Cosmological Inflation and primordial non-Gaussianities Sbastien - - PowerPoint PPT Presentation

Cosmological Inflation and primordial non-Gaussianities

Sébastien Renaux-Petel

LPTHE - ILP LPSC, Grenoble. 05.02.2014

Outline

• 1. Description of inflation
• 2. Beyond the simplest models
• 3. Primordial non-Gaussianities
• 4. Quasi-single-field inflation

Outline

• 1. Description of inflation
• 2. Beyond the simplest models
• 3. Primordial non-Gaussianities
• 4. Quasi-single-field inflation

What is at the origin of all the structures in the universe?

Cosmic history

Inflation Big Bang Nucleosynthesis Cosmic Microwave Background Structure formation LHC

3 main puzzles: Dark Matter, Dark Energy, Inflation: a period of accelerated expansion before the radiation era that solves the problems of the Hot Big Bang model

The horizon problem of the Hot Big-Bang model ...

ds2 = −dt2 + a(t)2d⇥ x 2 = a()2 −d 2 + d⇥ x 2

cosmic time scale factor comoving distance comoving (conformal) time

H = ˙ a a

Hubble scale

(aH)−1

... solved by a schrinking comoving Hubble sphere

d dt(aH)−1 < 0

Guth (80)

3 equivalent definitions of inflation

• Violation of strong energy condition:

p < −1 3ρ ⇔ w ≡ p ρ < −1 3

Ninf ≡ ln ✓af ai ◆ & 60 Big-Bang puzzles solved:

• Schrinking Hubble radius:

d dt(aH)−1 < 0

• Accelerated expansion:

d dt(aH)−1 = −¨ a (aH)2

< 1

with

¨ a a = H2(1 − ) and ≡ − ˙ H H2

✏ ⌧ 1 ds2 ' dt2 + e2Htd x 2 Almost de Sitter:

(solving the horizon problem)

Slow-roll single field inflation

• Simplest implementation of the above mechanism: scalar field

with flat potential in Planck units

S = Z d4x√−g M 2

P

2 R − 1 2gµν∂µφ ∂νφ − V (φ)

• M 2

pl

2 ✓V,φ V ◆2 ⌧ 1

η ⌘ M 2

pl

V,φφ V ⌧ 1

V (φ) ' 3H2M 2

p

reheating

From quantum to temperature fluctuations

Gauge-invariant curvature perturbation

δT T

hζkζk0i = (2π)3Pζ(k)δ(k + k0)

Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

⇣ = + 1 √ 2✏

From quantum to temperature fluctuations

Gauge-invariant curvature perturbation

δT T

hζkζk0i = (2π)3Pζ(k)δ(k + k0)

Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

⇣ = + 1 √ 2✏ vk = a √ 2✏ ⇣k Canonically normalized field

v00

k +

• k2 2a2H2

vk ' 0

sub − Hubble

From quantum to temperature fluctuations

Gauge-invariant curvature perturbation

δT T

hζkζk0i = (2π)3Pζ(k)δ(k + k0)

Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

⇣ = + 1 √ 2✏ Quantization (commutation relations) + choice of vacuum fix initial conditions

sub − Hubble

From quantum to temperature fluctuations

Gauge-invariant curvature perturbation

δT T

hζkζk0i = (2π)3Pζ(k)δ(k + k0)

Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

⇣ = + 1 √ 2✏ vk = a √ 2✏ ⇣k Canonically normalized field

v00

k +

• k2 2a2H2

vk ' 0

sub − Hubble

From quantum to temperature fluctuations

Gauge-invariant curvature perturbation

δT T

hζkζk0i = (2π)3Pζ(k)δ(k + k0) ⇣k(⌧) ' H p 4✏k3 (1 + ik⌧)e−ikτ

Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

⇣ = + 1 √ 2✏

sub − Hubble

˙ ζ = 0

super − Hubble

From quantum to temperature fluctuations

Gauge-invariant curvature perturbation

δT T

hζkζk0i = (2π)3Pζ(k)δ(k + k0)

Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

⇣ = + 1 √ 2✏

sub − Hubble

super − Hubble

˙ ζ = 0

From quantum to temperature fluctuations

prediction

• bservation

δT T

Pζ ∼ H4 M 2

p ˙

H

Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

super − Hubble

˙ ζ = 0

predicts

universe on large scales is:

homogeneous isotropic flat

+

density fluctuations are:

almost scale-invariant almost Gaussian adiabatic (no spatial variation of composition of the cosmic fluid) superhorizon at recombination

Inflation

l(l + 1)Cl/2π [µK2]

flat adiabatic superhorizon isotropic Gaussian homogeneous scale-invariant

Observations

The simplest inflationary models are in full agreement with data

Outline

• 1. Description of inflation
• 2. Beyond the simplest models
• 3. Primordial non-Gaussianities
• 4. Quasi-single-field inflation

Microphysical origin of inflation?

• So far, merely phenomenological description
• Physics at the energy scale of inflation is unknown!

Observational probe of very high-energy physics

• Candidate physical theories motivate much more complicated

dynamics than the simplest scenarios (toy models).

The Eta problem

V (φ) ' 3H2M 2

p

M 2

pl

2 ✓V,φ V ◆2 ⌧ 1

η ⌘ M 2

pl

V,φφ V ⌧ 1 η ⇡ m2

φ

H2 ⌧ 1

Why is the inflaton so light?

m2

φ ∼ Λ2 uv H2

like the Higgs hierarchy problem

The Eta problem

V (φ) ' 3H2M 2

p

M 2

pl

2 ✓V,φ V ◆2 ⌧ 1

η ⌘ M 2

pl

V,φφ V ⌧ 1 η ⇡ m2

φ

H2 ⌧ 1

Why is the inflaton so light?

Supersymmetry ameliorates the problem but doesn’t solve it. m2

φ ∼ H2

UV sensitivity of inflation

Unless symmetry forbids it, presence of terms of the form ∆V = cV0(φ) φ2 Λ2 L = −1 2(∂φ)2 − V0(φ) + X

δ

Oδ(φ) Λδ−4

Corrections to the low-energy effective action Slow-roll action

∆m2

φ ∼ c V0

Λ2 ∼ c H2 ✓MP Λ ◆2 ∆η & 1 Sensitivity of slow-roll inflation to Planck-suppressed operators Wilson coefficient c ∼ O(1) Λ . MP +

Gravitational Waves

CMB polarization measures:

Pt ∼ H2 M 2

p

Energy scale

• f inflation

Gravitational Waves

CMB polarization

• bservable if:

tensor-to-scalar-ratio

r ≡ Pt Pζ & 0.01

r < 0.11 (95%CL) Current constraints:

∆φ Mp ≈ ⇣ r 0.01 ⌘1/2

r = 8 ✓ dφ dN 1 Mp ◆2

dN ≡ Hdt

with

Field evolution

• ver 60 e-folds

Observable gravitational waves require super-Planckian field-variation

Lyth, 96

The Lyth bound

Observable GWs require a smooth potential over a range

∆φ & Mp

The Lyth bound

Sensitivity to the UV-completion of large-field inflation

LDBI = − 1 f(φ) ⇣p 1 − 2f(φ)X − 1 ⌘ − V (φ)

Prototypical example: L(X ≡ −1 2∂µφ ∂µφ, φ)

K-inflation

f(φ) = λ φ4

V (φ) = m2 2 φ2 m MP p λ 1

f ˙ φ2 ⌧ 1 c2

s ⌘ 1 f ˙

φ2 ⌧ 1

• Slow-roll regime:
• ‘Relativistic’ DBI regime:

S = Z dt d3x a3 ✓1 2 ˙ φ2 − V (φ) ◆

Silverstein, Tong (04)

Inflation despite steep potential!

• vercomes the eta-problem?

e.g: and Condition for inflation:

Multifield inflation

φ1

φ2

Gordon et al, (00)

θ

In general (bending trajectories): super Hubble evolution of the curvature perturbation

(δφ)σ (δφ)s

⇣ = ()σ √ 2✏

˙ ζ ∝ ˙ θ(δφ)s + O ✓ k2 a2H2 ◆

L = −1 2GIJ(φK)∂µφI∂µφJ − V (φI)

Ne

Pi Pnaive

An illustration

naive;

• ne-field;

exact (6-field)

