Page 21: Although not a typo, you might stress
that the *rho*_{eq} in Eqs 2.42 and 2.44 is the density
of
each component, rather than the total, by underlining the word `each'
two
lines after Eq2.42.

Page 22: In Eq2.45, the central and
right-hand
terms should both be multiplied by *a*_{0}^{3}.
This
is required to correctly allow for the inability to set *a* = 1
after
instead deciding to set *K* = -1. The parameter *psi* in
Eqs2.46
and 2.47 actually coincides with conformal time *tau*.

Page 24: In Eq2.54 the final quantity, d*phi*,
should be squared.

Page 46: In Eq3.19 the sign of the last term
on the right-hand side should be positive. See this paper for a much
more detailed treatment of the e-foldings relation.

Page 47: In mentioning eternal inflation, the
citations should reflect that the idea originated in a 1983 paper by
Alex
Vilenkin, "Birth of inflationary universes", Phys. Rev. D27, 2848
(1983),
who discussed the scenario in the context of `new inflation'. The Linde
papers cited extended the picture to chaotic inflation.

Page 49: Last paragraph of 3.5.1, the formula
should be w=2/3p - 1, and refer to Eq2.38 rather than Eq2.7.

Page 57: for clarity, Example 3.6 should say `for the slow-roll approximations Eqs3.7 and 3.8 to be valid

Page 66: The second line of Eq4.21 has got
jumbled
up. The term inside the square brackets should read

Sum over *n* of [ ln *N _{n}*
- (

Page 69: In Eqs4.37 and 4.38, the *Y _{lm}*(

Page 79: Three lines after Eq4.77, the
equation
for *Phi*_{gr} should contain an additional factor
*G*.
Likewise, the first term on the right-hand side of Eq4.83 should also
have
an additional *G*, to that the numerator reads `2 *pi G*'.

Page 80: In Eq4.92, the factor *Omega*
should
be raised to the power -1. That is, for a fixed value of the potential
perturbation, the density contrast should be greater if the density
parameter
is reduced. The correct version was used where this equation was needed
later, notably in Section 6.2.1.

Page 82: In Eqs4.102 and 4.103, the prefactors
*a*
should be raised to the power -1 (in both the central and
right-hand
parts of the equalities). In Eqs 4.104 and 4.105, the powers of *H*
should **not** be raised to the power -1.

Page 82: In Eq4.109, *delta H* should be
just *H*.

Page 83: In the sentence between Eqs4.117 and
4.118, **v _{k} **should be

Page 85: In Eq4.126, the right-hand side
should
be (1+*z*), not its reciprocal.

Page 92: Eqns 4.138 and 4.139 would be better
written using a single function \rho(x,\tilde t), whose average (ie.
unperturbed)
value is \rho(\tilde t). Then they giving the splitting into perturbed
and unperturbed values on the two slices as

\rho(x, \tilde t(x,t)
) = \rho(t) + \delta \rho(x,t)

\rho(x,\tilde t) =
\rho(\tilde
t) + \tilde{\delta \rho(x,\tilde t) }

With this notation, Eq4.141 can be derived by
substituting Eq4.137 into Eq4.138, and then setting t=\tilde t so that
we are dealing with slices corresponding to the same unperturbed value
of \rho.

This direct argument is an alternative to the one in the text, invoking the interpretation of $\delta t$ as a time displacement between slices corresponding to the same unperturbed value of \rho (Figure 4.5). That interpretation indeed follows from Eq4.140, in which a final equality `=t(x,t)' would have been helpful.

Page 93: The Raychaudhuri equation, Eq4.146,
is
not correct. The first term on the right-hand side should be (*rho*
+ 3*P*) rather than just *rho*. Accordingly, the second
sentence
on page 94 should be modified to read "The Euler equation is the same
as
in the Newtonian case, except that the inertial mass ...". The correct
version of the Raychaudhuri equation is used later on, e.g. Eq4.151.

Page 99: In Eq4.169, the first *phi*
should
be upper case, not lower case. Two lines above that, `Eq. (4.90)'
should
be replaced by `Eq. (4.91)'.

