This document outlines Emiliano Sefusatti's presentation on testing the initial conditions of the universe using data from the Planck satellite. The presentation covers predictions from inflation like a flat, homogeneous universe with a nearly scale-invariant power spectrum. It discusses how Planck improved constraints on non-Gaussianity parameters like fNL compared to WMAP. For example, Planck reduced errors on the local fNL parameter by a factor of 2-4 depending on the shape. The implications of Planck's results are explored through the example of constraints on a DBI inflation model.

1. Emiliano Sefusatti
Tests of the Initial Conditions of the Universe after Planck
BW2013,Vrnjačka Banja
April 27th, 2013

2. Outline
• Initial Conditions from Inflation
• CMB Constraints
• Implications of Planckʼs results (a sample)
• Beyond fNL
• Prospects for Large-Scale Structure Observations
• Conclusions

3. Predictions of Inflation
• A flat, homogeneous Universe
PLANCK (2013)
Planck Collaboration: The Planck mission
Fig. 14. The SMICA CMB map (with 3 % of the sky replaced by a constrained Gaussian realization).

4. Predictions of Inflation
Planck Collaboration: Cosmological parameters
• A flat, homogeneous Universe
• A (nearly) scale invariant power spectrum for (highly Gaussian) initial fluctuations
PLANCK (2013)

5. Predictions of Inflation
• A flat, homogeneous Universe
• A (nearly) scale invariant power spectrum for (highly Gaussian) initial fluctuations
Φk1
Φk2
= δD(k1 +k2)PΦ(k1)
Φk1
Φk2
Φk3
Φk4
= δD(k1 + ... +k4) TΦ(k1,k2,k3,k4) = 0
Φk1
Φk2
Φk3
= δD(k1 +k2 +k3) BΦ(k1, k2, k3) = 0

6. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum

7. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum

8. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum

9. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum

10. Assumptions for a simple inflation model
• A single, weakly coupled scalar field
• with canonical kinetic term
• slow rolling down a smooth potential
• initially in a Bunch-Davies vacuum
BΦ(k1, k2, k3) = 0
TΦ(k1,k2,k3,k4) = 0
Non-Gaussian Initial Conditions

11. The shape of non-Gaussianity
Most models predict a scale-invariant curvature bispectrum
BΦ(k, k, k) ∼ P2
Φ(k) ∼
1
k6
What distinguish them is the shape
“shape” = the dependence of the curvature bispectrum predicted
by a given model of inflation on the shape of the triangular
configuration k1, k2, k3
BΦ(k1, k2, k3) = fNL
1
k2
1k2
2k2
3
F
r2 =
k2
k1
, r3 =
k3
k1

12. Models of primordial non-Gaussianity
Multiple fields
Modified vacuum
Modified vacuum
Non-Canonical
Kinetic term

13. Text
!#$%'(%)*+,)-).)
!#$%'(%)*+,)-)/...)
Polarization *+,)-).)
012%34516)*+,)-)/...)
!
Liguori et al. (2007)
The CMB Bispectrum

14. The CMB Bispectrum
The Bispectrum of the CMB is the most
direct probe of the initial bispectrum
Bl1l2l3
∼
BΦ(k1, k2, k3)∆l1
(k1)∆l2
(k2)∆l3
(k3)jl1
(k1r)jl2
(k2r)jl3
(k3r)
curvature
bispectrum
transfer
functions
CMB angular
bispectrum
WMAP 7 years:
Local -10 fNL 74
Equilateral -214 fNL 266
Orthogonal -410 fNL 6
@ 95% CL Komatsu et al. (2009)
• The CMB provides a snapshot of density perturbations at early times
• Power spectrum measurements (Clʼs) are matched by linear predictions
• The CMB bispectrum is equally sensitive to any model of non-Gaussianity

15. The CMB Bispectrum
The Bispectrum of the CMB is the most
direct probe of the initial bispectrum
Bl1l2l3
∼
BΦ(k1, k2, k3)∆l1
(k1)∆l2
(k2)∆l3
(k3)jl1
(k1r)jl2
(k2r)jl3
(k3r)
curvature
bispectrum
transfer
functions
CMB angular
bispectrum
WMAP 7 years:
Local -10 fNL 74
Equilateral -214 fNL 266
Orthogonal -410 fNL 6
@ 95% CL Komatsu et al. (2009)
• The CMB provides a snapshot of density perturbations at early times
• Power spectrum measurements (Clʼs) are matched by linear predictions
• The CMB bispectrum is equally sensitive to any model of non-Gaussianity
Planck (T only):
Local -8.9 fNL 14.3
Equilateral -192 fNL 108
Orthogonal -103 fNL 53
@ 95% CL Ade et al. (2013)