McAllister, S.RP , Xu, JCAP , 12

Hubble crossing

Mass scales in realistic set-up

MP Mmoduli Mφ H

Hope: light inflaton, Planck-mass moduli

hard to achieve unnatural (eta problem) MP Mmoduli Mφ H

Find: many masses

• f order H

Quasi-single-field

Chen, Wang 09

3 numbers to explain them all

• Plethora of inflationary models versus three numbers

P(k) = As(k⇥) ✓ k k⇥ ◆ns(k)−1

As = (2.441+0.088

−0.092) × 10−9

Planck 2013

Amplitude known since COBE ns = 0.9603 ± 0.0073 (68%CL) k? = 0.05 Mpc−1 Scale invariance ruled out at more than 5 sigma r < 0.11 (95%CL)

How can we learn more?

Outline

• 1. Description of inflation
• 2. Beyond the simplest models
• 3. Primordial non-Gaussianities
• 4. Quasi-single-field inflation

• Gaussian approximation: freely propagating particles
• Non-Gaussianities measure the interactions of the field(s)

driving inflation. Discrimination amongst models which are degenerate at the linear level Cosmology

Non- Gaussianities

Particle physics

Colliders

Primordial non-Gaussianities

Beyond toy-models

• Embedding inflation into high-energy physics requires the

understanding of the cosmological perturbations generated in much more complicated scenarios than the simplest models:

• multiple fields
• non-standard kinetic terms
• intermediate masses
• modified gravity
• General formalisms -- analytical, numerical -- to predict

cosmological observables (in particular NGs) in a wide variety

• f situations.
• Applications to interesting early universe models.

I have developped:

Maldacena’s 2003 result

• Single field
• Standard kinetic term
• Slow-roll
• Initial vacuum state
• Einstein gravity

Very small non-Gaussianities (much more quantitative statement actually!) UNDER HYPOTHESES It is now clear that violating any of these assumptions might lead to

• bservably large NGs.

A simple example and orders of magnitude

δT T ∼ ζ ∼ 10−5 ζ = ζG + 3 5f loc

NLζ2 G

(local)

WMAP , ApJS 10

f loc

NL = 32 ± 21 (68% CL)

(CMB) (LSS)

f loc

NL = 28 ± 23 (68% CL)

Slosar et al, JCAP 08

f loc

NL ≈ 10−2

• Slow-roll single field prediction:

f loc

NL = 2.7 ± 5.8 (68 % CL)

Planck 2013

hζk1ζk2i = Pζ(k1)(2π)3δ3(k1 + k2)

• Beyond the

power spectrum:

• Higher-order connected, n-point functions:

hζk1ζk2ζk3i = Bζ(k1, k2, k3)(2π)3δ3(k1 + k2 + k3) hζk1ζk2ζk3ζk4ic = Tζ(k1, k2, k3, k4)(2π)3δ3( X

i

ki) 3 point: bispectrum 4 point: trispectrum

k1 k2 k3

Primordial non-Gaussianities

Shape (dependence on the configuration of triangles) k1 k2 k3

ζ(k1)ζ(k2)ζ(k3)⇥ = (2π)7δ(

3

X

i=1

ki)P2

ζ

S(k1, k2, k3) (k1k2k3)2

dimensionless measure

• f the amplitude of the bispectrum

fNL ∼ S

The bispectrum

Scale-dependence (growing or shrinking on small scales?) Sign (more or less cold spots?) Each of these features can rule out large classes of models

‘Happy families are all alike; every unhappy family is unhappy in its own way.’ Anna Karénine, Tolstoï

Primordial non-Gaussianities

Gaussian distribution are all alike; every non-Gaussian distribution is non-Gaussian in its own way. Cosmologist.

Primordial non-Gaussianities

Langlois & S. RP JCAP 08 Langlois, S. RP , Steer, Tanaka PRD 08

Multifield inflation with non-standard kinetic terms

L(XIJ ≡ −1 2∂µφI∂µφJ, φK)

The most general Lorentz invariant Lagrangian function of an arbitrary number of scalar fields and their first derivatives

• General study of bakground and fluctuations at first and

second order. Reference formalism for many works on inflation and dark energy.

• K-inflation and ‘standard’ multi-field inflation are subclasses of

gµν = ¯ gµν(t) + δgµν(t, xi) φI = ¯ φI(t) + δφI(t, xi)

• Study of coupled fluctuations metric-

scalar fields at non-linear level.

