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Inflationary Theory of Primordial Cosmological Perturbation

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).

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Inflationary Theory of Primordial Cosmological Perturbation

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

  2. 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

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

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

  5. 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!

  6. 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

  7. Hubble Friction 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

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

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

  10. Basic inflation mechanism: particle production

  11. 1st order Perturbations around the inflationary background Perturbation equations

  12. 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

  13. 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…

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