Consider the energy-momentum tensor Tμv = (p+p) uu+P9μ applied to the matter/energy distribution in the universe on large scales, and assume an equation of state of the form p = wp, with w a constant. Determine the type of matter/energy dominating the universe if the energy-momentum tensor is traceless, that is, T"μ = 0.
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- The lifetime of a muon is 2.20 ?s. If you measured its mass to be 105.7 MeV/c2, what would be the minimum (Heisenberg) uncertainty in this value? Sketch the situation, defining all of your variablesSuppose the Universe is dominated by a strange substance with an equation of state w = -0.7. This substance fills the Universe in a uniform way, and is the only dynamically important constituent. Suppose further that in some time interval the Universe doubles in (linear) size, i.e. the scale factor doubles. By what factor has the energy density of this substance changed during this time interval, i.e., what is εfinal/εinitial? The energy density substance dilutes in proportion to a to some power p, i.e. ε(a) ∝ apYou are performing work as an assistant to a cosmology professor. She asks you to estimate the temperature of the Universe at a time after the Big Bang when neutral atoms could form from the plasma and the Universe became transparent. She tells you that the energy required to excite an atom is on the order of 1 eV. She suggests you use the Boltzmann distribution function e-E/k BT to find the order of magnitude of the threshold temperature at which 1.00% of a population of photons has energy greater than 1.00 eV.
- I need help :(Consider the following line element, ds^2 = −dt^2 + a^2(t) (dx^2 + dy^2) + b^2(t) dz^2, where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.An electron-positron collider runs with symmetric beam energies of E(e^+) = E(e^−) = 102 GeV.At each orbit ∆E = 2.2 GeV has to be replaced for each beam particle by the accelerating units.The accelerator has 24 units available; each unit can replace an energy of ∆E = 100 MeV perorbit. a). The researchers want to create the Standard-Model Higgs boson but don’t know its massyet. Argue why the production rate via the direct process e +e− → H is negligible and name the process which can be used instead. Draw a Feynman diagram of this process. State the mechanism responsible for the energy loss and state how the energy loss per orbit scales with the beam energy. b). Name two possible final states of this process and how they can be detected in a modernparticle detector, which consists of a tracker, an EM calorimeter, a hadronic calorimeterand a muon system in radial direction. Calculate the maximum mass of the Higgs Boson, which the experiment can create c). When no Higgs is found in the…
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