Consider a flat expanding universe with no cosmological constant and no curvature (k=0 in the Einstein...

Consider a flat expanding universe with no cosmological constant and no curvature (k=0 in the Einstein equations). Show that if the Universe is made of "dust", so the energy density scales like 1/a^3, then the scale factor, a(t), grows as t^(2/3). Show if it is made of radiation (so the energy density scales as 1/a^4 -- the extra factor of a comes from the redshift), then it grows as t^(1/2). In both cases, show that for early times, the scale factor grows faster than light. Is this a problem?

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

The Hubble Constant, the density of the universe, and the cosmological constant are all vital to...

The Hubble Constant, the density of the universe, and the cosmological constant are all vital to the evolution of our universe. Briefly discuss why each is so important -and- what would happen if we tweaked each one up or down a little. Are there other constants that are equally important? If so, which and why?

K CONSTANT EQUILIBRIUM What does it mean when K=1 and when K= 0

Consider a circular (cylindrical) pin fin attached to a flat plane with the following properties: k...

Consider a circular (cylindrical) pin fin attached to a flat plane with the following properties: k = 237 W/mC (thermal conductivity) L = 100mm (length) r = 2mm (radius) T_b = 80 C (temperature at fin base) T_inf = 20 C (air temperature) h = 12 W/m^2C (Convection Coefficient) Find the following using the infinitely long and insulated (adiabatic) tip methods: The temperature of the fin at a distance L/2 Heat transfer rate from the fin Fin efficiency Fin Effectiveness...

Consider the velocity potential phi = -k( y^2 - x^2 ) where k is a constant....

Consider the velocity potential phi = -k( y^2 - x^2 ) where k is a constant. This velocity potential is commonly used to describe flow impinging upon a plate. Derive an equation for dP/dy, the pressure gradient in the y-direction, if the fluid has density, rho.

Consider the equilibrium N2(g) + O2(g) ⇄ 2 NO(g) At 2300 K the equilibrium constant K...

Consider the equilibrium N2(g) + O2(g) ⇄ 2 NO(g) At 2300 K the equilibrium constant K = 1.7 × 10-3. Suppose that 0.0150 mol NO(g), 0.250 mol N2(g), and 0.250 mol O2(g) are placed into a 10.0-L flask and heated to 2300 K. The system is not at equilibrium. Determine the direction the reaction must proceed to reach equilibrium and the final equilibrium concentrations of each species. to the right to the left [N2] =____ mol/L [O2] = ____mol/L [NO]...

Consider a classical harmonic oscillator of mass m and spring constant k . What is the...

Consider a classical harmonic oscillator of mass m and spring constant k . What is the probability density for finding the particle at position x ? How does this compare to the probability density for the ground state of a quantum mechanical harmonic oscillator

Consider the following reaction at constant P. Determine the value of ΔSsurroundings at 298 K? Predict...

Consider the following reaction at constant P. Determine the value of ΔSsurroundings at 298 K? Predict whether or not this reaction will be spontaneous at this temperature. N2(g) + 2 O2(g) → 2 NO2(g); ΔH = +66.4 kJ (Please show work and thank you for taking the time to answer.)

Consider a representative firm that faces a constant returns to scale production function Y = zF(K,...

Consider a representative firm that faces a constant returns to scale production function Y = zF(K, Nd ), where Y is output of consumption goods, z is TFP, K is physical capital, and Nd is labour input. The amount of capital is assumed to be given and fixed. The production function exhibits a positive marginal product of labour, as well as diminishing returns to labour. The firm seeks to maximize profits. Suppose that the government imposes an output tax Ty...

Consider a mass spring system. The spring has a constant k=30N/m and mass=3kg. The mass oscillates...

Consider a mass spring system. The spring has a constant k=30N/m and mass=3kg. The mass oscillates w/amplitude of 10cm. a.)what is the frequency of oscillation b.) what is the displacement at time t=0 c.) when is the first time the mass is at maximum displacement? (t=?) d.) what is the maximum acceleration felt by the mass? Where in the motion does this occur? e.)what is the minimum acceleration felt by the mass? Where in the motion does this occur? f.)What...

Consider steady heat transfer between two large parallel plates at constant temperatures of T1 582 K...

Consider steady heat transfer between two large parallel plates at constant temperatures of T1 582 K and T2 196 K that are 6.8 cm apart. Assuming the surfaces to have emissivity 0.9 , determine the rate of heat transfer between the plates per unit surface area assuming the gap between the plates is (a) filled with atmospheric air (b) evacuated (c) filled with fiberglass insulation, and (d) filled with super insulation having an apparent thermal conductivity of 0.00045 W/m ·...

Subjects