1. 最新CMB观测结果对暴胀势的限制
胡建伟
中科院理论物理所
2014年 郑州
2014/07/07

2. Outline Inflationary Cosmology
Reconstructing the promodial power spectrum
Reconstructing the inflationary potential
Summary

6. 4 dimensional Inflation predicts
No classical inhomogeneities from the past
Scale free gaussian fluctuations of all light scalars
No vector perturbations
Scalar (almost scale free gaussian) metric perturbations
Tensor (scale free gaussian) metric perturbations
Creation of all SM particles in preheating/thermalization

7. Inflation in the context of ever changing fundamental theory
1980
-inflation
Old Inflation
New Inflation
Chaotic inflation
SUGRA inflation
Power-law inflation
Double Inflation
Extended inflation
1990
Hybrid inflation
Assisted inflation
SUSY F-term inflation
SUSY D-term inflation
Brane inflation
Super-natural
Inflation
2000
SUSY P-term inflation
K-flation
N-flation
DBI inflation
inflation
Warped Brane inflation
Tachyon inflation
Racetrack inflation

8. Reconstruction strategy
assuming scalar field is a monotonically varying function of cosmic time
PhysRevD

9. Perturbative reconstruction
During reconstruction, there are three types of expansion being carried out. There is an expansion in terms of observables, an expansion in terms of slow-roll parameters, and an expansion of the potential itself.
RevModPhys

10. BICEP2 V.S. Planck
But...
M. J. Mortonson and U. Seljak, arXiv: [astro-ph.CO].
R. Flauger, J. C. Hill and D. N. Spergel, arXiv: [astro-ph.CO]

11. Reconstruction of the primordial power spectra with Planck and BICEP2
arXiv: [astro-ph.CO]
Bin Hu , Jian-Wei Hu , Zong-Kuan Guo , Rong-Gen Cai

12. Reconstruction of the primordial power spectra with Planck and BICEP2
arXiv: [astro-ph.CO]
[astro-ph.CO]

13. Reconstruction of the primordial power spectra with Planck and BICEP2
arXiv: [astro-ph.CO]
Bin Hu , Jian-Wei Hu , Zong-Kuan Guo , Rong-Gen Cai

14. Reconstruction of the inflation potential with Planck and BICEP2

15. Reconstruction of the inflation potential with Planck and BICEP2

16. Reconstruction of the inflation potential with Planck and BICEP2
Fix k0 at 0.05, then we run MCMC. It could output the parameters that we need, including (As, ns, αs, r) at fix point k = 0.05, using the formula above, one can get the values of (As, ns, αs, r) at any point k,
Let ∆ ln k = −1, using equation (10) or (15), it is easy to calculate the corresponding ∆φ,
For every lnki = lnk0 +i∆lnk(i = 1,2,3,...), we can compute the values of V(ki), V ′(ki), V ′′(ki), V ′′′(ki) according to equations (22-25). Also utilising the relationship between k and φ, one can rewrite the V (φi) and its high derivatives,
to use the interpolate method to reconstruct the inflation potential for a long range.

17. Reconstructed potential

18. Summary
we reconstructed the primordial scalar power spectra using the cubic spline interpolation method from recently CMB data, and find that the vanishing scalar index running model is disfavored at more than 3\sigma level
the power-low parameterization gives a blut-tilt tensor spectrum, no matter using only the first 5 bandpowers or the full 9 bandpowers of the BICEP2 data sets
Given that the hint of a large running of the scalar power spectrum, and a nonzero tensor-to-scalar ratio r, we reconstruct the inflationary potential in the perturbative reconstruction framework

19. Thank You