Page 99: Footnote 11: in the equation the *delta
P* should have a plus sign, not a minus. The last sentence of the
footnote
would be much less obscure if it read `Eq (4.171) is obtained by
inserting
this result into the right-hand side of Eq (4.166), and for the
left-hand
side using Eq (7.81) which gives the time-dependence of *R*_*k.*'.

Page 101: In Eq4.180, the second term on the left-hand side should be multiplied by 2.

Page 103: In the line after Eq4.187, `consider' to `considered'.

Page 107: In the first line of Eq5.9, where *k*_{eq}
is defined, there should be additional brackets enclosing the phrase
`14
... Mpc', which is all to be raised to the power minus one (see Eq2.37).

Page 107: Two lines before Eq5.10, `matter-density contrast' should be just `matter density'.

Page 107-108: Contrary to the implication of the text, the logarithmic growth of the power spectrum within the horizon during radiation domination does not require the Meszaros equation to hold. The Meszaros equation however remains useful because (again contrary to the text) it remains valid in matter domination and should be derived using Eq2.42, not the approximation H=1/2t. For a fuller discussion click here.

Page 108: Not strictly an error, but the
reader
might wish to know that there is no physical motivation for the
functional
form of Eq5.14, which has arisen as a historical accident. The baryonic
damping could only depend on the physical parameters at that epoch, and
so in particular *Omega*_{B} couldn't really appear on
its
own.

Page 120: The equation two lines before Eq5.38
should read *theta* simeq 2*pi/l*, and Eq5.38
should
read

* k ^{-}*

The 2

This change additionally means that the l corresponding to the thickness of the last-scattering surface should be approx 5000, and that for decoupling as approx 400. In each case, the identification of an l with a scale is imprecise and only for guidance.

Page 121: The last sentence in the figure
caption should read `... is just proportional to the area under the
curves.'

Page 127: In the first line of the paragraph
containing
Eq5.62, it should be `*x*-*y *plane', not `*x*-*z *plane'.

Page 132/133: The algebra in Eq5.88 is not
quite
right. First, it would be better if a factor of the speed of light *c*
were written explicitly in the numerator of the central expression.
Secondly,
the 0.050 should be 0.061. This then leads to corrections in Eq5.89,
where
0.033 should be 0.041, and in Eq5.90 where the 5 should be a 7. You
might
also note that the current fashion is for a higher nucleosynthesis
value
of *Omega*_{B}*h*^{2}=0.02 which would lead
to
a yet higher number in Eq5.90 by a factor of 5/4. For both these
reasons,
the curves in Figure 5.12 could be shifted upwards.

Page 138: In Eq6.2, the numerical prefactor
should
be 2x10^{5}, not 6x10^{4}.

Page 144: In Eq6.10, there should be no *Omega*
on the left-hand side, which should just read *ag = ...*

To make this clearer, you might consider
modifying
the two sentences before this equation to read

"From Eq4.92, the time
dependence
of *delta _{k}* is

matter-dominated Universe is simply proportional to

normalized Eq 4.104 determines

Notice that there are corrections to both these quoted equations given earlier in this errata.

Page 146: We didn't mention explicitly that
the
horizon distance *x*_{ls} changes in the low-density case
from the value 2*H*_{0} which applies in the critical
density
case (page 119). The horizon distance for LambdaCDM is given by Eq2.60;
in particular this is what now appears in the generalization of Eq5.38.
From this one can conclude that in the spatially-flat case the *l *
values of the oscillatory features in the potential hardly change as *Omega*_{0}
is varied, according to the argument at the end of Section 2.4, as
their
location is governed by the horizon size at decoupling.

Page 148: In Eq6.22, both instances of the
scale
factor *a* should be replaced by *a*/*a*_{0},
as
we have chosen to set the curvature *K* equal to minus one rather
than the present scale factor to unity. Also, the minus sign between
the
two terms in the brackets should be a plus.

Page 148: In Eq6.27, the second term in the
square
bracket [the one with *l*(*l*+1)] should have a minus sign
in
front, not plus. This error seems to be quite widespread in the
literature.

Page 149: In Eq6.33, the subscript *f*
on
the right-hand side should be *g*.

Page 150: To remove ambiguity, replace `growth suppression factor is larger' with `growth suppression is more pronounced'.

