1. 暴涨宇宙学及其检验 郭宗宽（中科院理论物理研究所） 北京工业大学应用数理学院 2012.10.18

2. 一．暴涨宇宙学 二．宇宙微波背景辐射 三．微波背景对暴涨模型的检验 四．展望 报告提纲

3. 一. 暴涨宇宙学 V (φ) φ inflation reheating slow-roll inflation criterions: cosmic acceleration e-folding number perturbations successful exit reheating  some problems in the hot Big Bang model ： flatness problem, horizon problem, relic density problem

4. Single-field, minimally-coupled, canonical kinetic, slow-roll inflation generates almost scale-invariant, adiabatic, Gaussian perturbations. phenomenological models fine-tuning problems nature of inflaton field to predict perturbations Higgs field, D-brane, … old inflation, large-field, small-field, hybrid, curvaton, k-inflation, G-inflation, trapped, warm, eternal, … potential, field, kinetic, coupling large-scale structure, CMBR

5. (1) power-law inflaton coupled to the Gauss-Bonnet (GB) 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 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

6. ① an exponential potential and an exponential GB coupling ② In the GB-dominated case, ultra-violet instabilities of either scalar or tensor perturbations show up on small scales. ③ In the potential-dominated case, the GB correction with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio. ④ constraints on the GB coupling power-law inflation

7. (2) Slow-roll inflation with a GB correction introduce 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 a)the scalar spectral index contains not only the Hubble but also GB flow parameters. b)the degeneracy of standard consistency relation is broken.

8. 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.

9. Shortly after recombination, the photon mean free path became larger than the Hubble length, and photons decoupled from matter in the universe. (1) formation of the CMB 二. 宇宙微波背景辐射

10. George Gamow et al. estimated a temperature of 50K in 1946 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, 30 months (5 full sky) Other experiments ground based experiments: QUaD, BICEP, SPT, SPTpol from 2012, ACT, ACTPol from 2013 balloon borne experiments: BOOMRANG, MAXIMA (2) story of the CMB observation

11. (3) CMB data analysis pipeline time-ordered data full sky map spectrum parameter estimates  time-ordered data  the temperature anisotropies can be expanded in spherical harmonics

12.  for Gaussian random fluctuations, the statistical properties of the temperature field are determined by the angular power spectrum For a full sky, noiseless experiments,  cosmological parameter estimation likelihood function for a full sky: the sky-cut, MCMC

13. (4) physics of CMB anisotropies  primary CMB anisotropies (at recombination) spherical harmonicsFourier space

14. the linearized Einstein equations: the Einstein equations:

15.  reionization  thermal Sunyaev-Zel ’ dovich effect  lensing effect  integrated Sachs-Wolf effect  secondary CMB anisotropies (after recombination)

16. (5) COBE, WMAP, Planck, CMBPol, COrE, …

17. 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! 三. 微波背景对暴涨模型的检验

18.  constraints on the power spectrum  a single CDM isocurvature mode  constraints on non-Gaussianity (95% CL)  constraints on n s and r for a pure power-law for a running index

19.  Determining the energy scale of inflation is crucial to understand the nature of inflation in the early Universe. to leading order in the slow-roll approximation Z.K. Guo, D.J. Schwarz, Y.Z. Zhang, PRD 83 (2011) 083522 (1) CMB constraints on the energy scale of inflation the inflationary potential can be expanded as

20. 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% CL):

21. Forecast constraints (68% and 95% CL) on the V 0 -V 1 plane (left) and the V 1 -V 2 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.

22. (2) Reconstruction of the primordial power spectrum Relation between the inflation potential, the primordial power spectrum of curvature perturbations and the angular power spectrum of the CMB It is logarithmically expanded parameterizations: scale-invariant (A s ) power-law (A s, n s ) running spectral index (A s, n s,  s )

23. our method: advantages: ① It is easy to detect deviations from a scale-invariant or a power-law spectrum because they are just straight lines in the ln k-ln P plane. ② Negative values of the spectrum can be avoided by using ln P(k) instead of P(k) for the spline with steep slops. ③ 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. ZKG, D.J. Schwarz, Y.Z. Zhang, JCAP 08 (2011) 031

24. 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.

25. (3) uncorrelated estimates from Planck simulated data ZKG, Y.Z. Zhang, JCAP 11 (2011) 032  The spectrum parameters are correlated due to the geometrical project. With the localized principle component analysis we make uncorrelated estimates of the primordial power spectrum with five wavenumber bins.

26. (4) primordial power spectrum versus extension parameters ZKG, Y.Z. Zhang, PRD 85 (2012) 103519 WMAP7+ACT+H0+BAO WMAP7+SPT+H0+BAO We find that a scale- invariant primordial spectrum is disfavored by the data at 95% CL even in the presence of massive neutrinos, however it can lie within the 95% confidence region if the effective number of relativistic species or the primordial helium abundance is allowed to vary freely.

27. (5) Lorentz invariance violation in the neutrino sector ZKG, Q.G. Huang, R.G. Cai, Y.Z. Zhang, PRD 86 (2012) 065004  Neutrino oscillations can be explained by small Lorentz invariance violation even without introducing neutrino mass.  The breaking of Lorentz symmetry may leave some imprints in astrophysical observations such as the CMB anisotropies. the deformed dispersion relation for massive neutrinos can be generally parameterized by we consider the n=2 case

28. the FRW metric in the synchronous gauge the Lagrangian for neutrino the Boltzmann equation in the synchronous gauge

30. theoretical prospects the primordial scalar perturbations? entropy perturbations? non-Gaussianity? the primordial gravitational wave? 四. 展望 observational prospects new physics?

31. 谢谢！