Inflation Physics from the CMB and LSS Thursday, July 17, 14 What - - PowerPoint PPT Presentation

Inflation Physics from the CMB and LSS

Leonardo Senatore (Stanford)

Thursday, July 17, 14

• The only observable we are testing from the background solution is
• All the rest, comes from the fluctuations
• For the fluctuations

– they are primordial – they are scale invariant – they have a tilt – they are quite gaussian – both tensors and scalar

• Is this enough to conclude it is slow-roll Inflation?

– and in general, what is the dynamics of this inflaton?

What are we seeing?

ns 1 ' 0.04 ⇠ O ✓ 1 Ne ◆ .

NG ⇠ h⇣3i h⇣2i3/2 . 103 ✓

ΩK . 3 ⇥ 10−3

Thursday, July 17, 14

The general theory of the fluctuations

Thursday, July 17, 14

The Effective Field Theory of Inflation (Inflation as the Theory of a Goldstone Boson)

with C. Cheung, P. Creminelli, L. Fitzpatrick, J. Kaplan JHEP 2008

Thursday, July 17, 14

The Effective Field Theory of Inflation

• Analogous of the Chiral Lagrangian for the Pions and W bosons S. Weinberg PRL 17, 1966
• Goldstone boson equivalence principle
• Used in WMAP9 and Planck papers (thanks!, but attributed to Weinberg)
• Maybe because Weinberg is the true scientific father of all of us?

⇧ ⇥ ⌥

Inflation: quasi dS phase with a privileged spacial slicing: Inflation: the Theory of the Goldstone Boson of time translations

Thursday, July 17, 14

The Effective Field Theory of Inflation

• Dispersion relations

⇧ ⇥ ⌥

Inflation: quasi dS phase with a privileged spacial slicing: Inflation: the Theory of the Goldstone Boson of time translations

!2 = c2

sk2 + k4

M 2

Thursday, July 17, 14

The Effective Field Theory of Inflation

• Dispersion relations

⇧ ⇥ ⌥

Inflation: quasi dS phase with a privileged spacial slicing: Inflation: the Theory of the Goldstone Boson of time translations

!2 = c2

sk2 + k4

M 2

Thursday, July 17, 14

The Effective Field Theory of Inflation

• Dispersion relations

⇧ ⇥ ⌥

Inflation: quasi dS phase with a privileged spacial slicing: Inflation: the Theory of the Goldstone Boson of time translations

!2 = c2

sk2 + k4

M 2

Thursday, July 17, 14

The Effective Field Theory of Inflation

• Interactions
• at leading order in derivatives and in fluctuations

⇧ ⇥ ⌥

Inflation: quasi dS phase with a privileged spacial slicing: Inflation: the Theory of the Goldstone Boson of time translations

˙ ⇡3 , ˙ ⇡(@i⇡)2 , (@2⇡)(@⇡)2

Thursday, July 17, 14

A lesson from B-modes

Thursday, July 17, 14

The amplitude and the tilt

• This Lagrangian is fine to make all predictions
• The Amplitude
• The tilt
• No potentials terms

– just symmetry – just how history of a mode depends on time

ns 1 = ˙ H H2 + ¨ H ˙ HH + ˙ cs csH Z

M 2

Pl

✓V 0 V ◆2 , M 2

Pl

V 00 V .

h⇣2i ⇠ H4 ˙ HM 2

Plcs

, h2i ⇠ H2 M 2

Pl

Thursday, July 17, 14

• Imagine at each step one produces
• Imagine decay to
• In this decay,

– gravitational bremsstrahlung is produced – This can be larger than standard signal – Also scalar are produced and they induce NG

No vacuum sources of B-modes

φ V (φ)

n

n

with Silverstein and Zaldarriaga 1109

hh2i ⇠ ⇢χ ⇢total HMχ M 2

Pl

with Mirbabayi, Silverstein and Zaldarriaga in progress

n

Thursday, July 17, 14

Non-Gaussianities

• Large non-Gaussianities are possible and technically natural

– Having these operators large is not in contrast with de Sitter epoch – Demystification of non-Gaussianities (after 25 years!)

