The Klein-Gordon equation at background level for a scalar field φ is given by (found in image below) where H is the Hubble parameter, V the potential of the scalar field, and V′ = dV/dφ. Assume a flat Friedmann-Robertson-Walker universe, dominated by the scalar field. i) State the conditions for slow-roll inflation. Write down the Friedmann equation and the Klein-Gordon equation valid for slow-roll inflation. ii) For a scalar field potential V =1/2m^2φ^2, where m is the mass of the field, calculate the time evolution of the field φ in the case of slow-roll inflation.

A survey that uses Type la supernovae as standard candles to measure the distances to galaxies, combined with spectroscopic analysis of those galaxies Select one: to obtain their redshifts and recession velocities, yields the data shown in the The Universe is undergoing а. table. Use the data to sketch a diagram of velocity versus distance. Choose the accelerated expansion statement given below that can be O b. The Universe is contracting. inferred from the data. Velocities and distances to Ос. The data does not provide sufficient galaxies information to determine the rate of Distance (Mpc) expansion of the Universe. Velocity (km/s) 10 730 d. The expansion rate of the Universe is 250 16250 constant 500 30000 e. The expansion of the Universe is 800 40000 decelerating. 1000 45000

Suppose that the universe were full of spherical objects, each of mass m and radius r, with the objects distributed uniformly throughout the universe as in the previous problem.   (Assume nonrelativistic objects.) Given the density of these spherical objects (as you would have found in the previous problem), how far would you be able to see in meters, on average, before your line of sight intersected one of them? Values (note, different from the above problem): m = 3 kg r =  0.03 m Answer must be in scientific notation and include zero decimal places (1 sig fig).

Over the lifetime of the Universe, the dynamics of its expansion are dominated by the density of different constituents at different times. Ignoring expansion, what is the proper order for which constituent dominates from early to later times? Select one: a. First matter, then dark energy, then radiation b. First radiation, then matter, then dark energy c. First dark energy, then radiation, then matter d. First radiation, then dark energy, then matter

Briefly explain what is meant by “particle horizon” and “event horizon” in cosmology. Calculate the physical particle horizon, RH(t), at time t. Assume a flat FRW universe whichis dominated by a fluid that gives rise to scale factor evolution  where n is a constant with 0 < n < 1, and a(t0) = a0.

Why does the cosmic microwave background (CMB) shine in low-energy microwave wavelengths? O The trapped photons within the plasma of the earliest universe originally had wavelengths in the microwave band due to rapid inflation O The CMB was originally emitted as high-energy gamma rays and x-rays, but the light has redshifted downward to lower-energy microwaves through time When nuclei of H and He first combined with free electrons to create atoms, photons of light were released as microwaves The photons released in the CMB were intensely hot, with energy levels in microwave wavelengths The early universe 380,000 years after the Big Bang was cold (2.7 kelvins) the temperature of microwave energy

What magnetic field B is needed to keep 943-GeV protons revolving in a circle of radius 1.0 km ? Use the relativistic mass. The proton's "rest mass" is 0.938 GeV/c². (1 GeV = 10⁹ eV) [Hint: In relativity, mrelv²/r = quB in still valid in a magnetic field, mrel = ym.] Express your answer to two significant figures and include the appropriate units B = μA Value Units ?

In Chapter 7 we discussed the need for the addition of the cosmological constant A to the Einstein Field Equations and further to our derived equations. iii. Starting with the fluid equation, show that the pressure exerted due to the cosmological constant is PA = -Pac? (Recall that we define an energy density due to the cosmological constant as the following scaled parameter PA = THIS IS A COSMOLOGY QUESTION!!!!!!!!