Observational constraints on inflationary models

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

2. content • inflationary models • cosmic microwave background (CMB) • CMB constraints on inflationary models • outlook

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

4. 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

5. (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) 063523

6. 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

7. (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. Z.K. Guo, D.J. Schwarz,PRD 81 (2010) 123520

8. Consider a specific inflation model: n = 2 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.

9. 2. cosmic microwave background (CMB) (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.

10. (2)CMB experiments • 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 basedexperiments (QUaD, BICEP, ACT, ACTPolfrom 2013) balloon borneexperiments (BOOMRANG, MAXIMA)

11. (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,

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

13. 3. CMB constraints on inflationary models • 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!

14. 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)

15. (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 Z.K. Guo, D.J. Schwarz, Y.Z. Zhang, PRD 83 (2011) 083522

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 constantand the distance ratios from the BAO (at 95% CL):

17. 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.

18. (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. Z.K. Guo, D.J. Schwarz, Y.Z. Zhang, JCAP 08 (2011) 031

19. 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.

20. Uncorrelated estimates from Planck simulated data. Z.K. Guo, Y.Z. Zhang, arXiv:1109.0067

21. 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?)

22. Thanks!