• NG do not need to be tiny, but just small

–Smallness of NG simply corresponds to weakly coupled field theory at – EFT automatically gives operators and size:

• Canonically normalize, and get NG: Example:

»as for dim=6 operators

˙ ⇡3 , ˙ ⇡(@i⇡)2 , (@2⇡)(@⇡)2

Z  E ⇠ H

˙ π3

c

Λ2

U

) NG ' fNLζ ⇠ H2 Λ2

U

)

Thursday, July 17, 14

Large non-Gaussianites

with Smith and Zaldarriaga, JCAP2010

A function of two variables: like a scattering amplitude There are two templates With this, we could prove inflation

Thursday, July 17, 14

Limits in terms of parameters of a Lagrangian

• .
• These are contour plots of parameters of a fundamental Lagrangian
• Same as in particle accelerator Precision Electroweak Tests.
• Thanks to the EFT: A qualitatively new (and superior) way to use the cosmological data
• Universal limit

cs & 0.02

with Smith and Zaldarriaga, JCAP2010 Planck Collaboration 2013

Thursday, July 17, 14

• Higher derivative opts can be the leading ones

– QFT fact: the following theory is technically natural

• loops do not generate lower derivative opts.
• it could come from integrating out a high spin particle
• Apply this logic to the EFT of Inflation

– we can start at very high number of derivatives – Many shapes are similar – The first non-trivial ones are at 7- and 9-derivs

• and

Enhanced Symmetries

with Behbahani, Mirbabayi, Smith to appear

⌃ ⌃ S ⇥ ⌃ d4x (µ)2 + 1 Λ4n(n)4

∂4φ ∂4φ ∂4φ ∂4φ ∂4φ ∂4φ ∂4φ ∂4φ

Thursday, July 17, 14

• Optimal analysis of WMAP9 (could not do Planck)
• Results
• About 2.5

– we know with Planck goes down,.... wait and see

Enhanced Symmetries

with Behbahani, Mirbabayi, Smith to appear

Thursday, July 17, 14

• Multifield Inflation offers a plethora of interesting signatures. Multiple fields can be

– goldstone bosons

• abelian
• non-abelian

– Susy (introduced in the EFT to study NG for the first time)

• unless coupled to inflaton sector, SUSY broken just by
• But if BICEP is true?! multiple fields must dominate the signal of fluctuations

– Call with – Since

• some room left, but not very large
• Many signals, analysis in progress

The EFT of Multifield Inflation

with Zaldarriaga 1109

Thursday, July 17, 14

• Another option is to have particles in intermediate states

– If they are not observed, but they are light

• Several examples

– effective opts – Conformally coupled sector – Quasi single field

• a scalar

–protected as a Pseudo Goldstone –protected by SUSY

• All this quite unconstrained

Particles in intermediate states

˙ π ˙ π ˙ π OOO

with Nacir, Porto, and Zaldarriaga 1109 with Green, Lewandowski, Silverstein, and Zaldarriaga 1301 Senatore in progress Senatore and Zaldarriaga 1109 Baumann and Green 1205 Craig and Green 1404 Chen and Wand 0909

Thursday, July 17, 14

• Planck improve limits wrt WMAP by a factor of ~3.
• We can think of Inflation as being characterized by higher dimension opt.s
• Since
• Given the absence of known or nearby threshold, this is not much.
• Planck is great
• but Planck is not good enough

– not Plank’s fault, but Nature’s faults

• Please complain with Nature
• Planck was an opportunity for a detection, not much an opportunity to change the

theory in absence of detection

• On theory side, little changes

– contrary for example to LHC, which was crossing thresholds

• Any result from LHC is changing the theory

What has Planck done to theory?

