinity
- p195 Equation (7.74): Factor to the left of [ ] should be inside a square root
- p195 Last word: than -> then
- p206 Line 3: results results -> results
- p217 Equation (8.4): q doubledot -> q_i doubledot
- p225 In equation (8.30), the derivative with respect to p_i is not taken at p_i=0, although it is taken at p_i=0 in earlier expressions
- p227 Before equation (8.37), "...be changed as follows:" -> "...be changed as follows (in the limit of small theta):"
- p233 Equation (8.57): The bracket on line 3 should contain a factor 1/2, as in the first line.
- p234 Line after (8.63): G^{mu nu} -> G_{mu nu}
- p277 Line following (9.12): dS parts -> dT parts
- p280 Lines 12 & 13 of Neutrino decoupling section: R^{-3} -> R^3, R{-2} -> R^{2}
- p280 Neutrino decoupling section, last line: Chapter 18 -> section 9.3
- p284 Last para of Section 9.2, line 3: >> -1 -> large and negative
- p285 Equation (9.44): E^{-p^2/2m} -> e^{-p^2/2mkT}
- p287 First line after (9.51): The criterion -> This equation
- p287 Second line after (9.51): It defines -> This criterion defines
- p289 Caption to Figure 9.1: solid and broken lines are swapped. Also, the plot shows earlier, less restrictive, distortion limits than the final 4-year COBE values. A corrected version is available.
- p301 Line 3: remove parenthesis
- p331 2 lines before equation (11.21): langle phi rangle , -> langle phi rangle ),
- p383 8 lines from the bottom: Mev -> MeV
- p384 9 lines from the bottom: Gev -> GeV
- p385 Line 9: Gev -> GeV
- p395 3 lines before equation (13.12): "in frequency ; The K correction...". The -> the
- p400 6 lines before equation (13.22): the the -> the
- p410 Line 8: makes -> make
- p431 Line 7: missing space between 500 and Angstrom
- p434 1 line before equation (14.31): Bernouilli -> Bernoulli
- p435 1 line after equation (14.32): Bernouilli -> Bernoulli
- p451 Equation (14.66) m_e -> m_p, although the numerical value for the Eddington luminosity is correct
- p452 Equation (14.67) is affected by the error in (14.66). It should have m_p m_e^2 in the denominator, rather than m_e^3, and the numerical value of the Salpeter time is about 10^8.64 years
- p473 3 lines after equation (15.59): rms -> rhs
- p478 2 lines before equation (15.72): : -> .
- p481 4 lines after equation (15.83) Starobinksy -> Starobinsky
- p509 Equation 16.57 g(Omega) -> g^2(Omega)
- p512 Equation (16.67) The coefficients here are results from an early version of the analysis in Peacock & Dodds (1996). The results in the PD96 paper are of higher accuracy, and equation (16.67) should have been updated. The PD96 coefficients were used in making Fig. 16.3
- p513 Line 9: "are normalized to be equal" -> "has a fixed normalization"
- p570 3 lines from the bottom: mass-to light -> mass-to-light
- p592 Following Equation (18.20), add: "where mu = hat k cdot hat r."
- p597 Equation (18.40) should have a factor 1/Omega^2 on the rhs, not 1/Omega, and the subscript on Omega_G should be lower case: Omega_g
- p597 Equation (18.41) is in error as a result of (18.40): the factor 1/sqrt{Omega} should be just sqrt{Omega}
- p608 4 lines from the bottom: is is -> is
- p617 8 lines from the bottom: "so there must other distortions to the orbit than" -> "so there must be distortions to the orbit other than"
- p623 Line 6 of solution 6.1: give -> gives
- p624 4 lines from the bottom: recoves -> recovers
- p628 3 lines from the bottom: thus -> Thus
- p629 Line 11 of solution 9.1: "at the temperature" -> "as the temperature"
- p632 Solution 11.1: should be epsilon=1/p in the penultimate line
- p655 Irwin et al. (1989) reference: missing page number is also 1989
- p663 S.I. conversion of ergs: W -> J
- p664 Density of universe: 1.8791 -> 1.8789 and 2.2277 -> 2.7752
- p670 The misprint from p451 in equation (14.66) for the Eddington luminosity is repeated here
- p671 Bernouilli's -> Bernoulli's
I have also taken the opportunity of the 3rd reprint to produce revised versions of two figures, where high-quality new datasets have clarified the position considerably. These are the supernova Hubble diagram (Fig. 5.4) and the CMB power spectrum (Fig 18.2), and the new diagrams are available here.