• Identification of the gauge-invariant physical dofs. Calculations done

in the ADM formalism. Quantization of the linear theory.

⇥Q(t)⇤ = ⇥0| " ¯ T exp i Z t

1(1+i)

HI(t0)dt0 !# QI(t) " T exp i Z t

1(1i)

HI(t00)dt00 !# |0⇤

Schwinger (61), Keldysh (64), Weinberg (05)

• Higher-order correlation functions in the

Schwinger-Keldysh, or in-in, formalism:

• T
• ols: Gravitational Theory and perturbative Quantum Field Theory

in curved spacetime.

S = ¯ S + S(2)(δgµν, δφI) + S(3)(δgµν, δφI) + S(4)(δgµν, δφI) + . . .

In practice, accurate analytically only until a few e-folds after Hubble crossing

General strategy

The delta-N formalism

Light fields acquire vacuum quantum fluctuations during inflation ¯ φA

∗ → ¯

φA

∗ + QA

Delta-N formalism: Taylor expansion of the curvature perturbation in terms of the field fluctuations at Hubble crossing

ζ = NAQA + 1 2NABQAQB + . . .

Sasaki, Stewart (96) Lyth et al (95)

Origin of the bispectrum

hζ(k1)ζ(k2)ζ(k3)i = NANBNChQA(k1)QB(k2)QC(k3)i

1 H

H−1 λ = a k

Log(a)

Log(physical scale)

Origin of the bispectrum

hζ(k1)ζ(k2)ζ(k3)i = NANBNChQA(k1)QB(k2)QC(k3)i

1 H

Quantum

H−1 λ = a k

Log(a)

Log(physical scale) Quantum NGs of the fields around Hubble crossing k1 ∼ k2 ∼ k3 Suppressed by the flatness of the potential in standard slow-roll single and multifield models Important for models with non-standard kinetic terms

Maldacena (03) Lidsey, Seery (05) Chen et al (06) Langlois, S. RP , Steer, Tanaka 08

1 c2

s

− 1 = 2XL,XX L,X

Key quantity:

L ⊃ ✏ c2

s

✓ ˙ ⇣2 − c2

s

(@⇣)2 a2 ◆

+ ✓1 − c2

s

H ◆ ˙ ζ (∂ζ)2 a2 Reduced ‘speed of sound’

• f fluctuations ...

... comes with non- trivial derivative interactions

LDBI = − 1 f(φ) ⇣p 1 − 2f(φ)X − 1 ⌘ − V (φ)

Prototypical example: L(X ≡ −1 2∂µφ ∂µφ, φ)

K-inflation

f eq

NL ∼ 1

c2

s

Origin of the bispectrum

hζ(k1)ζ(k2)ζ(k3)i = NANBNChQA(k1)QB(k2)QC(k3)i

+1 2NANBNCDhQA(k1)QB(k2)(QC QD)(k3)i + 2 perms.

1 H

Quantum

H−1 λ = a k

Log(a)

Log(physical scale) Quantum NGs of the fields around Hubble crossing k1 ∼ k2 ∼ k3

Origin of the bispectrum

hζ(k1)ζ(k2)ζ(k3)i = NANBNChQA(k1)QB(k2)QC(k3)i

Non-zero even for Gaussian fields (Wick)

+1 2NANBNCDhQA(k1)QB(k2)(QC QD)(k3)i + 2 perms.

1 H

Quantum

H−1 λ = a k

Log(a)

Log(physical scale) Quantum NGs of the fields around Hubble crossing k1 ∼ k2 ∼ k3

Origin of the bispectrum

hζ(k1)ζ(k2)ζ(k3)i = NANBNChQA(k1)QB(k2)QC(k3)i

+1 2NANBNCDhQA(k1)QB(k2)(QC QD)(k3)i + 2 perms.

Super-Hubble nonlinear relation between zeta and the fields

1 H

Quantum Classical

H−1 λ = a k

Log(a)

Log(physical scale) Quantum NGs of the fields around Hubble crossing k1 ∼ k2 ∼ k3

k3 ⌧ k1, k2

Local non-Gaussianities

Origin of the bispectrum

hζ(k1)ζ(k2)ζ(k3)i = NANBNChQA(k1)QB(k2)QC(k3)i

+1 2NANBNCDhQA(k1)QB(k2)(QC QD)(k3)i + 2 perms.