˙ ⇡3 Λ2

U

Z 

• NG ⇠ H2

Λ2

U

) Λmin, Planck

U

' p 3 Λmin, WMAP

U

Thursday, July 17, 14

• No matter BICEP, non-Gaussianities crucial to increase our understanding
• In order to increase our knowledge of interactions in Inflation, we need more modes

– Planck will not do it, nor BICEP

• Large Scale Structures offer the ideal place for hunting for more modes

– I will show results from the EFTofLSS that, if verified and extended to all

• bservable, can increase limits to

– We can argue that absence of detection of NG up to this level implies

• bservational proof of slow-roll inflation
• Because every other theory gives larger non-Gaussianities
• This is learning even without detection
• This also offers us a way to study large scale structures (which are nice)

NG and the future

f equil, orthog, loc.

NL

. 1

2 2

Thursday, July 17, 14

The Effective Field Theory

• f

Cosmological Large Scale Structures

Leonardo Senatore (Stanford)

Thursday, July 17, 14

• Plank will increase by a factor of less than 2.
• Next are Large Scale Structures
• Like moving from LEP to LHC:

– much dirtier, but much more potential

• How many modes are there?

– this is the question

What is next?

Thursday, July 17, 14

The Effective Field Theory of Cosmological Large Scale Structures

with Carrasco, Foreman and Green 1310 with Baumann, Nicolis and Zaldarriaga JCAP 2012

Cosmological Non-linearities as an Effective Fluid The Effective Theory of Large Scale Structure (EFTofLSS)

with Carrasco and Hertzberg JHEP 2012

The 2-loop power spectrum and the IR safe integrand The Lagrangian-space EFTofLSS

with Porto and Zaldarriaga 1311

The EFTofLSS at 2-loops

with Carrasco, Foreman and Green 1304

The IR-resummed EFTofLSS

with Zaldarriaga 1304

The one-loop bispectrum in the EFTofLSS

with Angulo, Foreman, Schmittful 1306 see also Baldauf, Mirbabayi, Mercolli,Pajer 1306

Bias in the EFTofLSS

Senatore alone 1306

Thursday, July 17, 14

• Non-linearities at short scale

A well defined perturbation theory

Thursday, July 17, 14

• Non-linearities at short scale

A well defined perturbation theory

Thursday, July 17, 14

• Standard perturbation theory is not well defined
• Standard techniques

– perfect fluid – expand in and solve iteratively

• Perturbative equations break in the UV

– . – no perfect fluid if we truncate

A well defined perturbation theory

klow klow khigh khigh

˙ ρ + ∂i

• ρvi

= 0 ,

δ ⇠ δρ ρ Z ⇠ ρ δ(n) ⇠ Z GreenFunction ⇥ Source(n) ⇥ δ(1), δ(2), . . . , δ(n1)⇤

2 4

δ ⇠ k kNL 1 for k kNL

) h(2)

k (2) k i ⇠

Z d3k0 h(1)

kk0(1) kk0i h(1) k0 (1) k0 i

Thursday, July 17, 14

Idea of the Effective Field Theory

Thursday, July 17, 14

• Similar to a dielectric material
• For E&M waves with with do not study Maxwell equations with many

atoms, we study Dielectric Maxwell equations, where effect of atoms is in gross features as

• The universe looks like a dielectric, just replace

– E&M with GR – atoms with galaxies

Main Idea

atomic

d datomic

Dielectric Fluid

~ ddipole ⇠ ↵ ~ Eelectric

Thursday, July 17, 14

• Similar to a dielectric material
• For E&M waves with with do not study Maxwell equations with many

atoms, we study Dielectric Maxwell equations, where effect of atoms is in gross features as

• The universe looks like a dielectric, just replace

– E&M with GR – atoms with galaxies

Main Idea

atomic

d datomic

Dielectric Fluid

~ ddipole ⇠ ↵ ~ Eelectric

Dielectric Fluid

EM ! GR ✓

Thursday, July 17, 14

– Like Chiral Lagrangian

• weakly coupled at long distances
• strongly coupled at short distances

Main Idea

Dielectric Fluid

EM ! GR ✓

Thursday, July 17, 14

• A well defined perturbation theory
• 2-loop in the EFT, with IR resummation
• Data go as : factor of 200 more modes than naive