16. The CMB Bispectrum: Planck
• Planck temperature data improve WMAP
results by a factors of 2 to 4 (depending on
the shape!)
• Planck is very close to the
ideal CMB experiment (ΔfNLlocal ~ 1)
ΔfNL, local ΔfNL, equil. ΔfNL, orth.
WMAP 21 140 104
Planck 5.8 75 39

17. The CMB Bispectrum: Planck
dvances in Astronomy 2
1
2
3
4
5
10
20
∆fNL
200 300 500 700 1000 1500 2000 3000
Local model
Imax
WMAP (T/T+P)
Planck (T/T+P)
CMBPol (T/T+P)
(a)
20
30
40
50
100
∆fNL
200 300 500 700 1000 1500 2000 3000
Equilateral model
Imax
WMAP (T/T+P)
Planck (T/T+P)
CMBPol (T/T+P)
(b)
• Planck temperature data improve WMAP
results by a factors of 2 to 4 (depending on
the shape!)
• Planck is very close to the
ideal CMB experiment (ΔfNLlocal ~ 1)
Liguori et al. (2010)
ΔfNL, local ΔfNL, equil. ΔfNL, orth.
WMAP 21 140 104
Planck 5.8 75 39
Forecasted
temperature
polarization
constraints

18. Implications of Planck’s results: an example
DBI inflation (IR)
Having characterised single-field inflation bispectra using com-
binations of the separable equilateral and orthogonal ans¨atze
we note that the actual leading-order non-separable contribu-
tions (Eqs. (6, 7)) exhibit significant differences in the collinear
(flattened) limit. For this reason we provide constraints on DBI
inflation (Eq. (7)) and the two effective field theory shapes
(Eqs. (5, 6)), as well as the ghost inflation bispectrum, which
is an exemplar of higher-order derivative theories (specifically
Eq. (3.8) in Arkani-Hamed et al. 2004). Using the primordia
modal estimator, with the SMICA foreground-cleaned data, we
find:
fDBI
NL = 11 ± 69 (F
DBI−eq
NL = 10 ± 77) ,
fEFT1
NL = 8 ± 73 (F
EFT1−eq
NL = 8 ± 77) ,
fEFT2
NL = 19 ± 57 (F
EFT2−eq
NL = 27 ± 79) ,
fGhost
NL = −23 ± 88 (F
Ghost−eq
NL = −20 ± 75) . (86)
where we have normalized with the usual primordial f con-
where ds2
4 g dx dx is the metric of the four-
dimensional space-time and is a dimensionless parame-
ter. The inflaton and the parameter are related to the
notations of Refs. [3,4] by r T3
p
and T3R4 N.
The has the same order of magnitude as the effective
background charge N of the warped space and character-
izes the strength of the background. The low-energy dy-
namics is described by the DBI–Chern-Simons action
S
M2
Pl
2
Z
d4
x g
p
R
Z
d4
x g
p 4
1 4
g @ @
s
4
V : (2.3)
In the nonrelativistic limit, this action reduces to the usual
minimal form.
We start the inflaton near 0 through a phase tran-
sition.1
Without the warped space, the scalar will quickly
roll down the steep potential ( * 1) and make the infla-
t comes from backreactions of the
[1,4,9] and the de Sitter (dS) space
space. These effects will smooth out th
of a certain IR region of the warped sp
if we start the inflaton from that reg
period cannot be further increased in t
magnitude. For the case that we consi
gest lower bound is the closed string c
background. This gives t
p
H 1
number of e-foldings in this model i
latest e-fold Ne is given by
Ne
p
H= :
It has an interesting relation to the
factor of the inflaton,
Ne=3:
Since the sound speed cs
1, durin
1
This initial condition can be naturally obtained without tun-
ing in e.g. a scenario of Refs. [3,4].
2
This corresponds to the case of a single
throat in Refs. [3,4].
3
So we cannot use the results of Ref. [1
tion has been made that cs departs from un
less than one.
notations of Refs. [3,4] by r T3
p
and T3R4 N.
The has the same order of magnitude as the effective
background charge N of the warped space and character-
izes the strength of the background. The low-energy dy-
namics is described by the DBI–Chern-Simons action
S
M2
Pl
2
Z
d4
x g
p
R
Z
d4
x g
p 4
1 4
g @ @
s
4
V : (2.3)
In the nonrelativistic limit, this action reduces to the usual
minimal form.
We start the inflaton near 0 through a phase tran-
sition.1
Without the warped space, the scalar will quickly
roll down the steep potential ( * 1) and make the infla-
space. These effect
of a certain IR regio
if we start the infl
period cannot be fu
magnitude. For the
gest lower bound is
background. This
number of e-foldin
latest e-fold Ne is g
It has an interestin
factor of the inflato
Since the sound spe
1
This initial condition can be naturally obtained without tun-
ing in e.g. a scenario of Refs. [3,4].
2
This corresponds
throat in Refs. [3,4].
3
So we cannot use
tion has been made th
less than one.
123518-2
background charge N of the warped sp
izes the strength of the background. T
namics is described by the DBI–Chern
S
M2
Pl
2
Z
d4
x g
p
R
Z
d4
x g
p 4
1 4
g
s
4
V :
In the nonrelativistic limit, this action r
minimal form.
We start the inflaton near 0 thr
sition.1
Without the warped space, the
