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. I. 宇宙微波背景辐射 II. 暴涨模型 III. 微波背景对暴涨模型的检验 IV. 展望 内容

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

4. the first discovery of CMB radiation in 1964-1965 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)  timeline of the CMB observation

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

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

7.  COBE, WMAP and Planck

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

9. solve some problems phenomenological models fine-tuning problems predict perturbations nature of inflaton field Higgs field, D-brane inflation, … Single-field, minimally-coupled, canonical kinetic, slow-roll inflation generates almost scale-invariant, adiabatic and Gaussian primordial 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, … potential, field, kinetic, coupling

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) 063523

11. power-law solution: which satisfy Conclusions: 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 acceleration condition:

12.  Slow-roll inflation with a Gauss-Bonnet correction Hubble and GB flow parameters: 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 ? To first order in the slow-roll approximation Z.K. Guo, D.J. Schwarz, PRD 81 (2010) 123520 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

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 = 2 n = 4 The Gauss-Bonnet term may revive the quartic potential ruled out by recent cosmological data.

14. 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! III. 微波背景对暴涨模型的检验

15. 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 The 95% limit from WMAP7 are a single CDM isocurvature mode

16. Grid-based likelihood analysis Markov Chain Mont Carlo (MCMC) method Code: CosmoMC (http://cosmologist.info/cosmomc/) OpenMP MPI  MCMC likelihood analysis

17. 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) 083522  CMB constraints on the energy scale of inflation

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.) 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 It is logarithmically expanded Our method: Comments: scale-invariant (A s ) power-law (A s, n s ) running spectral index (A s, n s,  s ) 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 N bin = 1, 2, respectively. Z.K. Guo, D.J. Schwarz, Y.Z. Zhang, arXiv:1105.5916

21. WMAP7+H0+BAO WMAP7+ACT+H0+BAO The Harrison-Zel ’ dovich spectrum is disfavored at 2  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！