I also added to the preface a list of highlights of recent research. It is interesting to note that these in general fit with the basic cosmological picture outlined in the original verion of the text. Our knowledge is becoming more precise, but revolutionary change has not yet occurred.

## Errors that should have been corrected in the 4th reprint (January 2002):

Unfortunately, this reprint was issued without the majority of the corrections given above.

- p39 Equation (2.21): last terms on 3rd and 4th lines should gain a factor 1/c
- p39 Equation (2.22): last term on rhs should gain a factor 1/c^2
- p56 Equation (2.86): factor 1/5 should be 3/10
- p57 Equation (2.88): factor 5/3 in E_V should be 3/5
- p57 Equation (2.89): error from (2.88) propagates: 0.80 -> 3.7 and 1.5 -> 7. For consistency, this also requires "larger" -> "smaller" just before (2.90).
- p74 Equation (3.27): the rhs should be divided by c^2
- p77 Before equation (3.43): dt = d eta/R -> c dt = R d eta
- p88 Equation (3.72): should begin r = c sqrt(t^2 - t'^2)
- p134 After equation (5.10): 20160 -> 40320 pi
- p135 Before equation (5.15): "and surface brightness" -> "and velocity dispersion"
- p330 Line 4: V = - mu^2 + lambda phi^4 should read V = - mu^2 phi^2 + lambda phi^4
- p370 3 lines from bottom. Should be V propto 1/r^{1/2}
- p379 2 lines after (12.89): "on the range" -> "in the range"
- p382 line 13: "is" -> "in"
- p460 Equation (15.6): Omega_B -> Omega_B^2 (cf. Equation 15.80)

## Errors corrected in the 5th reprint (January 2003):

The 5th reprint also includes an update to the highlights of recent research in the preface.

- p5 Equation (1.7): Omega dot cross r should have a factor m in front
- p34 Line 7: "of of" -> "of"
- p70 2 lines after equation (3.15): "to R_0, the" -> "to 1/R_0, the reciprocal of the"
- p89 Equation in text between 3.77 and 3.78: "[ ( Omega(1+z)]" -> "[Omega(1+z)]"
- p93 Final line: "unity" -> "unit"
- p115 Equation (4.38): The last term on the rhs requires a factor 1/2
- p244 Final line requires a closing parenthesis
- p265 Final line requires a closing parenthesis
- p275 Line 21: "timescales" -> "time scales"
- p292 4 lines after equation (9.65): "N_n/N_p simeq 1/6" -> "N_n/N_p simeq 1/7"
- p295 Penultimate line: "nucleon" -> "nucleus"
- p307 Line 16: "rotations in in" -> "rotations in"
- p405 Caption to Figure 13.5: 0.1 Gyr on line 4 should be 0.01 Gyr
- p426 Equation (14.13): E_min should gain a factor (7/6)(3/2)^(4/7)
- p437 Equation (14.39): numerator of rhs should be beta sin(theta)
- p439 3rd line of OBSCURATION subsubsection: "a obscuring" -> "an obscuring"
- p441 Last line of 14.4: "1993" -> "1995"
- p448 2 lines before equation (14.60): "is it" -> "it is"
- p449 1 line before equation (14.63): "term" -> "terms"
- p453 5 lines before equation (14.71): "and and" -> "and"
- p463 3 lines after equation (15.19): equation at start of line should have dot u as first term, and rhs should be g/a
- p465 Final line: "that" -> "than"
- p467 2 lines after equation (15.32): "t = kGM" -> "ct = (kGM/c^2)"
- p471 Line 4: "g simeq Omega^0.6" -> "f simeq Omega^0.6"
- p511 Equation (16.64) should be followed by ",", not "."
- p513 3 lines before equation (16.69): "x^alpha" -> "x^(alpha+1)"
- p517 2 lines after equation (16.85): " <= k" -> ">= k"
- p519 2 lines before equation (16.96): "j_ell" -> "j_n"
- p523 Equation (16.113): "{\bf x}" -> "{\bf x}_i"
- p525 Equation (16.122): "{\bf x}" -> "{\bf x}_i"
- p554 Line 9: "a equilibrium" -> "an equilibrium"
- p557 Line 12: "is is" -> "it is"
- p570 Line after equation (17.44): "K" unit should be in Roman font, not italic
- p585 7 lines from bottom of page: "galaxies" -> "the galaxy"
- p592 Final line: "omega_B" -> "omega_B^2"
- p605 2 lines after equation (18.62): "as index" -> "as the index"
- p620 Problem 4.3, second line: "primes denotes" -> "primes denote"
- p640 Problem 15.4, 2 lines after bold "WKB method": "(kc)^(-1/2)" -> "(kc_s)^(-1/2)"
- p667 5th equation from top (mass in cycloid solution): "k(omega -1)" -> "k/(omega -1)"

