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!!