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| The Early Universe |
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1. | As the Universe expands, the temperature and density both drop but the density decreases faster than the temperature. How does this effect the Jeans mass (the minimum mass of a cloud that leads to gravitational instability)? |
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2. | Estimate the Jeans mass at photon-matter decoupling. Take an average matter density of 10-18 kg/m3, assume the gas to be hydrogen, and assume the decoupling temperature to be 3000 K. |
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3. | What temperature is required in the early Universe so that an average photon has enough energy to create an electron-positron pair? The rest mass of the electron and positron are each 0.511 MeV, and you may assume that the radiation is described by the blackbody formula, E = kT, where E is the average energy, k the Boltzmann constant, and T the temperature. |
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4. | Repeat question 3 but replace electrons and positrons with protons and antiprotons, which have a rest mass of a little less than 1 GeV. |
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5. | We cited evidence that in the early Universe there were many collisions and interactions between galaxies. Does the Hubble Law allow such collisions, since according to it all galaxies should be receding from any one galaxy? |