roll down the steep potential ( * 1) a
1
This initial condition can be naturally o
ing in e.g. a scenario of Refs. [3,4].
s improvements, may come at least in two occasions
—where the redshifted string scale is too low so that
gy effects become significant or where the relativistic
ating is happening in a relatively deep warped space so
cosmological rescaling [9] takes effect. We discuss the
in Sec. IV.
II. THE IR MODEL
this section, we study the non-Gaussianity in the
plest IR DBI inflation model. We begin with a brief
ew on the model. Details can be found in Refs. [3,4].
he inflaton potential is parametrized as
V V0
1
2m2 2
V0
1
2 H2 2
; (2.1)
re the Hubble parameter H is approximately a con-
t. In many inflationary models, there is always natu-
a contribution to the potential with j j 1. In these
els, such a potential is too steep to support a long
od of slow-roll inflation. This is the well-known
lem which plagues slow-roll inflation [10].
owever, it is shown [4] that, with warped space, the
inflation can happen for both small and large
t generates a scale-invariant spectrum for the density
urbations with a tilt independent of the parameter . In
case, the steepness of the potential does not play such
mportant role. The inflaton stays on the potential due to
arping in the internal space
tion impossible. To obtain inflation, it is natural to e
that the speed limit should be nearly saturated. In
solving the equations of motion, we find
p
t
9
p
2 2
H2
1
t3
; t H 1
;
where the time t is chosen to run from 1. The in
travels ultrarelativistically with a Lorentz contractio
tor
1 _ 2
= 4 1=2:
Nonetheless, the coordinate speed of light is very sma
to the large warping near 0, and in such a wa
inflaton achieves ‘‘slow rolling.’’ The potential stays n
constant during the inflation, and we have a peri
exponential expansion with the Hubble constant
_a=a V0
p
= 3
p
MPl. There is no lower bound on the
tionary scale, and the approximations that H is co
and dominated by the potential energy during infl
require an upper bound on V [4],
V
M4
Pl
1
Ne
:
Generally speaking, this bound is not significant, sin
get enough e-foldings, we need only * 104. How
for some specific models, such as the simplest one th
focus on in this paper, is determined by density p
As shown in Table 21
ndard deviation shows
asets. That means that
ant, as they do not bias
t increase the variance
MB primordial signal.
l
− fclean
NL on a map-by-
ion. This is used as an
realization due to the
ed from the negligible
wo samples, the vari-
o very small: Table 21
6 for any given shape,
for that shape. As an
ed values of flocal
NL for
ILC samples, compar-
evident also from this
including residuals is
ween the two compo-
ice.
m the comparison be-
hods in Sect. 7, we can
eground-cleaned maps
n this work provide a
s
The DBI class contains two possibilities based on string con-
structions. In ultraviolet (UV) DBI models, the inflaton field
moves under a quadratic potential from the UV side of a warped
background to the infrared side. It is known that this case is al-
ready at odds with observations, if theoretical internal consis-
tency of the model and constraints on power spectra and primor-
dial NG are taken into account (Baumann McAllister 2007;
Lidsey Huston 2007; Bean et al. 2007; Peiris et al. 2007). Our
results strongly limit the relativistic r´egime of these models even
without applying the theoretical consistency constraints.
It is therefore interesting to look at infrared (IR) DBI mod-
els (Chen 2005b,a) where the inflaton field moves from the IR to
the UV side, and the inflaton potential is V(φ) = V0 − 1
2 βH2
φ2
,
with a wide range 0.1 β 109
allowed in principle. In
previous work (Bean et al. 2008) a 95% CL limit of β 3.7
was obtained using WMAP. In a minimal version of IR DBI,
where stringy effects are neglected and the usual field the-
ory computation of the primordial curvature perturbation holds,
one finds (Chen 2005c; Chen et al. 2007b) cs (βN/3)−1
,
ns − 1 = −4/N, where N is the number of e-folds; further,
primordial NG of the equilateral type is generated with an
amplitude fDBI
NL = −(35/108) [(β2
N2
/9) − 1]. For this model,
the range N ≥ 60 is compatible with Planck’s 3σ limits on
ns (Planck Collaboration XXII 2013). Marginalizing over 60 ≤
43
Planck Collaboration: Pl
N ≤ 90, we find
β ≤ 0.7 95% CL ,
dramatically restricting the allowed parameter s
model.
Power-law k-inflation: These models (Armendariz
1999; Chen et al. 2007b) predict f
equil
NL = −170/(
(non-canonical kinetic term)
Constraints on the amplitude
of the predicted bispectrum
Constraints on the model parameters