Bottom line result

k3

max

Thursday, July 17, 14

Better Limits

Thursday, July 17, 14

Better Limits

Thursday, July 17, 14

Look at the dot, to scale

Better Limits

Thursday, July 17, 14

Construction of the Effective Field Theory

Thursday, July 17, 14

• On short distances, we have point-like particles

– they move – induce overdensities – Source gravity

Point-like Particle versus Extended Objects

@2Φ(~ x) = H2(~ x) Z

H 1 + (~ x, ⌘) = Z d3q (3)(~ x ~ z(~ q, ⌘))

Thursday, July 17, 14

• But we cannot describe point-like particles: we need to focus on long distances.

– We deal with Extended objects

• they move differently:

Point-like Particle versus Extended Objects

Thursday, July 17, 14

• But we cannot describe point-like particles: we need to focus on long distances.

– We deal with Extended objects

• they move differently:
• the center of mass moves from force on center of mass, but also from tidal force

proportional to quadrupole of mass distribution

Point-like Particle versus Extended Objects

Thursday, July 17, 14

• .

– .

• they induce number over-densities and real-space multipole moments
• they source gravity with the `overall’ mass
• These equations can be derived from smoothing the point-particle equations

–but actually these are the assumption-less equations

Point-like Particle versus Extended Objects

⇠ Energyelectrostatic = q V + ~ d · ~ E + . . .

Thursday, July 17, 14

• Similar to treatment of material polarizability:
• Take moments:
• Expectation value
• Response (non-local in time)
• Stochastic noise
• Overall
• In summary: we obtain an expression just in terms of long-wavelength variables

How do we treat the new terms?

hQSi = 0

hQSQS . . .i 6= 0

Qij = l2

0 ij + l2 1 @i@jΦL + . . . + Qij,S

!

~ ddipole ⇠ ~ dintrinsic + ↵ ~ E

hQijiS = l2

S(⌘)ij

Qij,R ⇠ l1(⌘)2 @i@jΦL(~ zL(~ q, ⌘)

Thursday, July 17, 14

• Similar to treatment for material polarizability:
• Short distance physics is taken into account by expectation value, response, and noise
• Poisson equation breaks when

– gravitational potential from quadrupole moment ~ the one from center of mass

• By dimensional analysis, this happens for distances shorter than a critical length

– the non-linear scale – on long distances, , write as many terms as precision requires.

• Manifestly convergent expansion in

When do we stop?

~ ddipole ⇠ ↵ ~ Eelectric k & kNL

k ⌧ kNL

✓ k kNL ◆ ⌧ 1

, Qelectric

ij

= c EiEj , . . .

Thursday, July 17, 14

• In the universe, finite-size particles move
• In Lagrangian space, we do not expand in
• In Eulerian, we do: we describe particles from a fixed position

– Expand in

Connecting with the Eulerian Treatment

~ z(~ q, t) = ~ q + ~ s(~ q, t) Z

+ ~ s(~ q, t) Z

Thursday, July 17, 14

• The resulting equations are equivalent to Eulerian fluid-like equations

–here it appears a non trivial stress tensor for the long-distance fluid

Connecting with the Eulerian Treatment

r2 = H2⇢ ⇢ @t⇢ + H⇢ + @i(⇢vi) = 0 ˙ vi + Hvi + vj@jvi = 1 ⇢@j⌧ ij

⌧ij = p0 ij + c2

s ij @2⇢ + . . .

