Cosmology
Steven Weinberg

Corrections to the First Printing1
1. The name “Borgnani” in footnote 7 on p. 85 and in the index on p.
576 should be “Borgani”.
2. In ﬁgure 9.2, the point labelled γ should instead be labelled Y.
3. On page 451, in the discussion of the lensing of QSO 0957+561, theredshifts of the source and lens were interchanged: the source has
redshift 1.41, and the lens has redshift 0.36.
4. On p. 454, on the second line after Eq. (9.5.9), “al a the line of sight”
should be “along the line of sight”.
5. In the second line of Eq. (9.5.61) on page 464, the exponent −5 of r
should be −6. No change is needed in the third line.
6. In footnote 15 on p. 65, and in the author index on p. 579, the name
“R. Jiminez” should be “R. Jimenez”; also in footnote 2 on p. 153,
and in the author index on p. 581, the names “G. Pastor” and “M.
Peiso” should be “S. Pastor” and “M. Peloso”. (Thanks to U. Franca̧
for these corrections.)
7. In footnote 2 on p. 1, “300 light years” should be “300 million lightyears”. (Thanks to F. Maienschein for this correction.)
8. In the term on the left of Eq. (10.4.3) on p. 498, the superscript n on
φ should be m.
9. Due to a copying error, the ﬁtting formula (6.5.14) for the function∆(κ) is incorrect. Eq. (6.5.14) should be replaced with∆(κ) =(1.1547κ)2 + (0.5986κ)4 + (0.2578κ)6.
1 + (1.723κ)2 + (0.8707κ)4 + (0.4581κ)6 + (0.2204κ)81
To find the printing of your copy of Cosmology, look at the page on the reverse of thetitle page, on which the copyright notice and ISBN number appear. At the bottom of thispage is a decreasing sequence of integers: 10, 9, 8 · · ·. The last integer in this sequencegives the printing of your copy.