1 H

Quantum Classical

H−1 λ = a k

Log(a)

Log(physical scale) Quantum NGs of the fields around Hubble crossing k1 ∼ k2 ∼ k3 Because on super-Hubble scales in single- field inflation, important only for multiple field models

ζ = cte

f loc

NL = 5

6 NABN AN B (NCN C)2

sNL = f eq

NLf loc NL

Extra dimensions mobile D3-brane

φ1

φ2

• Brane inflation: moving D3-brane in higher

dimensions, non-standard kinetic terms

• Inflaton: position of the brane, multifeld.
• Multifield effects reduce the amplitude of

equilateral non-Gaussianities

D.Langlois, SRP , D.Steer, T.Tanaka, PRL 08

f eq

NL

• Unique signature in the 4pf function:

new shape with a consistency relation

SRP , JCAP 09

f loc

NL

Super-Hubble non-linear evolution in a simple model

Combined local and equilateral non-Gaussianities

Example of multifield brane inflation

Inflationary physics and shapes of non-Gaussianities

Non-standard kinetic terms: DBI, low sound speed models. Multiple degrees of freedom: Multified inflation, curvaton... Equilateral type (quantum) Local type (classical)

Planck 13

f eq

NL = −42 ± 75 (68% CL)

f loc

NL = 2.7 ± 5.8 (68 % CL)

Planck 13

Inflationary physics and shapes of non-Gaussianities

Non-standard kinetic terms Multifield Modified vacuum Features

And more!

Single field consistency relation

With f sq

NL & 1

If of primordial origin is robustly detected, all single field models would be ruled out! Any single-clock inflation (irrespective of kinetic terms, potential etc) f sq

NL(k1) = 5

12(1 − ns(k1)) f sq

NL(k1) ≡ lim k3→0 fNL(k1, k2, k3)

with

Maldacena (03), Creminelli & Zaldarriaga (04), SRP (10)

ns = 0.9603 ± 0.0073 (68%CL)

ζkl ζks

Understanding the theorem (1)

In the squeezed limit, one correlates one very long wavelength mode with two shorter wavelength modes

hζk1ζk2ζk3isq ' h(ζks)2ζkli

(ζks)2

ζkl

The theorem says does not care about if is exactly scale-invariant.

ζk

Understanding the theorem (II)

A very long wavelength mode acts as a local rescaling of the spatial coordinates (equivalently, of the scale factor) ds2 ' dt2 + a(t)2e2ζld x 2

ζkl

• x1 =

x0eζ1

• x2 =

x0eζ2

(ζks1)2

(ζks2)2

• 30
• 20
• 10

• 1.0
• 0.5

ns − 1 = d ln Pζ(k) d ln k

The effect of the long-wavelength modulation is proportional to

Computing fNL local (and beyond)

• Origin of local type non-Gaussianities is purely classical:

non-linear evolution of perturbations on super-Hubble scales.

• Derivation of the exact super-Hubble equations of motion for

gauge-invariant variables at second- and third-order in 2-field models! SRP

, Tasinato JCAP 08, Lehners, SRP PRD 09

• Efficient numerical method. Alternative to the deltaN formalism.
• Pure General Relativistic calculations (covariant formalism).

Computing fNL local (and beyond): an idea...

Lehners, SRP PRD 09

Planck implications

Constrain multi-field effects f loc

NL = 2.7 ± 5.8

f eq

NL = −42 ± 75

f orth

NL = −25 ± 39

cs ≥ 0.02 (95% CL) Lower bound on the inflaton speed of sound Strong constraints on light hidden sector fields coupled to the inflaton via operators suppressed by a high mass scale.

Λ > 105H

Λ > 102H

depending on assumptions on the hidden sector

Assassi et al, 2013.

