1. 暴涨模型及观测检验
郭宗宽
中科院理论物理所
中国科技大学交叉学科理论研究中心
2011年6月30日

2. 内容
宇宙微波背景辐射
暴涨模型
微波背景对暴涨模型的检验 展望

3. I. 宇宙微波背景辐射 the formation of the CMB
Shortly after recombination, the photon mean free path became larger than the Hubble length, and photons decoupled from matter in the universe.

4. timeline of the CMB observation
the first discovery of CMB radiation in
the Nobel Prize in Physics 1978: A.A. Penzias and R.W. Wilson
COBE (Cosmic Background Explorer), launched on 18 Nov. 1989, 4 years
the Nobel Prize in Physics 2006: J.C. Mather and G.F. Smoot
WMAP (Wilkinson Microwave Anisotropy Probe), launched on 30 June 2001, 9 years
Planck, launched on 14 May 2009
Other experiments:
ground based experiments (QUaD, BICEP, ACT, ACTPol from 2013)
balloon borne experiments (BOOMRANG, MAXIMA)

5. CMB data analysis pipeline
The temperature anisotropies can be expanded in spherical harmonics,
For Gaussian random fluctuations, the statistical properties of the
temperature field are determined by the angular power spectrum
For a full sky, noiseless experiments,

6. thermal Sunyaev-Zel’dovich effect lensing effect
secondary CMB anisotropies
primary CMB anisotropies secondary CMB anisotropies
reionization
thermal Sunyaev-Zel’dovich effect
lensing effect
integrated Sachs-Wolf effect

7. COBE, WMAP and Planck

8. II. 暴涨模型 V (φ) φ slow-roll inflation slow-roll parameters
e-folding number
perturbations
reheating
inflation φ
reheating

9. phenomenological models fine-tuning problems predict perturbations
flatness problem, horizon problem, origin of large-scale structure, relic density problem
large-field, small-field, hybrid, curvaton k-inflation, G-inflation, trapped, warm, eternal, …
solve some problems
phenomenological models
fine-tuning problems
predict perturbations
nature of inflaton field
potential, field, kinetic, coupling
Higgs field, D-brane inflation, …
Single-field, minimally-coupled, canonical kinetic, slow-roll inflation generates almost scale-invariant , adiabatic and Gaussian primordial perturbations.

10. power-law inflaton coupled to the Gauss-Bonnet term
It is known that there are correction terms of higher orders in the curvature to the lowest effective supergravity action coming from superstrings. The simplest correction is the Gauss-Bonnet (GB) term.
Does the GB term drive acceleration of the Universe? If so, is it possible to generate nearly scale-invariant curvature perturbations? If not, when the GB term is sub-dominated, what is the influence on the power spectra? How strong WMAP data constrain the GB coupling?
Our action:
Z.K. Guo, D.J. Schwarz, PRD 80 (2009)

11. Conclusions: power-law solution: which satisfy acceleration condition:
In the GB-dominated case, ultra-violet instabilities of either scalar or tensor perturbations show up on small scales.
In the potential-dominated case, the Gauss-Bonnet correction with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio.
constraints on the GB coupling

12. Slow-roll inflation with a Gauss-Bonnet correction
Is it possible to generalize our previous work to the more general case of slow-roll inflation with an arbitrary potential and an arbitrary coupling?
Hubble and GB flow parameters:
To first order in the slow-roll approximation
Comments:
The scalar spectral index contains not only the Hubble flow parameters but also the GB flow parameters.
The degeneracy of standard consistency relation is broken.
horizon-crossing time
Z.K. Guo, D.J. Schwarz, PRD 81 (2010)

13. Consider a specific inflation model:
Defining in the case, the spectral index and the tensor-to-scalar ratio can be written in terms of the function of N:
n = 4
The Gauss-Bonnet term may revive the quartic potential ruled out by recent cosmological data.

14. III. 微波背景对暴涨模型的检验
primordial power spectrum of curvature perturbations: scale-invariant? slightly tilted power-law? running index? suppression at large scales? local features?
a critical test of inflation!
non-adiabaticity: matter isocurvature modes (axion-type, curvaton-type)? neutrino isocurvature modes?
a powerful probe of the physics of inflation!
non-Gaussianity: local form (multiple fields)? equilateral form (non-canonical kinetic)? orthogonal form (higher-derivative field)?
a powerful test of inflation!
primordial gravitational waves: the consistency relation？
smoking-gun evidence for inflation!

15. The 95% limit from WMAP7 are
Relation between the inflation potential, the primordial power spectrum of curvature perturbations and the angular power spectrum of the CMB:
Constraint on n_t and r
a single CDM isocurvature mode
The 95% limit from WMAP7 are

16. MCMC likelihood analysis
Grid-based likelihood analysis
Markov Chain Mont Carlo (MCMC) method
Code: CosmoMC (
OpenMP
MPI

17. CMB constraints on the energy scale of inflation
Determining the energy scale of inflation is crucial to understand the nature of inflation in the early Universe.
The inflationary potential can be expanded as
To leading order in the slow-roll approximation, the power spectra:
Z.K. Guo, D.J. Schwarz, Y.Z. Zhang, PRD 83 (2011)

18. We find upper limits on the potential energy, the first and second derivative of the potential, derived from the 7-year WMAP data with with Gaussian priors on the Hubble constant and the distance ratios from the BAO:
at 95% confidence level.

19. Forecast constraints (68% and 95% C. L
Forecast constraints (68% and 95% C.L.) on the V0-V1 plane (left) and the V1-V2 plane (right) for the Planck experiment in the case of r = 0.1.
Using the Monte Carlo simulation approach, we have presented forecasts for improved constrains from Planck. Our results indicate that the degeneracies between the potential parameters are broken because of the improved constraint on the tensor-to-scalar ratio from Planck.

20. The shape of the primordial power spectrum
Comments:
scale-invariant (As)
power-law (As, ns)
running spectral index (As, ns, as)
It is logarithmically expanded
Our method:
Advantages:
It is easy to detect deviations from a scale-invariant or a power-law spectrum.
Negative values of the spectrum can be avoided by using ln P(k) instead of P(k).
The shape of the power spectrum reduces to the scale-invariant or power-law spectrum as a special case when Nbin= 1, 2, respectively.
Z.K. Guo, D.J. Schwarz, Y.Z. Zhang, arXiv:

21. WMAP7+H0+BAO
WMAP7+H0+BAO
WMAP7+ACT+H0+BAO
WMAP7+ACT+H0+BAO
The Harrison-Zel’dovich spectrum is disfavored at 2s and the power-law spectrum is a good fit to the data.

22. IV. 展望
The shape of the primordial power spectrum of scalar perturbations?
Entropy perturbations?
Non-Gaussianity (surprise?)
The primordial gravitational wave (surprise?)
the consistency relation?
the shape of the power spectrum?

23. 谢谢！