1. Inflation and the cosmological density perturbation
Courtesey: NASA/WMAP Science Team
Subir Sarkar
University of Oxford
‘Dark energies, Dark matters’, Institut Henri Poincare, Paris, April 2005

2. The Beam: inflationary density perturbations
The formation of large-scale structure is akin to a scattering experiment …
The Beam: inflationary density perturbations
No ‘standard model’ – usually assumed to be adiabatic and ~scale-invariant
The Target: dark matter (+ baryonic matter)
Identity unknown - usually taken to be cold (sub-dominant ‘hot’ component?)
The Detector: the universe
modelled by a FRW cosmology with parameters h, ΩCDM, ΩB, ΩΛ, ΩK
The Signal: CMB anisotropy, galaxy clustering …
measured over scales ranging from ~ 1 – Mpc (⇒ ~8 e-folds of inflation)
cannot simultaneously determine the properties of both target and detector with unknown beam … hence must adopt ‘priors’ to break degeneracies

3. If the primordial fluctuations are adiabatic and scale-invariant
(as is supposedly “expected in the simplest models of inflation”)
then the CMB and LSS data are consistent with the ΛCDM model
Courtesey: Max Tegmark + SDSS Collaboration

4. However when examined more closely, the fit to WMAP data is not so good
Ωmh2= 0.14 ± 0.02, ΩBh2= ± 0.001, h = 0.72 ± 0.05 — Best-fit ΛCDM model
The c2/dof = 973/893 ⇒ probability of only 3% that this model is correct!

5. The lack of power on large angular scales is most noticeable
... but the statistical significance is not high (chance probability of O(1%)?)
Moreover unexpected alignments of low multipoles (with ecliptic plane), differerences between North and South ecliptic hemispheres … foreground subtraction problems?

6. In fact the excess χ2 comes mostly from the ‘glitches’ at smaller angles
… hard to tell by eye from Cℓ ’s since neighbouring data points are correlated

7. Similar features seen also by Archeops (with lower significance)

8. Several groups have reconstructed the primordial spectrum (assuming ΛCDM)
Bridle, Lewis, Weller & Efstathiou ‘03; Cline, Crotty & Lesgourgues ’03, Mukherjee & Wang ’03; Hannestad ‘04; Kogo, Sasaki & Yokoyama ‘04; Tocchini-Valentini, Douspis & Silk ’04 …
Shafiloo & Souradeep ’03

9. Astronomers have traditionally assumed a Harrison-Zeldovich spectrum:
P(k) ~ kn, n = 1
But models of inflation generally predict departures from scale-invariance
e.g. in single-field slow-roll models: n = 1 + 2V’’/ V – 3 (V’/V)2
Since the potential V(Φ) steepens towards the end of inflation, there will be a
scale-dependent spectral tilt on cosmologically observable scales:
e.g. in simple F-term SUGRA model: V(Φ) ≈ Vo – αΦ3 + … ⇒ n ≈ 1 – 4/N* ~ 0.9
where N* ≈ 50 + ln (k-1/3000h-1 Mpc) is the #-e-folds from the end of inflation
In hybrid models, inflation is ended by the ‘waterfall’ field, not by steepening of V(Φ), so spectrum can be quite close to scale-invariant …
However, in general there are many other fields present, whose dynamics may influence the inflaton’s slow-roll (rather than terminate it altogether)
→ can generate features in the spectrum (‘steps’, ‘oscillations’ …)

14. This assumes that the initial conditions are thermal (so the fields are confined at the origin) and that (this last phase of) inflation lasts just ~50 e-folds so as to create our present Hubble volume
Seems fine-tuned but the data does indicate an infrared cut-off in the spectrum at a scale ~H-1 !

17. (Hunt & Sarkar, astro-ph/0408138)

18. (Hunt, Morgan & Sarkar 2005)

27. physics beyond the Standard Model
Conclusions
The extraction of cosmological parameters from CMB and LSS data is sensitive to the assumed primordial spectrum
We do not know the physics of inflation hence it is premature to assume that the generated density perturbation is ~scale-invariant
Must resolve degeneracies experimentally, using e.g. polarisation data and independent measurements of cosmological parameters
Present data provides intriguing hints for non-trivial inflationary dynamics … possibly a direct link between astronomical data and
physics beyond the Standard Model