宇宙微波背景辐射与早期宇宙物理 郭宗宽（中科院理论物理研究所） 南开大学物理学院 2012年3月16日

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

一. 宇宙微波背景辐射 (1) 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.

(2) story of the CMB observation 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, ACT, ACTPol from 2013) balloon borne experiments (BOOMRANG, MAXIMA)

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

(4) physics of CMB anisotropies ► primary CMB anisotropies (at recombination) ► secondary CMB anisotropies (after recombination) reionization thermal SZ effect lensing effect integrated Sachs-Wolf effect

(5) COBE, WMAP and Planck

二. 暴涨模型 V (φ) φ slow-roll inflation criterions: slow-roll parameters e-folding number perturbations reheating inflation φ reheating

phenomenological models fine-tuning problems nature of inflaton field flatness problem, horizon problem, relic density problem large-field, small-field, hybrid, curvaton, k-inflation, G-inflation, trapped, warm, eternal, … to solve some problems phenomenological models fine-tuning problems nature of inflaton field to predict perturbations potential, field, kinetic, coupling Higgs field, D-brane, … Single-field, minimally-coupled, canonical kinetic, slow-roll inflation generates almost scale-invariant, adiabatic, Gaussian perturbations. 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: ZKG, D.J. Schwarz, PRD 80 (2009) 063523

power-law inflation: 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

(2) 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 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. ZKG, D.J. Schwarz, PRD 81 (2010) 123520

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.

三. 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!

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

(1) 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 ZKG, D.J. Schwarz, Y.Z. Zhang, PRD 83 (2011) 083522

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 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.

(2) 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 N bin= 1, 2, respectively. ZKG, D.J. Schwarz, Y.Z. Zhang, JCAP 08 (2011) 031

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.

(3) uncorrelated estimates from Planck simulated data We use the localized principle component analysis to detect deviations from scale invariance of the primordial curvature perturbations. ZKG, Y.Z. Zhang, JCAP 11 (2011) 032

(4) primordial power spectrum versus extension parameters ZKG, Y.Z. Zhang, arXiv:1201.1538

四. 展望 theoretical prospects (new physics?) observational prospects the shape of the primordial power spectrum of scalar perturbations? entropy perturbations? non-Gaussianity (surprise?) the primordial gravitational wave (surprise?)

谢谢！