Outline

• 1. Description of inflation
• 2. Beyond the simplest models
• 3. Primordial non-Gaussianities
• 4. Quasi-single-field inflation

Mass scales in realistic set-up

MP Mmoduli Mφ H

Hope: light inflaton, Planck-mass moduli

hard to achieve unnatural (eta problem) MP Mmoduli Mφ H

Find: many masses

• f order H

Quasi-single-field

Chen, Wang 09

Non-Gaussianity as a particle detector with the soft limits

ˆ τNL ⌘ 1 4 lim

k12!0

hζ

k1ζ k2ζ k3ζ k4i0

P1P3P12

• k1
• k3
• k4
• k1 +

k2

• k2

ˆ fNL ⌘ 5 12 lim

k3!0

hζ

k1ζ k2ζ k3i0

P2P3

• k2
• k1
• k3
• Squeezed limit of the bispectrum:
• Collapsed limit of the trispectrum:

cf soft limits in QCD

Non-Gaussianity as a particle detector

√ηH

H

Mp

Single-field inflation Quasi-single- field inflation Multi-field inflation

k2 k

3 2 −ν

k0

✓6 5 ˆ fNL ◆2

• ✓6

5 ˆ fNL ◆2

≥ ✓6 5 ˆ fNL ◆2

lim

k→0 k3hζ kζ k1ζ k2i

ˆ τNL

ν ≡ r 9 4 − m2 H2

Suyama-Yamaguchi (08) Chen-Wang (09) Baumann-Green (11) Assassi et al (12)

Random potentials from Planck- suppressed interactions

• High energy physics motivates considering many fields of

intermediate masses governed by a complicated potential induced by Planck-suppressed couplings: V (φ1, ..., φN) =

∞

X

J=1

c(J)

i1...iJ

φi1...φiJ ΛJ−4

• The form of the potential can be computed with some effort, but

computing the coefficients is hopeless in general.

• Key question: when inflation arises in this context, what are its

characteristic properties? What universal properties can we learn without knowing the details of the Wilson coefficients?

(motivation/analogy: Random Matrix Theory)

Quasi-single-field inflation

McAllister, S.RP , Xu, JCAP , 12

• I studied in detail the first microphysical realizations of quasi-

single-field inflation (and in EFT framework).

• Precise set-up is warped D-brane inflation (6 fields)

but methods and findings have much broader applicability:

• statistical study of a large ensemble of potentials
• mass spectrum predicted by Random Matrix Theory
• reveal physics by comparing exact numerical results and

truncated models of the perturbations.

• Rich phenomenology is natural (not put by hand): slow-roll

violation, bending trajectories and ‘many-field’ effects are

• commonplace. New unexpected effects.

+

Mass spectrum and random matrix theory

• Masses of order H
• Almost never two tachyonic directions
• m3 ∼ m4

m5 ∼ m6

• m2

1 & −0.1H2 consequence of conditioning on

prolonged inflation

eigenvalues of the mass matrix at Hubble crossing m2

1 ≤ . . . ≤ m2 6 =

McAllister, S.RP , Xu, JCAP , 12

+ Data Random Matrix Model

Marsh, McAllister, Wrase, 2011

Qualitative features of the mass spectrum can be reproduced in a random matrix model of supergravity

Data

Mass spectrum and random matrix theory

McAllister, S.RP , Xu, JCAP , 12

+

Reaching the adiabatic limit

Masses of order H Suppression of the entropic modes by the end of inflation

Multifield effects and definite predictions without a description of (p)reheating

McAllister, S.RP , Xu, JCAP , 12

+

Two-field versus many-field

Exclusively many-field effects! Exclusively two-field effects McAllister, S.RP , Xu, JCAP , 12

+

Destructive multifield effects

Destructive multifield effects: consequence of bending trajectories and quantum interferences.

Numerical calculation of non-Gaussianities

Efficient numerical method to calculate primordial non- Gaussianities based on spectral methods. Predictions in form ready for data-analysis.

• H. Funakoshi, S. RP JCAP 12

Other subjects I have worked on I could have developped...

• Orthogonal non-Gaussianities
• Trispectrum
• Effective Field Theory of inflation
• Inflation and modified gravity

Cosmological inflation Primordial non-Gaussianities Fondamental theories Cosmological

• bservations

Concrete models Statistical methods Analytical formalism Numerical tools Phenomenology

Some observational perspectives

• Primordial gravitational waves (COrE, CMBPol ...)
• Constraints on non-Gaussianities from Large

Scale Structure (Euclid ...)

• Spectral distorsions of the CMB (Prism, Pixie)