110. A factor of the gravitational constant G should appear in the deﬁnition of ΩL in the ﬁrst line after Eq. (9.2.20) on page 440, and theresult NS = 4ΩL on the fourth line of page 442 should be NS = 2ΩL .
(Thanks to H. Zhang for these corrections.)
11. In the Author Index on page 581, the name Mo, M. J. should be Mo,
H. J. (Thanks to G. Liu for this correction.)
12. On page 67, seven lines from the bottom, “Eqs. (1.4.9) and (1.4.11)”
should read “Eqs. (1.4.9) and (1.4.12)”. In Eq. (1.9.13) on page 71,
the subscript M should be B. In the last two lines of Eq. (9.3.14) on
page 445, and in Eq. (9.3.16), π 2 should be π 3 . (Thanks to H. Zhang
for these additional corrections.)
13. On page 446, in the line just above Eq. (9.3.16), the reference to Eq.
(9.3.15) should be to Eq. (9.3.14).
14. On page 50, in the line just above Eq. (1.6.2), “Eq. (1.5.46)” should be“Eq. (1.5.45)”. In the unnumbered equation on p. 418, the factor a0
in the argument of the sine should be removed. On p. 419, in the line
just below Eq. (8.1.50), there should be a factor 4 in the denominatorof the formula for R. On page 455, the factor a2 in the numerator of
Eq. (9.5.10) should be removed. On page 456, the subscript d in thesecond term of the right-hand side of Eq. (9.5.17) should be b. On
page 464, the factor r −5 in Eq. (9.5.61) should be r −6 . (Thanks once
more to H. Zhang for these corrections.)
15. In the second sentence on page 1, “about one part in 10−5 ” should
be “about one part in 105 ”. In the middle of page 28, “superceded”
should be “superseded.” (Thanks to H. Lewis for these corrections.)
16. On page 89, in the second sentence of the third paragraph of Sec. 1.12,“that are vary little” should be “that vary little.” In Eq. (6.4.22) on
page 294, there should be a multiplication sign at the beginning of
the second line. On page 303, in the line above Eq. (6.4.64), there
should be a δ in front of uγq . In footnote 1 on page 333, ΩV shouldbe ΩΛ . In footnote 1 on page 334, “(5.3.42)” should be “(5.3.43)”. In
Eq. (7.1.18) on page 336, the “approximately equal” sign under thesummation sign should be an equal sign. In the third line above Eq.
(9.2.1) on page 436, the word “between” should be deleted. In Eq.
(C.25) on page 536, the multiplication sign beginning the second line
should be removed, as these are two separate equations. (Thanks to
J. Meyers for these corrections.)217. On page 379, equation numbers (7.4.37) and (7.4.38) refer to the same
equation. This should be numbered as equation (7.4.37). On page 393,
the next-to-last equation, which gives a formula for the EE multipole
coeﬃcient and is now unnumbered, should be numbered as equation(7.4.70). As a result of these two changes, the numbers of all equations
that are now numbered as equations (7.4.39) through (7.4.70) should
be decreased by one, so that they will appear as equations (7.4.38)
through (7.4.69). (Thanks to J. Meyers for pointing this out.)
18. As a result of a last minute insertion of an equation, there are errors
in the references in Section 7.4 to equations appearing in this section.
After making the changes indicated in item 17 above, the equation
numbers in all references to equations from (7.4.31) to the end of
Section 7.4 should be increased by one. Thus, for instance, on page378, in the line just above what now appears as Eq. (7.4.35), “Eq.
(7.4.31) then reads” should be “Eq. (7.4.32) then reads”. The samechanges should be made to references to equations from Section 7.4
appearing in Section 9.5 on pages 465 and 466. For instance, on page465, three lines above Eq. (9.5.64), “from Eqs. (7.4.76)—(7.4.78)”
should be “from Eqs. (7.4.77)—(7.4.79).” (Thanks to H. Zhang and J.
Meyers for these corrections.)
19. In footnote 10 on page 179, the name “Klinkhammer” should be“Klinkhamer”. The same change should be made in the Author Index,
on page 579. (Thanks to C. Rampf for this correction.)
20. The date 1978 in reference 7 on page 176 should be 1979.
21. The second sentence of the last paragraph on page 177 should begin“The conditions for thermal equilibrium will remain violated as longas H stays above the X-particle decay rate, but as long as...” (Thanks
to C. Rampf for alerting me to this error.)
22. On page 519, in the unnumbered equation under Eq. (B.34), thefunction f (y) on the left-hand side should be f (x), and the function
f (x) on the right-hand side should be f (y). (Thanks to E. Sabancilar
for this correction.)
23. On page 201, ﬁve lines from the bottom of the secibd paragraph, thesecond “was” should be deleted in the sentence “Why was the curvature was so small in the early universe?” In the second term on
the second line of Eq. (10.4.18) on page 500 and in the second term3

of what was originally Eq. (10.4.24) on page 501, the dot and overbar should be directly above ϕ, as ϕ̄˙ . (Thanks to S. Miller for these
corrections.)
24. On page 16, in the fourth line of the ﬁrst marked paragraph, “because
they all at the same” should read “because they are all at the same”.
(Thanks to B. Diamond for pointing this out.)
25. On page 41, in the line just before Eq. (1.5.39), the second “and”
should be deleted. On page 333, in the sixth line of footnote 1, andalso in the author index on page 575, the name “Ashfordi” should be“Afshordi.” (I thank S. Mahmoodifar for these corrrections.)
26. On page 197, two lines above Eq. (3.4.15), “the form (B.44)” should
be “the form (B.63)”. (Thanks to S. Miller for pointing this out.)
27. On the right-hand sides of both Eq. (6.1.15) on page 262 and Eq. (6.1.44)
on page 269, pj should be p̂j .
28. In the last term in the parenthesis on the right-hand side of Eq. (10.4.3)
on page 498, ϕm should be ϕn .
29. On the second line of the caption of Figure 7.7 on page 392, “ref. 21”
should be “ref. 22”.
Corrections to the Second Printing2