Thursday, July 17, 14

Perturbation Theory with the EFT

Thursday, July 17, 14

• In the EFT we can solve iteratively (loop expansion)

Perturbation Theory within the EFT

⌅ ⇥

• ⌥, v⌥, Φ⌥ ⌅ 1

r2 = H2⇢ ⇢ @t⇢ + H⇢ + @i(⇢vi) = 0 ˙ vi + Hvi + vj@jvi = 1 ⇢@j⌧ ij ⌧ij = p0 ij + c2

s ij @2⇢

Thursday, July 17, 14

• Regularization and renormalization of loops (scaling universe)

– evaluate with cutoff. By dim analysis:

Perturbation Theory within the EFT

P I

2-loop = (2π)

" cΛ ✓ Λ kNL ◆2 ✓ k kNL ◆1 P11 + cΛ

1

✓ Λ kNL ◆1 ✓ k kNL ◆2 P11 +cΛ

2 log

✓ k Λ ◆ ✓ k kNL ◆3 P11 + cfinite

1

✓ k kNL ◆3 P11 +c1/Λ

1

✓ k Λ ◆1 ✓ k kNL ◆3 P11 + subleading finite terms in k Λ #

P11 = 1 kNL

3

✓ k kNL ◆3/2

Thursday, July 17, 14

• Regularization and renormalization of loops (scaling universe)

– evaluate with cutoff. By dim analysis: – absence of counterterm

Perturbation Theory within the EFT

P I

2-loop = (2π)

" cΛ ✓ Λ kNL ◆2 ✓ k kNL ◆1 P11 + cΛ

1

✓ Λ kNL ◆1 ✓ k kNL ◆2 P11 +cΛ

2 log

✓ k Λ ◆ ✓ k kNL ◆3 P11 + cfinite

1

✓ k kNL ◆3 P11 +c1/Λ

1

✓ k Λ ◆1 ✓ k kNL ◆3 P11 + subleading finite terms in k Λ #

P11 = 1 kNL

3

✓ k kNL ◆3/2

⌧ij = p0 ij + c2

s ij @2⇢

Thursday, July 17, 14

• Regularization and renormalization of loops (scaling universe)

– evaluate with cutoff. By dim analysis: – absence of counterterm – One divergent term – Sum up and

Perturbation Theory within the EFT

P I

2-loop = (2π)

" cΛ ✓ Λ kNL ◆2 ✓ k kNL ◆1 P11 + cΛ

1

✓ Λ kNL ◆1 ✓ k kNL ◆2 P11 +cΛ

2 log

✓ k Λ ◆ ✓ k kNL ◆3 P11 + cfinite

1

✓ k kNL ◆3 P11 +c1/Λ

1

✓ k Λ ◆1 ✓ k kNL ◆3 P11 + subleading finite terms in k Λ #

)

P2-loop counter = (2π)cΛ

counter

✓ Λ kNL ◆ ✓ k kNL ◆2 P11 cΛ

counter = −cΛ 1 + δccounter

✓kNL Λ ◆ as Λ → ∞. P I

2-loop + P2-loop counter = (2π)δccounter

✓ k kNL ◆2 P11 + (2π)cfinite

1

✓ k kNL ◆3 P11

P11 = 1 kNL

3

✓ k kNL ◆3/2

⌧ij = p0 ij + c2

s ij @2⇢

Thursday, July 17, 14

• Has everything being lost?

– to make result finite, we need to add a counterterm with finite part

• need to fit to data (like a coupling constant), but cannot fit the k-shape

Calculable terms in the EFT

P I

2-loop + P2-loop counter = (2π)δccounter

✓ k kNL ◆2 P11 + (2π)cfinite

1

✓ k kNL ◆3 P11

Thursday, July 17, 14

• Has everything being lost?

– to make result finite, we need to add a counterterm with finite part

• need to fit to data (like a coupling constant), but cannot fit the k-shape

– the subleading finite term is not degenerate with a counterterm.