Page 151: In the caption, change *Omega*_{0}*h*
to *Omega*_{b}*h*^{2}.

Page 158: In the expression for the curvature scalar, the overall sign should be positive, not negative, with our conventions.

Page 159: In Eq6.49, to allow for the baryons
the third equality sign should be a `simeq', and the equation in text
after
it ought to read

*delta
rho*_{r} = - *delta rho*_{c} - *delta rho*_{b}*
\simeq *- *delta rho*_{c}

Also immediately after that, change `and the
last equality holds' to `where the approximate equalities hold'.

Page 172: In Eq7.48, the argument of *a-dagger*
should be -**p** rather than **p**. In this equation and in
Eq7.49,
*w*(**p**)
should be replaced by *w*(**p**.t).

Page 174: In sec 7.3.2, fourth line, *Z*_{1}should
be *Z*_{2}.

Page 177: In Eq7.64, the third term (*Nabla*^{2}*phi*)
should have a minus sign.

Page 177: After Eq7.65, in both the equations
for the Ricci scalar *R* the overall sign should be positive with
our conventions.

Page 178: In Eq7.68, there should be no factor 1/2 in the last term, as is obvious from comparison with Eq7.67.

Page 180: After Eq7.78, add the phrase "where
*k*_{1}*=a*_{0}*H*_{0}
is the wavenumber corresponding to the present horizon."

Page 182: Eq7.92, the argument on the
left-hand
side should be *tau*, not *t*.

Page 187: Although not strictly a typo, it would have been useful to remind the reader that the COBE normalization of Eq7.106 is for critical density only, and would be modified for a low-density cosmology as described in Chapter 9.

Page 188: The mathematical expression ending
the
paragraph after Eq7.116, giving the `new quantity' should have an
additional
multiplication by *V*^{-n} (for example to reproduce
Eq7.116
when *n*=3).

Pages 188/189: There is an overall sign error in all of Eqs7.112, 7.113, 7.114, 7.118 and 7.123. This is most easily corrected by adding a minus sign to the left-hand sides. Additionally, in Eq7.114 the first term on the right-hand side should have a 4 rather than a 2.

Page 190: The left-hand side Eq7.128 should be
multiplied by (1/*z*).

Page 191: The left-hand side Eq7.133 should be
multiplied by (1/*z*).

Page 191: Eq7.138 should have *eta*-*epsilon*
on the right-hand side rather than *epsilon*-*eta*.

Page 191: Eq7.139, replace `2*C*' with `3*C*'.

Page 192: In Eq7.146, the final denominator
should
contain *phi*-dot within the modulus signs, not *H*-dot.

Page 211: On the sixth line, there should be
no
`2' in the expression giving the contribution of the mass to *eta*.

Page 214: In Eq8.30, the *phi*(*N*)
should be divided by *M*_{Pl}.

Page 217: Two lines after Eq8.44, the term *lambda
phi*^{4}/4 should be replaced by *lambda*-prime *psi*^{2}*phi*^{2}.

Page 219: In Eq8.53, the *lambda* should
not be squared, while in Eq8.55 the square root of *lambda*
should
instead be the fourth root of *lambda* multiplied by the square
root
of 2.

Page 222: In Eq8.67, the factor *g*
should
be raised to the power one half.

Page 223: The right-hand side of Eq8.71 should
be divided by M_{Pl} (so as to make both sides dimensionless).

Page 232: The second part of Eq8.101 should be
*xi*=1/4*omega*,
not 1/8*omega*.

Page 325: Eq14.48 is wrong. On the right-hand
side the index mu should be
replaced by beta, and then
the rhs multiplied by a term (partial x^mu/partial x'^beta).
Incidentally Eq14.46 could be simplified by cancelling the partial x'^alpha.

Page 326: Immediately above Eq14.56, there
shoud be a minus sign in the equation for f, i.e. f = - dt/dt_{pr}.

Page 328: Two lines after Eq14.67, the reference should be to Eq14.35, not Eq14.34.

Page 330: Concerning Eq14.77, although it is
valid
as it stands, it would make more logical sense if the subscript on the
partial derivative were a *mu* rather than a *nu*, to mimic
Eq14.76.