1. On the fourth line from the bottom of footnote 1 on page 333, ΩVshould be ΩΛ .
2. On the third line after Eq. (7.4.49) on page 387, “(7.4.47)” should be“(7.4.48)”.
3. On the ﬁrst line of page 391, “(7.4.60)” should be “(7.4.61)”.
4. On the second line of page 398, “(7.4.74) and (7.4.75)” should be“(7.4.75) and (7.4.76)”.
5. On the ﬁrst line below Eq. (7.4.86) on page 398, “(7.4.57)” should be“(7.4.58)”.
2

All of the errors in the first printing listed above were corrected in the second printing,
except for these items.

4

Corrections to the First and Second Printing

1. On page 3, Eq. (1.1.4) should read x′ ≡ x/a ,z ′ ≡ z/a .

2. On page 19, in the 10th line from the bottom of the inset paragraphlabelled Main Sequence, “Including” should be “Included”.
3. On page 527, in the second line from the top, “Eq. (B.40)” should be“Eq. (B.52)”
4. On page 70, in the two displayed but unnumbered equations, a prime
should appear on r following the integral sign in both equations.
5. On page 140, in the displayed but unnumbered equation, a multiplication sign × should appear at the beginning of the second line.
6. On page 127, in the second line after the table, “ionization dropped
well below” should be “ionization became well above”.
7. On page 129, in the ﬁrst line, ln O(T ) should be ln[1 − O(T )].
8. On page 519, in Eq. (B.34), a subscript n should be supplied to theﬁnal x on both lines, so that these equations readµ

J (x) ≡= dxµ (u)

1
n

du
en δ4 xn (u) − x
du−Detg(x)n dxµ (t)1n.
en δ 3 xn (t) − x
dt−Detg(x) n(I am grateful to J. Ganc for corrections 1 through 8 to the ﬁrst andsecond printings.)
9. The derivation of the deﬂection of light by a cosmic string in Section
9.6 applies only for a linear array of non-relativistic masses. For a
relativistic string, such as a singularity in vacuum expectation values,
the post-Newtonian approximation does not apply. The deﬂection inthis case was derived by A. Vilenkin, Phys. Rev. D 23, 852 (1981).
The deﬂection by a relativistic string is given by Eq. (9.6.4), but withsin θ in the numerator rather than the denominator.
10. On page 250, in the fourth line, “4×4 matrix” should be “3×3 matrix”.
(Thanks to A. Boonstra for this correction.)511. On page 39, in the second line from the top, “is less than the Hubble
time” should be “is no greater than the Hubble time”.
12. On page 39, Eq. (1.5.29) should read t0 ≤ H0−1 .
13. On page 42, in the ﬁrst line after Eq. (1.5.44), “Eq. (1.5.43) has...”should be “Eq. (1.5.44) has...”.
14. On page 57, in the second line from the top, ΩV should be ΩΛ .
15. On page 61, in the fourth line from the top, the ﬁrst appearance of
the word “star” should be omitted.
16. On page 93, in the second line from the bottom, “whatever reservations
may have” should be “whatever reservations we may have”
17. On page 94, in the eighth line from the top, ΩV should be ΩΛ .
18. On page 95, two lines above Eq. (1.12.23), ΩV should be ΩΛ .
19. On page 150, the two lines above Eq. (3.1.2) should read “The second
law of thermodynamics implies that a slow change in a system, thattakes it from equilibrium at temperature T and volume V to equilibrium at temperature T + dT and volume V + dV , produces a change
in the entropy given by:”.
20. On page 181, in the line above Eq. (3.3.10), the condition |µ| ≪ 1should be |µ| ≪ kB T .
21. On page 184, in the ﬁfth line of subsection 5, “even the universe starts
in a state...” should be “even if the universe starts in a state...”.
22. On page 190, in Eq. (3.4.14), the exponent −.54 should be −0.54.
23. On page 214, in the fourth line from the top, “no longer be satisﬁed”
should be “no longer satisﬁed”.
24. On page 365, in Eq. (7.3.16), two primes should be added in the lefthand side, so that it reads β(q, λ) β ∗ (q′ , λ′ ) .
25. On pages 467 and 468, the minus signs should be deleted in Eqs. (9.6.1),(9.6.2) and (9.6.3).
26. On page 469, in the eighth line of the ﬁrst paragraph, “Eq. (5.4.24)”
should be “Eq. (5.4.22)”.
6

