COSMOLOGICAL INFLATION

Jason DekdebrunTheoretical Physics Institute, UvA

Advised by Kostas Skenderis

Introduction Gives answers to some of the earliest

moments of our history.

Proposed by Alan Guth in 1980.

Universe undergoes an early, exponential expansion.

Solves many of the BIG problems plaguing cosmology.

What Quantifies Inflation? Friedmann-Robertson-Walker (FRW)

metric for a flat universe:

Inflation when:

Why Does Inflation Occur? Occurs when the energy density of the

universe is constant:

Horizon Problem

° °° °

10 billion years 10 billion years

20 billion years total, Cosmic Microwave

Background

Observer

? BUT universe is only 14 billion years old!!!

Inflation Answer

H = ®, constant in time.

(aH)-1 = ®-1 e-® t, decreases with time!

During inflation, sphere of causal contact decreases with time. Objects that are in causal contact soon come out of causal contact.

Sphere Of Causal ContactNot In Causal

ContactCausal

Contact!

INFLATION!

My Research: The Standard Scenario

A single scalar field, the inflaton .

Background FRW space-time.

During inflation, V() dominates the universe.

The inflaton slowly rolls down its potential, causing inflation.

Slow-Roll Scenario

Inflation!

αβδ€ζΩΣπReheating!

Important Point!: Cosmic Microwave Background is NOT from Big Bang!

Perturbations

In the case of the inflaton, perturbations are considered quantum fluctuations:

Perturbations added to the FRW metric:

This leads to perturbed general relativity quantities (Einstein tensor, Christoffels, Ricci tensor, etc.)

Example:

Equations To Solve We would like to solve Einstein’s equations,

where the energy-momentum tensor,

is derived from the Lagrangian:

Example: Second Order (i,j) Einstein Equation

Also the Klein-Gordon equation:

This is derived from an action using the same Lagrangian.

Example: Second Order Klein-Gordon Equation

Gauge Invariant Variables Under a spatial translation by di, the

following perturbations transform as:

Combining these in just the right way leads to a variable with no transformation:

3 more gauge invariant variables:

First order Einstein equations:

Second Order Curvature Perturbation:

This gauge invariant variable will be the link between theory and observation.

fNL & Observations

What is fNL?

fNL is the amplitude of the three-point correlation function.

Correlation of curvature perturbations, ³(2).

Also known as the bispectrum.

Any detection of the bispectrum indicates non-Gaussianity.

Planck Satellite

Launched May 14th, 2009.

Finish collecting data in 2012.

Will provide very important measurements of non-Gaussianity.

Conclusion

Measurements of non-Gaussianity will help distinguish amongst the many different models of inflation.

This will give us a closer look and deeper understanding of the very beginning of our universe!