Observational constraints on inflationary models Zong-Kuan Guo (ITP, CAS) CosPA2011 (Peking Uni) October 31, 2011

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

1. inflationary models V (φ) φ inflation reheating slow-roll inflation criterions: cosmic acceleration e-folding number perturbations reheating

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

(1) 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)

an exponential potential and an exponential GB coupling 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 power-law inflation:

(2) 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) 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.

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.

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

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 other experiments: ground based experiments (QUaD, BICEP, ACT, ACTPol from 2013) balloon borne experiments (BOOMRANG, MAXIMA) (2) CMB experiments

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 (3) CMB data analysis pipeline time-ordered data full sky map spectrum parameter estimates

reionization thermal/kinetic Sunyaev-Zel ’ dovich effect lensing effect integrated Sachs-Wolf effect (4) secondary CMB anisotropies (after recombination)

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! 3. CMB constraints on inflationary models

constraint on n s and r constraints on non-Gaussianity (95% CL) a single CDM isocurvature mode Relation between the inflation potential, the primordial power spectrum of curvature perturbations and the angular power spectrum of the CMB

 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 Z.K. Guo, D.J. Schwarz, Y.Z. Zhang, PRD 83 (2011) (1) CMB constraints on the energy scale of inflation

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):

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.

(2) 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, JCAP 08 (2011) 031

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.

Uncorrelated estimates from Planck simulated data. Z.K. Guo, Y.Z. Zhang, arXiv:

4. outlook theoretical prospects observational prospects the shape of the primordial power spectrum of scalar perturbations? entropy perturbations? non-Gaussianity (surprise?) the primordial gravitational wave (surprise?)

Thanks!