19. Effective Field Theory of Inflation
Cheung et al. 2008) provides a general way to scan the NG pa-
rameter space of inflationary perturbations. For example, one
can expand the Lagrangian of the dynamically relevant degrees
of freedom into the dominant operators satisfying some under-
lying symmetries. We will focus on general single-field models
parametrized by the following operators (up to cubic order)
S =
d4
x
√
−g

−
M2
Pl
˙H
c2
s
˙π2
− c2
s
(∂iπ)2
a2
(97)
− M2
Pl
˙H(1 − c−2
s )˙π
(∂iπ)2
a2
+
M2
Pl
˙H(1 − c−2
s ) −
4
3
M4
3
˙π3
where π is the scalar degree of freedom (ζ = −Hπ). The mea-
surements on f
equil
NL and fortho
NL can be used to constrain the mag-
nitude of the inflaton interaction terms ˙π(∂iπ)2
and (˙π)3
which
give respectively fEFT1
NL = −(85/324)(c−2
s − 1) and fEFT2
NL =
−(10/243)(c−2
s − 1)
˜c3 + (3/2)c2
s
(Senatore et al. 2010, see also
Chen et al. 2007b; Chen 2010b). These two operators give rise
to shapes that peak in the equilateral configuration that are,
nevertheless, slightly different, so that the total NG signal will
be a linear combination of the two, possibly leading also to
an orthogonal shape. There are two relevant NG parameters,
cs, the sound speed of the the inflaton fluctuations, and M3
which characterizes the amplitude of the other operator ˙π3
.
10−2
−2000
Fig. 23. 68%, 95
field inflation pa
the change of va
Following Senat
less parameter ˜c
inflationary mod
non-interacting m
M3 = 0 (or ˜c3(c−
s
The mean va
onal NG amplitu
f
equil
NL =
1 − c2
s
c2
s
(
fortho
NL =
1 − c2
s
c2
s
(
eld Theory of Inflation
ch to inflation (Weinberg 2008;
eneral way to scan the NG pa-
erturbations. For example, one
e dynamically relevant degrees
perators satisfying some under-
on general single-field models
perators (up to cubic order)
c2
s
(∂iπ)2
a2
(97)
M2
Pl
˙H(1 − c−2
s ) −
4
3
M4
3
˙π3
reedom (ζ = −Hπ). The mea-
n be used to constrain the mag-
terms ˙π(∂iπ)2
and (˙π)3
which
5/324)(c−2
s − 1) and fEFT2
NL =
(Senatore et al. 2010, see also
These two operators give rise
ilateral configuration that are,
o that the total NG signal will
two, possibly leading also to
two relevant NG parameters,
inflaton fluctuations, and M3
3
10−2 10−1 100
cs
−20000−
Fig. 23. 68%, 95%, and 99.7% confidence regions in the single-
field inflation parameter space (cs, ˜c3), obtained from Fig. 22 via
the change of variables in Eq. (98).
Following Senatore et al. (2010) we will focus on the dimension-
less parameter ˜c3(c−2
s − 1) = 2M4
3c2
s /( ˙HM2
Pl). For example, DBI
inflationary models corresponds to ˜c3 = 3(1 − c2
s )/2, while the
non-interacting model (vanishing NG) correspond to cs = 1 and
M3 = 0 (or ˜c3(c−2
s − 1) = 0).
