1. probing inflation with CMB anisotropies Zong-Kuan Guo (ITP, CAS) ICFPC 2012 (Weihai) August 12, 2012

2. 1.inflation 2.cosmic microwave background (CMB) 3.CMB constraints on inflation 4.outlook content

3. 1. inflation V (  )  inflation reheating slow-roll inflation criterions: cosmic acceleration e-folding number perturbations successful exit reheating

4. Single-field, minimally-coupled, canonical kinetic, slow-roll inflation generates almost scale-invariant, adiabatic, Gaussian perturbations. it solves some problems flatness problem, horizon problem, relic density problem phenomenological models some fine-tuning problems potential parameters, initial value of the field, kinetic, coupling nature of the inflaton field it predicts perturbations large-scale structure, CMB

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/negative coupling may lead to a reduction/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 tensor-to-scalar ratio and the spectral index can be written in terms of the function of N: n = 4 The GB term may revive the quartic potential model ruled out by recent cosmological data.

9. 2. cosmic microwave background (CMB) 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

10. the first discovery of CMB radiation in 1964 COBE (Cosmic Background Explorer), launched on 18 Nov. 1989, 4 years WMAP (Wilkinson Microwave Anisotropy Probe), launched on 30 June 2001, 9 years Planck satellite, launched on 14 May 2009, 30 months other experiments: ground-based experiments ( QUaD, BICEP, ACT, ACTPol from 2013, SPT, SPTpol from 2012 ) balloon-borne experiments ( BOOMRANG, MAXIMA ) (2) CMB experiments

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. primordial curvature perturbations: exact 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 ？ a smoking-gun evidence for inflation! 3. CMB constraints on inflation

14.  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

15.  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

16. 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):

17. 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.

18. (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 )

19. 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

20. 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.

21. (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.

22. (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.

23. 4. outlook theoretical prospects observational prospects the primordial scalar perturbations? entropy perturbations? the primordial non-Gaussianity? the primordial gravitational wave? new physics in the early Universe?

24. Thanks for your attention!