27. On page 521, in the second line after the unnumbered displayed equation, “is because non-zero value...” should be “is because a non-zerovalue...”.
28. On page 529, in the line after Eq. (B.74), “This is why this is the linear
combination...” should read “This is why Rµν − gµν g λκ Rλκ /2 is thelinear combination...”.
(Thanks to R. Baierlein for corrections 11 through 28 to the ﬁrst andsecond printings.)
29. On page 128, two lines above Eq. (2.3.41), the reference to Eq. (2.3.36)
should be to Eq. (2.3.40).
30. On page 134, six lines from the bottom of the ﬁrst full paragraph,“as a function of photon wavelength, with a result” should be “as aphoton of photon wavelength (corrected to remove the eﬀect of thecosmological redshift), with a result”.
31. The ﬁrst sentence on page 131 should read “This eﬀect was ﬁrst observed in 1969 with a ground based radiometer, but at the time it was
only possible to measure the component of the Earth’s velocity on aﬁxed declinatiob δ = +32◦ , found to be 160 km/sec in a direction
corresponding to this declination and right ascension 13h.1 ”
32. On page 146, ﬁve lines and seven lines below Eq. (2.6.33), “ℓhorizon ”
should be “ℓH ” (deﬁned on the previous page). Also, “≈” on the seventh line below Eq. (2.6.33) should be “≡”, since this is the deﬁnitionof ℓH .
33. On page 147, four lines above Eq. (2.6.34), “ℓ ≥ 4” should be “ℓ ≥ 3”.
34. On page 147, two lines above Eq. (2.6.35), “10 ≤ ℓ ≤ 40” should be“3 ≤ ℓ ≤ 40”.
35. On page 147, next to last line of main text, “ℓ = 2 and ℓ = 3” should
be just “ℓ = 2”.
36. On page 148, top line, “ℓ ≥ 4” should be “ℓ ≥ 3”.
37. On page 147, last line of footnote 9, “astro-ph/9601088” should be“astro-ph/9601058”.
38. On page 157, middle, the sentence beginning “Once out of equilibrium...” should read “Once out of equilibrium, their momentum simply decayed as 1/a (as shown in Section 1.1), so if their chemical
7

potential was negligible their momentum distribution remained likethat of photons, aside from a + instead of a − sign in the denominator of the distribution function, with a temperature less by a factor(4/11)1/3 .”39. On page 162, second line below Eq. (3.2.11), “Q/k” should be “Q/kB ”.
40. On page 172, footnote 20, and on page 572 of the author index, thename “Eggleston” should be “Eggleton”.
41. On pages 176 and 177, the parenthetical remark beginning on the lastline of page 176 and continuing on page 177 should read “(For instance,
in some grand uniﬁed theories there are “leptoquarks” with mass oforder 1015 GeV, that decay into either two quarks, with baryon number
2/3 and lepton number zero, or into an antilepton and an antiquark,with baryon number −1/3 and lepton number −1.)”(Thanks to E. Komatsu for corrections 29 through 41 to the ﬁrst andsecond printings.)