• it cannot be changed
• it is calculable by the EFT

–so it predicts an observation

Calculable terms in the EFT

P I

2-loop + P2-loop counter = (2π)δccounter

✓ k kNL ◆2 P11 + (2π)cfinite

1

✓ k kNL ◆3 P11

cfinite

1

= 0.044

Thursday, July 17, 14

• Each loop-order contributed a finite, calculable term of order

– each higher-loop is smaller and smaller

• This happens after canceling the divergencies with counterterms
• each loop contributes the same
• Up to 2-loops, we need only the 1-loop counterterm

Lesson from Renormalization

L

Thursday, July 17, 14

IR-effects

Thursday, July 17, 14

• In Eulerian treatment one expands in

The Effect of Long-modes on Shorter ones

xEulerian x0 t0 δρshort wavelength

Thursday, July 17, 14

• Add a long `trivial’ force (trivial by GR)
• This tells you that one can resum the IR modes: this is the ~Lagrangian treatment

The Effect of Long-modes

δρshort wavelength x0 xEulerian x0 t0 δρshort wavelength t1 time

• ∇Φlong wavelenght

xEulerian

Big `trivial’ Perturbation

Thursday, July 17, 14

Results

Thursday, July 17, 14

• Well defined and manif. converg.
• Every perturbative order improves the agreement as it should
• We know when we should fail, and we fail when we should

EFT of Large Scale Structures

⇣

k kNL

⌘L

Thursday, July 17, 14

• The lines with oscillations are obtained without resummation in the IR

EFT of Large Scale Structures

with Carrasco, Foreman and Green 1310

Thursday, July 17, 14

• we fit until , as where we should stop fitting

– there are 200 more quasi linear modes than previously believed!

EFT of Large Scale Structures

⇠ kmax ' 0.6 h Mpc1

Thursday, July 17, 14

• Comparison with Standard Treatment
• For the EFT, change from 1-loop to 2-loop predicted

– the other new terms are clearly important – they `conspire’ to the right answer

EFT of Large Scale Structures

PEFT-2-loop = P11 +P1-loop +P2-loop 2 (2π)(c2

s(1) +c2 s(2)) k2

k2

NL

P11 +(2π)c2

s(1)P (cs,p) 1-loop +(2π)2c4 s(1)

k4 k4

NL

P11 (62)

Thursday, July 17, 14

• The EFT parameters can be measured from small N-body simulations

– similar to what happens in QCD: lattice sims

• As you change smoothing scale, the result changes
• Perfect agreement with fitting at low energies

– like measuring from lattice sims and scattering

Measuring parameters from N-body sims.

d cs dΛ = d d Λ Z Λ d3k P13(k)

Fπ ⇡⇡

with Carrasco and Hertzberg JHEP 2012

Thursday, July 17, 14

• At one-loop, similarly great results

– with no additional parameter

• Similar formulas just worked out for Bias

Momentum and Bispectrum

with Angulo, Foreman and Schmittful 1406 with Zaldarriaga 1404 alone 1406

Gain in Information

Thursday, July 17, 14

• A manifestly convergent perturbation theory
• we fit until , as where we should stop fitting

– there are 200 more quasi linear modes than previously believed! – huge impact on possibilities for

• Can all of us handle it?! This is an opportunity and a challenge for us

– Primordial Cosmology can still have a bright near future!

EFT of Large Scale Structures

⇠ kmax ' 0.6 h Mpc1

⇣

k kNL

⌘L ⇠

Pl ⇠

f equil., orthog.

NL

. 1 &

Thursday, July 17, 14

• Overview of observational status of Inflation

– The EFT and what we are really learning

• the 2-point function

– non-Gaussianities

• i.e. everything but the 2pt function
• to tell us about the physics of inflation (not just that it existed)
• some models are constrained, some other are very free

–prediction and analysis of new higher derivative shapes – The Effective Field Theory of Large Scale Structure

• very rich (Quantum) Field Theory
• amazing results so far
• together with B-modes, the opportunity of a bright 10yr future for cosmology

–With a growing number of (only young) collaborators

Conclusions

Thursday, July 17, 14