## Errors corrected in the 6th reprint (December 2004):

- p80 Equation (3.51) needs p -> p/c^2 (and also 1 line before, 1, 2 & 5 lines after)
- p87 Equation (3.67) rhs should be divided by c
- p88 Equation (3.68) factors of c^2 should appear before dtau^2 and dt^2
- p110 Equation (4.31): The I and S subscripts should be exchanged (also in equation 4.32), and the + sign on the rhs of (4.31) should be -
- p111 Equation (4.34): D_L should be on the top, not the bottom (cf. Equation 4.33)
- p122/123 Equations (4.53), (4.55) [plus the following line] and (4.58) need the same swapped sign for psi as in (4.31)
- p134 line after (5.10): "L =" -> "a flux density"
- p265 3 lines before (8.180): "In general" -> "For $n\ge 3$"
- p275 line 21: "time scales as R^-2 for radiation domination" -> "time scales as R^2 for radiation domination"
- p468 Equation (15.39): There should be no zero subscripts on the rhs, which should read Omega^{tot}(a) H^2(a) a^2 + K
- p558 Last two lines: two instances of h Mpc^-1 should be h^-1 Mpc
The 6th reprint also includes newly revised versions of the supernova Hubble diagram (Fig. 5.4) and the CMB power spectrum (Fig 18.2), plus updates to the highlights of recent research in the preface.

## Errors corrected in the 7th reprint (July 2007)

- p248 line 2: "alpha" -> "alpha^{-1}"
- p279 3 lines after (9.24): remove spurious bracket "/p)" -> "/p"
- p313 Equation (10.14): T^\mu_\mu should be (2T^{00} - T^\mu_\mu)
- p317 Equation (10.25): c should be c^2
- p341 Equation (11.46): The argument of the exponential should be +ik/aH, not -ik/aH
The 7th reprint again includes newly revised versions of the supernova Hubble diagram (Fig. 5.4) and the CMB power spectrum (Fig 18.2), plus updates to the highlights of recent research in the preface.

## Errors not corrected in any reprint at present

- p6 Equation (1.9): rhs should be a (4 pi G rho)/3 H_0^2
- p54 Equation (2.80): rhs should be just r^2/b^2
- p152 Equation (6.3): missing - sign in the first term on the lhs
- p158 4 lines after (6.19): "turned" -> "turn"
- p167 2nd last line before section 6.4: "muct" -> "must"
- p279 3 lines after (9.24) epsilon/p should be p c^2/epsilon
- p364 7 lines after (12.41): Omega_{HI} should be 10^{-6.6} h^{-1}, not 10^{-5.5} h^{-1}
- p463 Equation (15.16): The last term in the first equation should have a factor 1/(a^2 rho_0), not 1/(rho_0)
- p463 Two cases of a missing - sign in relating g to det Phi / a: 1 line after (15.16) and 3 lines before (15.19)
- p470 a missing - sign in relating g to del Phi / a: 1 line after (15.48)