UCSC ASTRO/PHYSICS 224 - Origin and Evolution of the Universe (22 pages)

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Origin and Evolution of the Universe



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Origin and Evolution of the Universe

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Lecture Notes


Pages:
22
School:
University of California, Santa Cruz
Course:
Astro/Physics 224 - Origin and Evolution of the Universe

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Astro Physics 224 Winter 2008 Origin and Evolution of the Universe Structure Formation Friday February 8 Joel Primack University of California Santa Cruz The Initial Fluctuations At Inflation Gaussian adiabatic Fourier transform Power Spectrum rms perturbation rr r i k r e x x k r k r 2 P k k k n Scale Invariant Spectrum Harrison Zel dovich mass M t M time Gravitational Instability Small fluctuations Continuity Euler Poisson Linear approximation growing mode irrotational potential flow comoving coordinates matter era Thus far we have considered only the evolution of fluctuations in the dark matter But of course we have to consider also the ordinary matter known in cosmology as baryons implicitly including the electrons See Madau s lectures The Astrophysics of Early Galaxy Formation http arxiv org abs 0706 0123v1 for a recent summary We have already seen that the baryons are primarily in the form of atoms after z 1000 with a residual ionization fraction of a few x 10 4 They become fully reionized by z 6 but they were not reionized at z 20 since the COBE satellite found that Compton parameter y 1 5 x 10 5 where This implies that Thus for example a universe that was reionized and reheated at z 20 to xe Te 1 4 105 K would violate the COBE y limit The figure at right shows the evolution of the radiation dashed line labeled CMB and matter solid line labeled GAS temperatures after recombination in the absence of any reheating mechanism From Madau s lectures The linear evolution of sub horizon density perturbations in the dark matter baryon fluid is governed in the matter dominated era by two second order differential equations 1 for the dark matter and Hubble friction for the baryons where dm k and b k are the Fourier components of the density fluctuations in the dark matter and baryons fdm and fb are the corresponding mass fractions cs is the gas sound speed k is the comoving wavenumber and the derivatives are taken with respect to cosmic time Here 2 is the time dependent



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