42. On page 106, in the caption to Figure 2.1, the ﬁrst sentence should
read “Comparison of the dipole part (discussed in Section 2.4) of theintensity of radiation observed with the FIRAS radiometer carried by
COBE with what would be expected for a black body spectrun withtemperature 2.728 K, from D. J. Fixsen et al., Astrophys. J. 478,
576 (1996) [astro-ph/9605054].” (I thank T. Kawarabayashi for thiscorrection.)
43. On page 91, third line above Eq. (1.12.8), “(1.1.2)” should be “(1.12.2)”.
44. On page 117, in Eq. (2.3.9), (B2 − Bn ) in the argument of the exponential should be (Bn − B2 ).
45. On page 156, fourth line from the bottom, “photons” should be “positrons”.
46. On page 183, ﬁrst line of Eq. (3.3.20), ñi should be n̄i .
47. On page 185, in Eq. (3.3.24), a minus sign should multiply the righthand side.
48. On page 190, third and sixth lines below Eq. (3.4.14), GF should be
Gwk .
49. On page 198, ﬁrst line below Eq. (3.4.18), “and Eq. (3.4.17) has”
should be “and Eq. (3.4.18) has”.
850. On page 198, second line below Eq. (3.4.8), a dot is missing over ϕ intwo places, so that “solutions ϕ = constant and ϕ ∝ 1/a3 ” should be“solutions ϕ̇ = constant and ϕ̇ ∝ 1/a3 ”
51. On page 212, on the sixth line below Eq. (4.2.16), “8πGϕ21 /α” should2
be “4πGϕ1 /α”. In consequence, on theeighth line below Eq. (4.2.16),“|ϕ1 | > 31/πG” should be “|ϕ1 | > 62/πG” and on the ﬁfth line
above the bottom of the page, “g ≪ 2 × 10−5 ” should be “g ≪ 5 ×
10−6 ”.
52. On page 224, in the ﬁrst and second lines of footnote 2, hjk should behij .
53. On page 225, in the tenth line from the top, p̄δij should be p̄hij .
54. On page 244, in the ﬁrst line below Eq. (5.3.50), “deﬁnitions (5.3.18)”
should be “deﬁnitions (5.3.17)”
55. On page 248, last displayed equation, the coeﬃcient −2 in the lastterm on the right-hand side should be +2a2 .
56. On page 262, in the second Eq. (6.1.18), the left-hand side δuBk (x, t)
should be δuBi (x, t)
57. On page 264, Eq. (6.1.24), a factor 1/a(t) should be supplied in thelast term on the right-hand side.
58. On page 265, Eq. (6.1.28), a factor 1/a(t) should be supplied in thelast term on the right-hand side.
59. On page 266, in the second of the three displayed but unnumberedequations in the middle of the page, q̂i should be q̂j .
60. On page 266, Eq. (6.1.34), a factor 1/a should appear on the left-handside.
61. On page 288, the line above Eq. (6.3.32), the formula δDq → 9q 2 tRoq /10a2
should be δDq → 9q 2 t2 Roq /10a2 .
62. On page 289, third and fourth lines below the displayed but unnumbered equation, ”Adding the inhomogeneous term (6.3.25),” should be”Adding the limit (6.3.31) of the inhomogeneous term,”
63. On page 294, two lines above Eq. (6.4.23), vs2 should be vs .
9

64. On page 305, two lines above displayed but unnumbered√ equation in
middle of page, “(t/3HEQ )(a/aEQ )3/2 ” should read “(2 2/3HEQ )(a/aEQ )3/2 ”.
65. On page 317, in the second line of Eq. (6.6.25), “Dq (t)” should be atime-derivative, “Ḋq (t)”.
66. On page 319, Eq. (6.6.34), a factor Pℓ (µ) should be inserted after(2ℓ + 1).
67. On page 319, in the last line of the last displayed but unnumberedequation on the page, p̂i p̂i p̂j p̂k should be p̂i p̂j p̂k p̂l .
(My thanks to A. Schafer for corrections 43 to 67 to the ﬁrst andsecond printings.)

10