Primordial Perturbations i h E l U iin the Early Universe
Xian Gao (07’Dr.)
Supervisor: Prof. Miao Li
ITP, 2009‐12‐22
Outline
• List of annual accomplishment
• Brief introductions
Summary of Annual Works1. Non‐linearity & non‐Gaussianity in multi‐field inflation
[1] Primordial Non‐Gaussianities from the Trispectra in Multiple Field Inflationary Models, with Miao Li & Chunshan Lin, arXiv:0906.1345 , JCAP.[2] Primordial Trispectrum from Entropy Perturbations in Multifield DBI Model, with Bin Hu, arXiv:0903 1920 JCAParXiv:0903.1920 , JCAP. [3] Loop Corrections to Cosmological Perturbations in Multi‐field Inflationary Models, with Fanrong Xu, arXiv:0905.0405, JCAP.
2. Primordial statistical anisotropy[4] Can Relic Superhorizon Inhomogeneities be Responsible for Large‐Scale CMB Anomalies?[4] Can Relic Superhorizon Inhomogeneities be Responsible for Large‐Scale CMB Anomalies? arXiv:0903.1412,
3. Cross‐correlations between curvature & isocurvature perturbations[5] On Cross‐correlations between Curvature and Isocurvature Perturbations during Inflation, arXiv:0908.4035, JCAP.arXiv:0908.4035, JCAP.
4. Cosmological perturbations in Horava gravity[6] Fluctuations in a Horava‐Lifshitz Bouncing Cosmology, with Yi Wang, Wei Xue and Robert Brandenberger, arXiv:0911.3196.[7] Cosmological Perturbations in Horava‐Lifshitz Gravity, with Y. Wang, R. Brandenberger and A. Riotto, [ ] g f y g garXiv:0905.3821, JHEP.[8] Cosmological Perturbations and Non‐Gaussianities in Horava‐Lifshitz Gravity, arXiv:0904.4187.
I. Primordial Non‐Gaussianity
The Microwave Sky
Gaussian v.s. Non‐GaussianPower spectrum:
More information is needed → Non‐Gaussianity!!o e o a o s eeded→ o Gauss a y
Free = Linear = Gaussian, Interaction = Non‐linear = Non‐Gaussian
Higher‐order Correlators
Origins of Non‐GaussianityScale
Wavelength k
Hubble scale
Timeδφ ΔT/Tζ
Initial NG:Inflaton interactions
Primordial NG:Non‐linearity in Gravitation
Observed NG:NL in Gravitational & Acoustic & Plasma physics
Characterizing Non‐Gaussianity
Gaussian Non‐GaussianNon‐linear map
Non‐linear parameters
Observational constraints
WMAP5
CMB LSS
Planck
Evaluating Non‐GaussianityCosmological Perturbation Theory + Quantum Field Theory
Gravitational gauge‐transformation:
Distribution functional:
Gravitational gauge‐transformation:
Single‐field slow‐roll inflation gives undetectable NG:
4 origins of large Non‐Gaussianity: • non‐canonical kinetic term (k, DBI, …)• non single field (multi field vector )
Single field slow roll inflation gives undetectable NG:
• non‐single‐field (multi‐field, vector, …)• non‐slow‐roll• non‐Bunch‐Davis vacua
Non‐Gaussianities in General Multi‐field Inflation Models
The most general two‐field model:
field Inflation Models
Perturbative action: ( )
Tri‐spectrum of Curvature Perturbation
Leading‐order trispectrum:
Curvature perturbation
ead g o de spec u
6 t ( d l d d t)6 parameters (model‐dependent):
Non‐Linear parameter:
Shapes of the Tri‐spectrum
Momenta parameter space of
II. Primordial Statistical Anisotropy
Large‐Scale CMB AnomaliesStatistically homogeneous and isotropic:
homogeneous isotropic
Two possible CMB large‐scale anomalies:
Suppresion of powerAnisotropic spectrum
Theoretical ExplanationsPossible theoretical explanations:
Lorentz violation, anisotropic inflation, ultra‐large‐scale structure, pre‐inflation, cosmic variance, foreground, …
DecoupleSuper‐Hubble background inhomogeneities
Couple
Non‐linearity!!
Anisotropic PerturbationsPerturbation around an inhomogeneous background
Super‐Hubble: →
Model:
Anisotropic kinetic term:Anisotropic kinetic term:
Breaking 3D spatial rotational symmetry!!
nAnisotropic SpectrumAnisotropic spectrum (large‐scales): θ
Anisotropic deformation:
θ
Both anisotropy and suppression are generated, and appear only on the largest scales!!
k
III. Cross‐correlation between Curvature & Isocurvature
PerturbationPerturbation
Cross‐correlations between Curvature & Isocurvature PerturbationsIsocurvature Perturbations
Curvature perturbation: Iso‐curvature perturbation:
Before Hubble crossing: ??Before Hubble‐crossing: ??
Propagating speeds:
Cross‐correlation
p g g p
Hubble‐crossing:
Cross‐power b d bCross‐power spectrum between curvature and isocurvature perturbations:
•Amplified when approaching horizon•Amplified by small λ ‐‐‐ isocurvature mode acts as source on curvature mode
Corrections to “Free” Powers
IV. Perturbations in Horava Gravity
Perturbations in Horava Gravity
Horava: a non‐relativistic theory of gravitation:
Breaking general covariance → additional degree of freedom??
Our conclusion: 1. non‐dynamical at linear‐order. 2 S li bl i l d b l i l b k d2. Strong coupling problem is relaxed by cosmological background.3. An odd propagating dof at non‐linear order. (XG, Xue, Wang and Brandenberger,
work in progress)4. Natural frame for a bouncing cosmology.4. Natural frame for a bouncing cosmology.
Th k !!Thank you!!