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.

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…

For a search volume that requires: 45 beam positions, 333 range bins, 32 Doppler bins, and a P FA of 5 × 10 − 3 , how many false alarms occur on average in a single search frame?

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.

Calculate the average energy E per mode of oscillation for (a) a long wavelength lambda sign=10 hc/kT, (b) a short wavelength lambda sign= 0.1 hc/kT

Scientists are conducting an experiment to determine if their hypothesis that a certain constant in the universe is 1.65. the uncertainties in the experiment result in a relative uncertainty of no more than 2%. After several experimental trials, the scientists obtained an average value of 1.7 for the constant. What can be said about the scientists hypothesis? Hint calculate the percent error and compare it to the relative uncertainty.

2.9. (a) Solve the integral ...| (dx .dx3N) 3N and use it to determine the "volume" the relevant region of the phase space of an extreme relativistic gas ( = pc) of 3N particles moving in one dimension. Determine, as well, the number of ways of distributing a given energy E among this system of particles and show that, asymptotically, w0 = h³N. (b) Compare the thermodynamics of this system with that of the system considered in Problem 2.8.

The question is show that E=(1/2)mgl(theta)^2 . Pls help with this one.