Inflationary Theory of Primordial Cosmological Perturbation Project for General Relativity (Instructor: Prof.Whiting) Sohyun Park

Brief introduction about the title It is firmly established by observation that our universe is homogeneous and isotropic on large scales (~ 100Mpc). has well developed inhomogeneous structure on small scales - p.4 Mukhanov There should be primordial perturbations to be the seeds of the structure formation! -> Inflation gives a very plausible mechanism for that! Inflationary Theory of Primordial Cosmological Perturbation

Two systems homogeneous, isotropic and spatially flat (zero spatial curvature) background 1st order perturbations around the inflationary background +

Spatially flat, FRW geometry Two functions in terms of a Definition of Inflation : accelerated expansion

Brief History of Universe q ~ -1 q = 1 q = 1/2 q(t_0) = -0.6 Today (t_0): inflating too, so the early one called Primordial Inflation!

Einstein eqns for FRW cosmology Symmetry of FRW -> only two nonzero parts for stress tensor: t only Energy density, pressure Q) What causes inflation? See A) ANYTHING with

How do we find something with ? Many!, some are very complicated, but we have two simple ones: Positive cosmological constant Minimally coupled scalar with a flat potential OK Scalar eq for FRW Hubble Friction

Basic inflation mechanism: particle production Take the massless, minimally coupled scalar V=0 good approx for flat potential With FRW metric Fourier transf, no coupling between different modes, consider one All free QFT: infinite collection of HO’s Bunch-Davis vacuum

Basic inflation mechanism: particle production Eq of motion Hubble Friction Solve it for the de Sitter case: Solution:where canonically normalized: The energy of state Now QM ?

Basic inflation mechanism: particle production

1 st order Perturbations around the inflationary background Perturbation equations

Observables: power spectra (which we can compare with data eg.CMB) For scalar perturbations the power spectrum in the post-inflationary, radiation-dominated epoch For metric perturbations the power spectrum

Conclusion Inflation “washes out’’ all pre-existing classical inhomogeneities by stretching them to very large scales. It sometimes called that Inflation removes the “classical hairs.’’ However, it cannot remove Quantum fluctuations (“quantum hairs”). In place of the stretched quantum fluctuations, new ones “are generated” via the Heisenberg uncertainty relation. -p.328 Mukhanov The formation of our galaxy began with a quantum fluctuation…