The mean values of the estimators for equilateral and orthog-
onal NG amplitudes are given in terms of cs and ˜c3 by
f
equil
NL =
1 − c2
s
c2
s
(−0.275 + 0.0780A)
fortho
NL =
1 − c2
s
(0.0159 − 0.0167A) (98)
one scalar DF
e Field Theory of Inflation
proach to inflation (Weinberg 2008;
a general way to scan the NG pa-
y perturbations. For example, one
of the dynamically relevant degrees
nt operators satisfying some under-
ocus on general single-field models
g operators (up to cubic order)
π2
− c2
s
(∂iπ)2
a2
(97)
+
M2
Pl
˙H(1 − c−2
s ) −
4
3
M4
3
˙π3
of freedom (ζ = −Hπ). The mea-
can be used to constrain the mag-
ction terms ˙π(∂iπ)2
and (˙π)3
which
−(85/324)(c−2
s − 1) and fEFT2
NL =
2)c2
s
(Senatore et al. 2010, see also
0b). These two operators give rise
equilateral configuration that are,
nt, so that the total NG signal will
10−2 10−1
cs
−20000−10
˜c3
Fig. 23. 68%, 95%, and 99.7% confidence regions in th
field inflation parameter space (cs, ˜c3), obtained from Fi
the change of variables in Eq. (98).
Following Senatore et al. (2010) we will focus on the dim
less parameter ˜c3(c−2
s − 1) = 2M4
3c2
s /( ˙HM2
Pl). For exam
inflationary models corresponds to ˜c3 = 3(1 − c2
s )/2, w
non-interacting model (vanishing NG) correspond to cs
M3 = 0 (or ˜c3(c−2
s − 1) = 0).
The mean values of the estimators for equilateral an
onal NG amplitudes are given in terms of cs and ˜c3 by
equil 1 − c2
s
Equilateral -192 fNL 108
Orthogonal -103 fNL 53
S = d4
x
√
−g
−
M2
Pl
˙H
c2
s
˙π2
− c2
s
(∂iπ)2
a2
− M2
Pl
˙H(1 − c−2
s )˙π
(∂iπ)2
a2
+
M2
Pl
˙H(1 − c
where π is the scalar degree of freedom (ζ
surements on f
equil
NL and fortho
NL can be used t
nitude of the inflaton interaction terms ˙π(∂
give respectively fEFT1
NL = −(85/324)(c−2
s
−(10/243)(c−2
s − 1)
˜c3 + (3/2)c2
s
(Senatore
Chen et al. 2007b; Chen 2010b). These two
to shapes that peak in the equilateral co
nevertheless, slightly different, so that the
be a linear combination of the two, poss
an orthogonal shape. There are two relev
cs, the sound speed of the the inflaton fl
which characterizes the amplitude of the
44
Implications of Planck’s results: an example

20. Implications of Planck’s results: an example
Senatore et al. (2010)

21. 10−2 10−1 100
cs
−20000−10000010000
˜c3(c−2
s−1)
Implications of Planck’s results: an example
Senatore et al. (2010), PLANCK (2013)

22. Beyond fNL
Running non-Gaussianity
A scale-dependent fNL
2 parameters:
amplitude (fNL) and running (nNG)
fNL(k) = fNL
k
kP
nNG
The level of non-Gaussianity could
be different at different scales
sh
a
on
us
w
pr
m
la
co
an
ta
Lo Verder et al. (2008), ES, Liguori, Yadav, Jackson, Pajer (2009)
Becker Huterer (2009) from WMAP data