Page 334: In the line preceding Eq14.90, the
curvature
*K*
should be raised to the power of minus a half*.*

Page 334: 2nd last line, the section referred
to should be 2.3.1, not 2.2.3. On the last line, the equation should
read
*R*^{(3)}
= 6*K*/*a ^{2}*.

Page 335: In Eq14.92, the entire denominator of the last term, including the `1+', should be squared.

Page 335: In Eq14.95, there should be a factor
2 before the *B _{i}*.

Page 336: The left-hand side of Eq14.96 should
be multiplied by 1/*a*(*tau*).

Page 336: The very last *dt* on the page
should be *dt*_{pr}.

Page 337: The right hand sides of Eqs 14.99
and
14.101 should be multiplied by -1. The left-hand sides of Eqs14.99 and
14.100 should be multiplied by *a,* and the left-hand sides of
Eqs14.101
and 14.102 by 1/*a*.

Page 340: In the second line of Eq14.120, the
second and third terms (the two terms of the form *B* partial *delta
x*) should both have minus signs. In fact this error is also in
Kodama
and Sasaki (1984) and probably many other places too.

Page 341: In Eq14.135 the right-hand side should be multiplied by a factor 2.

Page 342: The third line of Section 14.6.2 should say Chapter 15, not Chapter 10.

Page 343: In Eq14.145, and three lines after
it,
it makes better logical sense to replace *V* with *V*_{N
}(though
the two quantities are the same in this case).

Page 344: Second line of the paragraph after Eq14.152 should begin "Eqs. (14.149) and (14.150) are identical ...".

Page 355: Contrary to what is stated in the text, observation still allows significant neutrino asymmetry corresponding to a non-negligible chemical potential which would modify Eq 15.24.

Page 361: In Eq15.62, on the left hand side it
should be *delta* F_{l}, not *delta* f_{l}.

Pages 362, 364 and 368: In Eqs 15.70, 15.79
and
15.107, the right-hand side should have an additional term
+4 Phi-dot. In Eq15.71, the factor -*aHV _{nu}* should not
be there (ie the bracketed term should be multiplied by

Page 369: At the end of the line following
Eq15.114,
insert the phrase `and evaluating *Pi _{k}* from
Eqs15.72-15.74'.

Page 369: Before the last sentence, insert
`The
Newtonian-gauge density contrasts $\delta^N_i$ can then be calculated
from
the comoving gauge density contrasts $\delta_i$ using Eq 14.162.'

Page 370: Eq.~(15.120) should be replaced by
the pair $\Theta(\bfk,\ell)= \int^{\tau_0}_0 S_\Theta(\bfk,\tau)
j_\ell(x) d\tau$ and

$E(\bfk,\ell) = \int^{\tau_0}_0 S_E(\bfk,\tau) j_\ell(x)}/x^2 d\tau$,
with $x\equiv k(\tau_0-\tau)$, and $k$ should be replaced

by $\bfk$ in Eqs~(15.121) to (15.125).

Page 371: After Eq15.122, replace the first
part
of the sentence with `Here *A* is defined by Eq. (15.104) and is
gauge-invariant,
...'

Page 371: The variable *A*_{2}
in
Eqs15.122 to 15.125 should just be *A*. In Eq15.123 the last two
terms
should have a plus sign rather than a minus sign, the last term in
Eq15.124 should have its sign changed to minus and its denominator
should be `2' and not `4', and Eq15.125 should also
have
a plus sign on its right-hand side. [Thanks to Uros Seljak for pointing
out the errors in this and the previous two items, and even admitting
that
Seljak & Zaldarriaga (1996) might partly be to blame (though
CMBFAST
works fine)!]

Page 373: The exponent in the conversion of grams to GeV should be 23, not 25 as given.

Page 374: The answer to Example 3.6 should
specify
that Eqs 3.7 and 3.8 are the slow-roll equations to be used.

We are indebted to Toshiyuki Kanazawa for a comprehensive reading of
the book uncovering many of these errors.

If you are the sort of person who likes to correct
minor
typographical errors in a book, click here.

Back to the home page of the book.

Last updated: June 2009

Andrew Liddle