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Titre: Diapositive 1
Auteur: Jerome Martin

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Inflation after BICEP2
Jerome Martin
CNRS/Institut
d’Astrophysique de Paris

IAP Discussion on BICEP2
results
February 21, 2014
(Thanks to C. Ringeval & V. Vennin
for emergency figures, plots etc …)

Inflation solves the standard puzzles of the HBB phase

Inflation is a phase of accelerated expansion taking place in the
very early Universe. The scale factor is such that
This assumption allows us to solve several
problems of the standard hot Big Bang model:
•Horizon problem

•Flatness problem

•Monopoles problem …

2

Inflationary energy scale

 Inflation does not replace the Hot Big Bang model.
It is a new ingredient which completes the standard
model. It takes place before the Hot Big Bang phase

Inflation

 The energy scale of inflation can a priori be in a wide
range of values ~ 12 orders of magnitude! This is
probably the most important inflationary quantity!

Inflation

3

Structure formation and inflation

Quantum fluctuations as seeds of CMB anisotropy and large scale structures

Initial
quantum
state: ground
state of the
harmonic
oscillator

Inflation: everything is quantum
fluctuations stretched
over cosmological scales …!

inflation

radiation matter
4

Inflationary Observables

with

Inflationary
power spectrum

Translate 3d into 2d
Describes the evolution of
the pertubations when they
re-enter the Hubble radius

5

Calculating the two-point correlations: slow-roll parameters
The slow-roll parameters are
the “small parameters” of a perturbative
calculation of the power spectrum

inflation

radiation matter

Slow-roll

Reheating
6

Inflationary predictions: the two-point correlation function

- The amplitude is controlled by H
- For the scalar modes, the amplitude also
depends on  1
-

C~ -0.7
Consistency relation:

The power spectra are scale-invariant plus
logarithmic corrections the amplitude of
which depend on the sr parameters, ie on
the microphysics of inflation

The spectral indices are given by

Gravitational waves are subdominant

The running, i.e. the scale dependence of the spectral indices, of dp and gw are

7

Inflationary predictions: the slow-roll space

An example: « large field inflation »

8

8

The Planck numbers for inflation

Planck results in brief:

COBE (1992)

WMAP (2003)

Flat universe with adiabatic, Gaussian
and almost scale invariant fluctuations
Planck (2013)

9

Planck vs BICEP2

Message 1: the energy scale of inflation
Before BICEP2
Upper bound on the energy
scale of inflation ~ less than
the GUT scale

10

Planck vs BICEP2

Message 1: the energy scale of inflation
Before BICEP2
Upper bound on the energy
scale of inflation ~ less than
the GUT scale
After BICEP2
Energy scale of inflation
measured to be ~ the GUT
scale

11

Planck vs BICEP2

Message 2: first derivative of the potential
Before BICEP2

Upper bound
on the value of
the first
derivative
Second sr parameter
measured!

12

Planck vs BICEP2

An example: « large field inflation »

13
13

Planck vs BICEP2

An example: « large field inflation »

14
14

Planck vs BICEP2

An example: « large field inflation »

15
15

Planck vs BICEP2

An example: « large field inflation »

16
16

Planck vs BICEP2

Message 2: first derivative of the potential
Before BICEP2

Upper bound
on the value of
the first
derivative
Second derivative
measured!
After BICEP2

First
derivative
measured!

Second derivative
measured but
different value

17

Planck vs BICEP2

An example: « large field inflation »

18
18

Planck vs BICEP2

An example: « large field inflation »

BICEP2 2014

19
19

Planck vs BICEP2

Message 3: shape of the potential
Before BICEP2

20

Planck vs BICEP2

Message 3: shape of the potential
Before BICEP2

Plateau inflation

Starobinsky
model

21

Planck vs BICEP2

Message 3: shape of the potential
Before BICEP2

Plateau inflation

Starobinsky
model

After BICEP2

22

Planck vs BICEP2

Message 3: shape of the potential
Before BICEP2

Plateau inflation

Starobinsky
model

After BICEP2

23

Planck vs BICEP2

Message 4: more complicated class of models
Before BICEP2
Simplest models favored (ie more complicated not needed) because
no isocurvature modes, no NG etc …

24

Planck vs BICEP2

Message 4: more complicated class of models?
Before BICEP2
Simplest models favored (ie more complicated not needed) because
no isocurvature modes, no NG etc …
After BICEP2


K-inflation

• Multiple field inflation

Still true!
25

Planck vs BICEP2

Message 5: model building issues
Before BICEP2
No problem in principle, lot of activities trying to relate the Higgs with
the inflaton

26

Planck vs BICEP2

Message 5: model building issues
Before BICEP2
No problem in principle, lot of activities trying to relate the Higgs with
the inflaton
After BICEP2


New physics at the GUT scale, coupling with the Higgs??

• Difficult because of the Lyth bound:


Break-down of EFT??

27

Criticisms on inflation after Planck & BICEP2



Inflation uses a scalar field but nobody has ever seen a scalar field
- Higgs at the LHC



No prediction of inflation, only post-dictions …
- ns ~ 0.96 ≠1
- Presence of primordial gravity waves

• Alternatives to inflation??
- Ekpyrotic model predicts no detectable gw …
- String gas cosmology, bouncing models??
28

Inflation after BICEP2

Have we finally proven inflation????

29

Inflation after BICEP2

Have we finally proven inflation????

NO!

30

Inflation after BICEP2

Have we finally proven inflation????

NO!
We need to check the consistency relations

We need to measure the tensor spectral index; since r is large, this
seems feasible

31

Inflation after BICEP2
Can you
repeat??
CamC

CamC

- First calculation of gw production in curved spacetime, L. P. Grishchuk (1975)
- First application to an inflationary background, A. Starobinsky (1979)
32


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