23. Beyond fNL
The PLANCK analysis considered several models
• Feature and resonant models
• Non Bunch-Davies vacuum
• Quasi-single field inflation
• et al.
• + some preliminary tests of the initial trispectrum
No evidence so far!
However ...
!#$
#% #% ##% #% '##% '#% (##%
)*+,%0345,6%
Fig. 8. Modal bispectrum coefficients βR
n for the mode expansion
(Eq. (63)) obtained from Planck foreground-cleaned maps using
hybrid Fourier modes. The different component separation meth-
ods, SMICA, NILC and SEVEM exhibit remarkable agreement. The
variance from 200 simulated noise maps was nearly constant for
each of the 300 modes, with the average ±1σ variation shown in
red.
!!#$!!#%!!#!!#'!!#
!# (!!# $!!# )!!# %!!# *!!# !!#
+,-./01,#234
$#
567,#89:;,#!
!3=4
#?@A@5
#?5=B
(orthonormal basis for the primordial bispectrum)

24. From the CMB to the Large-Scale Structure

25. From the CMB to the Large-Scale Structure
No direct access to
matter perturbations ...
... but a large volume
to explore, with several
observables:
1. galaxies
2. weak lensing
3. clusters
4. Ly-alpha forest
5. 21 cm (?)
Predictions are
challenging!

26. The Matter Power Spectrum
matter overdensity: δm ≡
ρm(x) − ¯ρm
¯ρm
δk1
δk2
≡ δD(k1 + k2) Pm(k1)
0.01 0.1 1 10
0.01
1
100
k h Mpc1
k4ΠPkk3
Nbody
nonlinear
linear
matter power spectrum

27. 0.01 0.1 1 10
0.01
1
100
k h Mpc1
k4ΠPkk3
Nbody
nonlinear
linear
TextLarge scales:
initial conditions, inflation
matter overdensity: δm ≡
ρm(x) − ¯ρm
¯ρm
δk1
δk2
≡ δD(k1 + k2) Pm(k1)
matter power spectrum
The Matter Galaxy Power Spectrum
Pg(k) b2
Pm(k)
galaxy power spectrum

28. fNL = - 5000
fNL = - 500
fNL = + 500
fNL = + 5000
Ωm 0.271+0.005
−0.004 0.271+0.001
−0.001
σ8 0.808+0.005
−0.005 0.808+0.003
−0.003
h 0.703+0.004
−0.004 0.703+0.001
−0.001
0.96 0.965 0.97 0.975
!0.01
0
0.01
ns
s
Planck + EUCLID
Planck
0.26 0.27
0.79
0.8
0.81
0.82
#m
$8
Plan
Plan
Figure 3.1: The marginalized likelihood contours (68.3% and 95.4% CL) for Pla
The Galaxy Power Spectrum
Forecasted constraints on
spectral index and its running
for EUCLID
Amendola et al. (2012)
Constraints on the initial power spectrum:

29. The Galaxy Power Spectrum
using the halo auto spectra to compute
results as the cross spectra; i.e. we
stochasticity. Examples of the variou
resulting bias factors are plotted in F
As can be seen, we numerically co
predicted scale dependence. Becau
statistics of rare objects, the errors on
simulations plotted in Fig. 8 are lar
tempt to improve the statistics on the
bining the bias measurements from
Figure 8 plots the average ratio betwe
in our simulations and our analytic
using c ¼ 1:686 as predicted from t
model [78]. In computing the average
we used a uniform weighting across
IMPRINTS OF PRIMORDIAL NON-GAUSSIANITIES ON . . . PHYSICAL REVIEW
The bias of galaxies receives a
significant scale-dependent
correction for NG initial
conditions of the local type
Dalal et al. (2008)
“Gaussian”
bias
Scale-dependent correction
due to local non-Gaussianity
Large effect on large scales!
Pg(k) = [b1 + ∆b1(fNL, k)]2
P(k)
∆b1,NG(fNL, k) ∼
fNL
D(z) k2
Constraints on the initial bispectrum:

30. CMB WMAP (95% CL): -10 fNL 74
[WMAP7, Komatsu et al. (2009)]
QSOs (95% CL): -31 fNL 70
[SDSS, Slosar et al. (2008)]
AGNs (95% CL): 25 fNL 117
[NVSS, Xia et al. (2010)]
Limits from LSS are competitive with the CMB!
(at least for the local model ...)
The Galaxy Power Spectrum
Pg(k) = [b1 + ∆b1(fNL, k)]2
P(k)
The bias of galaxies receives a
significant scale-dependent
correction for NG initial
conditions of the local type
Constraints on the initial bispectrum:

