WMAP 3year constraints on the inflationary expansion

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WMAP 3-year constraints on the inflationary
expansion
Fabio Finelli
INAF/IASF-BO Istituto di Astrofisica Spaziale e
Fisica Cosmica di Bologna INAF/OAB Osservatorio
Astronomico di Bologna also supported by INFN
Bologna
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MOTIVATIONS
Inflation is the dominant paradigm. Inflationary
predictions survived many observations nearly
flat spatial sections, spectrum of gaussian
nearly scale invariant curvature fluctuations are
now firm points of our cosmological model.
WMAP1 has been able to first detect large scale
curvature perturbations (TE) and to constrain
inflationary models excityng times are coming
with future CMB and LSS data.
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OUTLINE
Analyze WMAP3 data (plus CMBsmall and LSS data)
with different methods of comparing inflationary
predictions with observations wtr to WMAP team
1. Constraints on inflation at first order in
HFF 2. Second order in HFF (i.e. including
running) 3. Relaxing theoretical priors a.
Tensor-to-scalar ratio as a free parameter b.
Blue spectrum for GW
Based on work in collaboration with Maria Rianna
and Reno Mandolesi, astro-ph/0608277
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Inflation driven by scalar field

• Einstein-Klein-Gordon action

Homogeneous EOM
Pressure and energy densities
Kinematic configuration
slow-roll
Accelerated expansion
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Standard Inflationary Predictions
where
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Courtesy by W. Kinney
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Courtesy by W. Kinney
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Horizon Flow Functions (Schwarz et al, 2001)
acceleration
Single-field models
Implicit relation can be inverted assuming first
two HFF small
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The zoo plot in (?2,?1) plane
Courtesy by Schwarz et al., JCAP 0408003
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A.Lewis S.Bridle
CosmoMC
Phys. Rev. D 66 (2002)
http//cosmologist.info/cosmomc
Markov Chain Monte Carlo
CAMB
Getdist
Parallelized Einstein-Boltzmann code
Statistical analysis

• Data

CMB
LSS 2dF (SDSS)
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First order HFF

• Expansion of the ln of the power spectra in
  terms of ln(k/k) when you sample HFF there is
  no danger that the PS go negative (even more
  important at second order in HFF).

Leach, Liddle, Martin, Schwartz (2002)
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Effect of gravity waves on CMB anisotropies in
temperature and polarization
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CDM
Flat
Data used

• CMB ACBAR, VSA, CBI, BOOMERANG03 (B03), WMAP1
  or WMAP3

• LSS 2dF e SDSS (used separately)

7-dim Parameter space
Although this pivot scale does not coincide with
the ones used by WMAP (0.002 and 0.05), it is
placed close to the range of k probed by the
whole dataset.
Derived parameters
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KG inflation
ACBARCBIVSAB032dF

WMAP1/WMAP3

• Priors

Errors reduced with respect to the first year,
tau and ns significantly decreased (see Spergel
et al. 06)
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WMAP1
WMAP3
WMAP1
WMAP3
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Comparison with WMAP team results
Tensor-to-scalar ratio (without marginalizing on
n)
WMAPIICMBsmall2dF
WMAPII2dF
Spergel et al. (2006)
Scalar spectral index (marginalized over all
other 6 params)
WMAPII only
Spergel et al. (2006)
PS do not quote the number in the abstract of
the WMAPII paper since there are no tensor
Spergel et al. (2006)
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Large field chaotic inflation
With WMAP3 models with an exit from inflation
(?2gt0) are definitively preferred!
Power-law inflation
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2dF02 vs SDSS
2dF allows more gravitational waves than SDSS
(this applies also to subsequent releases -2dF05-
and to the case with running)
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The effect of CMBsmall
Is Harrison-Zeldovich (nS 1,r 0) inside or
not 2??
The answer depends on systematics and
foregrounds, but also on the inclusion of
CMBsmall (ACBAR, VSA, CBI, B03). CMBsmall prefers
less power on small scales not only HZ is
disfavoured at 2?, but also nS 1 line.
NB Our results for WMAP3SDSS fully agree with
Kinney et al. 2006, Easther Peiris 2006.
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Running of the spectral index lt-gtSecond order in
HFF
In inflationary context both running and tensor
need to be included.
Running is included both in the scalar and in the
tensor spectral index (second order in SR
parameters as predicted by Kosowsky Turner
(1995)).
By using HFFs it is just needed an extra
parameter
A self-consistent expression at second order in
HFFs is needed also for amplitudes and spectral
indices, not just runnings.
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Second order in HFF I
Greens function method (GFM)
Stewart Gong (2001),
Leach, Liddle, Martin, Schwartz (2002)
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Second order in HFF II
Method of comparison equations (MCE)
Casadio,FF,Kamenschik,Luzzi,Venturi (2006)
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Wang, Mukhanov Steinhardt (1997)
Dotted 2nd HFF approximation
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WMAP1
WMAP3
CMBsmall SDSS
GFM formula
This result agrees with Leach and Liddle (2003)
for WMAPI and with Martin and Ringeval (2006) for
WMAPII.
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WMAP3CMBsmallSDSS
MCE
GFM
PS the analytic PS requires
and not
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WMAP1/WMAP3ACBARCBIVSAB03SDSS
WMAP1/WMAP3ACBARCBIVSAB03SDSS
Scalar running (marginalized over all other 7
params)
WMAPIICMBsmall2dF
WMAPIICMBsmallSDSS
WMAP team
WMAPIIB03ACBAR
Usefulness of our k_!
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• Second order HFF parametrization has one more
  parameter --gt constraints on
• cosmological parameters present in 1st order
  parametrization degrade

• Higher r, more blue ns are allowed, HZ is within
  2?, inflationary models with ns1 are allowed at
  1?.

for 2df02
Second order HFF
First order HFF
WMAP3CMBsmall2dF
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Tensor-to-scalar ratio as a free parameter
0.01 lt r lt 0.3
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NEC (null energy condition) violating Inflation
Hubble parameter growing in time
NEC_viol
K-G

• prior

ACBARCBIVSA B03 2dF
WMAP1/WMAP3

WMAP1
WMAP3
beyond
with WMAP3
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ConclusionsI

• First order in HFF

• Models with an exit from inflation (?2 gt0)
  preferred by WMAP3

• WMAP3 shows how quartic model and HZ are
  disfavoured wrt the massive model.

• With our combination of data also inflationary
  models with n ?1 are around the 2? contours (due
  to CMBsmall)

• Still early to decide if more or less tensors
  wrt to the consistency relation are preferred by
  data (less tensors are also predicted by
  non-minimal coupling of the inflaton) very
  important to predict the tensor-to-scalar ratio,
  otherwise difficult to constrain the potential.
  KG is well inside the present constraints.

• Models predicting a blue spectrum for tensors
  are equally good fit to the current data as
  standard inflationary models.

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ConclusionsII

• Runnings of the spectral indices (second order
  in HFFs)

Do not cut out running evidence with priors when
using HFFs!
Statistical evidence for running increased from
WMAPI to WMAPII it is zero at 2? or beyond.
If is not primordial and is due to systematics
then these have not been understood yet