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. 报告提纲. 暴涨宇宙学 宇宙微波背景辐射 微波背景对暴涨模型的检验 展望. 一 . 暴涨宇宙学. some problems in the hot Big Bang model ： flatness problem , horizon problem , relic density problem. slow-roll inflation. criterions: cosmic acceleration e-folding number
old inflation,large-field, small-field, hybrid, curvaton, k-inflation, G-inflation, trapped, warm, eternal, …
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
Z.K. Guo, D.J. Schwarz, PRD 80 (2009) 063523
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 GB 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
introduce Hubble and GB flow parameters:
to first order in the slow-roll approximation
the scalar spectral index contains not only the Hubble but also GB flow parameters.
the degeneracy of standard consistency relation is broken.
Z.K. Guo, D.J. Schwarz,PRD 81 (2010) 123520
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.
(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.
the Nobel Prize in Physics 1978: A.A. Penzias and R.W. Wilson
the Nobel Prize in Physics 2006: J.C. Mather and G.F. Smoot
ground based experiments:QUaD, BICEP, SPT, SPTpol from 2012, ACT, ACTPolfrom 2013
balloon borne experiments: BOOMRANG, MAXIMA
full sky map
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,
cosmological parameter estimation
likelihood function for a full sky:
the sky-cut, MCMC
the linearized Einstein equations:
thermal Sunyaev-Zel’dovich effect
integrated Sachs-Wolf effect
a critical test of inflation!
a powerful probe of the physics of inflation!
a powerful test of inflation!
smoking-gun evidence for inflation!
constraints on the power spectrum
for a pure power-law
for a running index
constraints on non-Gaussianity (95% CL)
constraints on ns and r
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
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):
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.
Relation between the inflation potential, the primordial power spectrum of curvature perturbations and the angular power spectrum of the CMB
It is logarithmically expanded
It is easy to detect deviations from a scale-invariant or a power-law spectrum because they are just straight lines in the lnk-ln P plane.
Negative values of the spectrum can be avoided by using ln P(k) instead of P(k) for the spline with steep slops.
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
The Harrison-Zel’dovich spectrum is disfavored at 2s and the power-law spectrum is a good fit to the data.
ZKG, Y.Z. Zhang, JCAP 11 (2011) 032
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.
ZKG, Y.Z. Zhang, PRD 85 (2012) 103519
the deformed dispersion relation for massive neutrinos can be generally parameterized by
we consider the n=2 case
ZKG, Q.G. Huang, R.G. Cai, Y.Z. Zhang, PRD 86 (2012) 065004
the Lagrangian for neutrino
the Boltzmann equation in the synchronous gauge