31. CMB WMAP (95% CL): -10 fNL 74
[WMAP7, Komatsu et al. (2009)]
QSOs (95% CL): -31 fNL 70
[SDSS, Slosar et al. (2008)]
AGNs (95% CL): 25 fNL 117
[NVSS, Xia et al. (2010)]
Limits from LSS are competitive with the CMB!
(at least for the local model ...)
The Galaxy Power Spectrum
Pg(k) = [b1 + ∆b1(fNL, k)]2
P(k)
CMB PLANCK (95% CL): -8.9 fNL 14.3
[PLANCK (2013)]?
EUCLID/LSST (95% CL): ΔfNL 5 (~1?), expected!
[Carbone et al. (2010), Giannantonio et al. (2012)]
The bias of galaxies receives a
significant scale-dependent
correction for NG initial
conditions of the local type
Constraints on the initial bispectrum:

32. The Galaxy Bispectrum
Future, large volume surveys
could provide:
ΔfNL
local ~ 5 and ΔfNL
eq ~ 10
i.e. competitive constraints
for all types of non-Gaussianity
ES Komatsu (2007), ES, Crocce Desjacques (2012)
The galaxy 3-point function is the
natural equivalent of the CMB
bispectrum
Bgal b3
1 [Binitial + Bgravity] + b2
1 b2 P2
m

33. 0.02 0.04 0.06 0.08 0.10
5
10
20
50
100
kmax h Mpc1
fNL
V 10 h3
Gpc3
, z 1
kmin 0.009 h Mpc1
b1 2, b2 0.8
P
B
PB
FIG. 15: One-σ uncertainty on the fNL parameter, mar
A Fisher matrix analysis for Galaxy correlators
The uncertainty on fNL (local)
from Power Spectrum
Bispectrum ( both)
marginalized (b1, b2)

34. • Abundance of galaxy clusters
Other probes
PNG affects the high-mass tail
of the cluster mass function
2 Williamson, et al.
10
SZ M500 (1014
Msol /h70)
1
10
LX/E(z)1.85
(1044
ergs-1
h70
-2
;0.5-2.0keV)
Fig. 4.— The X-ray luminosity and SZ inferred masses
500(ρcrit) for our cluster sample. We plot statistical uncertainties
ly, and note that the statistical uncertainty of the SZ mass esti-
ate is limited by the assumed scatter in the SZ significance-mass
ation. Clusters from the shallow fields are in blue, and clusters
m the deep fields are in red. We also show the best-fit relations
Pratt et al. (2009) (dotted), Vikhlinin et al. (2009a) (dash-dot),
d Mantz et al. (2010) (dashed).
ost massive galaxy clusters in this region of the sky,
dependent of the cluster redshift. These exceedingly
Fig. 5.— A Mortonson et al. (2010)-style plot showing the mass
M200(ρmean) and redshift of the clusters presented in this paper.
Some of the most extreme objects in the catalog are annotated with
the R.A. portion of their object name. The red solid line shows
the mass above which a cluster at a given redshift is less than
5% likely to be found in the 2500 deg2 SPT survey region in 95%
of the ΛCDM parameter probability distribution. The black dot-
dashed line shows the analogous limit for the full sky. The blue
open data point (redshift slightly offset for clarity) denotes the
mass estimate for SPT-CL J2106-5844 from combined X-ray and
SZ measurements in Foley et al. (2011). That work concludes that
this cluster is less than 5% likely in 32% of the ΛCDM parameter
probability distribution, and we show the corresponding Mortonson
Williamson et al. (2011)
Sample of the most
massive clusters in the
SPT catalog vs the
“probability of their
existence”
JCAP04(200
Effects of scale-dependent non-Gaussianity on cosmological structures
LoVerde et al. (2008)

35. • Abundance of galaxy clusters
• Weak Lensing
• ...
• 21cm (?)
• μ-distorsions of the CMB spectrum (??)
Other probes
PNG affects the high-mass tail
of the cluster mass function
PNG affects also the nonlinear
evolution of the matter power
spectrum at small scales
All probes present significant
theoretical and numerical challenges!

36. Conclusions
• After the first PLANCK results the simplest model of inflation is alive
and kicking: no indication of any departure from a single-field, slow roll
inflation with canonical kinetic term from a Bunch-Davies vacuum
• PLACK will further improve its constraints by adding polarization
information
• Constraints on non-Gaussianity can, in some cases, severely reduce the
parameter space of many non-minimal models (without, however, ruling
them out)
• Future cosmological observations will focus on the large-scale structure:
the large volume available makes them, in principle, an even more powerful
probe of the initial conditions than the CMB
• However, the analysis of its several observables is challenging: we
have to deal with the nonlinear evolution of structures and the complex baryon
physics (to mention two among many problems ...!)

37. New Light in Cosmology
from the CMB
SCHOOL WORKSHOP
22 - 26 July 2013 29 July - 2 August 2013
Miramare, Trieste, Italy
TOPICS of the School:
• EARLY UNIVERSE
• CMB THEORY
• CMB EXPERIMENTS
• PLANCK PRODUCTS
• LENSING ISW
• BIG SCIENCE FROM SMALL SCALES
The purpose of the School is to provide the theoretical and computational tools to study the implications of
the recent results from CMB experiments. It is intended for graduate students, as well as more senior non-
expert researchers that are interested in these fields. The Workshop is devoted to the discussion of the
experimental CMB results in all their aspects, their relation with other probes and the future prospects.
PARTICIPATION
Scientists and students from all countries which are members of the United Nations, UNESCO or IAEA may
attend the School and Workshop. As it will be conducted in English, participants should have an adequate
working knowledge of this language. Although the main purpose of the Centre is to help research workers
from developing countries, through a programme of training activities within a framework of international
cooperation, students and post-doctoral scientists from advanced countries are also welcome to attend.
As a rule, travel and subsistence expenses of the participants should be borne by the home institution.
Every effort should be made by candidates to secure support for their fare (or at least half-fare). However,
limited funds are available for some participants who are nationals of, and working in, a developing country,
and who are not more than 45 years old. Such support is available only for those who attend the entire
activity. There is no registration fee to be paid.
HOW TO APPLY FOR PARTICIPATION:
The application forms can be accessed at the School Workshop website: http://agenda.ictp.it/smr.php?2474
Once in the website, comprehensive instructions will guide you step-by-step, on how to fill out and submit
the application forms.
SCHOOL WORKSHOP SECRETARIAT:
Telephone: +39 040 2240 363 - Telefax: +39 040 2240 7363 - E-mail: smr2474@ictp.it
ICTP Home Page: http://www.ictp.it/
IN COLLABORATION WITH
THE ITALIAN INSTITUTE FOR
NUCLEAR PHYSICS
ORGANIZERS:
C. Baccigalupi (SISSA)
P. Creminelli (ICTP)
R. Sheth (ICTP UPenn)
A. Zacchei (INAF - OATS)
LECTURERS:
C. Baccigalupi (SISSA)
A. Jaffe (Imperial College)
J. Lesgourgues (CERN EPFL)
A. Lewis (Sussex University)
L. Senatore (CERN Stanford)
R. Stompor (APC, Paris)
A. Zacchei (INAF - OATS)
SCIENTIFIC SECRETARY:
D. Lopez Nacir (ICTP)
DEADLINE
for requesting participation
15 April 2013
extended to
28 April 2013
January 2013
Deadline in 2 days!

39. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
?
# of articles with
“Non-Gaussian”
in the title
on the ADS data base

40. PNG in the last 10 years
?
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
non-primordial NG

41. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)

42. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
Inflation / Theory
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)

43. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
Inflation / Theory
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
CMB COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)

44. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
Inflation / Theory
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
Large-Scale Structure
CMB COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)
Dalal et al.

45. 2000 2002 2004 2006 2008 2010 2012
0
20
40
60
80
100
120
140
PNG in the last 10 years
Inflation / Theory
non-primordial NG
# of articles with
“Non-Gaussian”
in the title
on the ADS data base
Large-Scale Structure
CMB COBE
(≪1σ)
WMAP1
(0.8 σ)
WMAP3
(0.7 σ)
WMAP7
(1.5 σ)
?
WMAP5
(1.7 σ)
Yadav Wandelt (2.8σ ?)
Planck
fNL = 0?
Dalal et al.