Use the Friedmann equation to a) determine the time, t, at which the of the universe...
Use the Friedmann equation to a) determine the time, t, at which the of the universe was 1x107 K, 2x108 K and 3x109 K. b) using information on the photodisintegration of deuterium, at what time were neutrons locked up in baryonic matter?
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Use the Friedmann equation to a) determine the time, t, at which
the of the universe...
2. The Friedmann equation 2 0 2 Cl tells us how the reduced scale factor ä changes with time. Fro...
If. Good Handwriting!! Thank You
2. The Friedmann equation 2 0 2 Cl tells us how the reduced scale factor ä changes with time. From astro- nomical observations we know we are in a flat, matter-Lemaitre universe where S2c-0, ΩΤη-0.3089. Or-5 x 10-5( 0) and Ωυ-0.6911. a) Using the 'second form' of the Friedmann equation show, for the current epoch, äo > 0. Thus, the expansion of the universe is accelerating (b) Is there any future time (any possible à...
The Friedmann equation describes the evolution in the scale factor a of our universe. () =...
The Friedmann equation describes the evolution in the scale factor a of our universe. () = 8cp - Keny Use this equation to derive a formula for the critical density of the universe at the present day – the density at which the universe will have a flat geometry. Carefully explain the steps you take in your derivation. You may assume that the Hubble constant H. =
2. The acceleration equation We have derived in lectures the Friedmann and fluid equations, that describe...
2. The acceleration equation We have derived in lectures the Friedmann and fluid equations, that describe the evolution of simple cosmologies. The Friedmann equation is usually given (adopting c 1) as where a(t) is the scale factor of the universe, p is the mass (energy) density, and k is constant. (a) (5 points) The simplest (although spectacularly uninteresting) cosmology has zero mass-energy, i.e. ρ 0. Solve the Friedmann equation under this condition to obtain an expression for at(t). Describe the...
2. Imagine a type of "phantom energy" with w<-1. (a) Write down the Friedmann equation for...
2. Imagine a type of "phantom energy" with w<-1. (a) Write down the Friedmann equation for a flat universe containing matter and phantom energy 1/(3 ) (b) Show that the matter-phantom equality scale factor is amp = (1- 0) (c) In the phantom energy dominated epoch show that a → at a finite time trip-to = 200-311+wl This is called a "big rip". Hint: integrate over the time range from to to trip. (d) Current data is consistent with w...
Newtonian Cosmology 1. In class, we solved the Friedmann equation for the critical case, where the...
Newtonian Cosmology 1. In class, we solved the Friedmann equation for the critical case, where the constant of integration was set to k 0; this resulted in the Einstein-de Sitter model, where a ox t2/3 Now, let us consider the closed case (k 1), where the universe starts with a Big Bang, reaches a maximum expansion, turns around, and eventually ends in a Big Crunch. For the closed model, it is convenient to write the Friedmann equation as follows: 8T...
3. The Cosmological constant When formulating general relativity, Einstein believed that the Universe was static. In or...
3. The Cosmological constant When formulating general relativity, Einstein believed that the Universe was static. In order to arrange a static Universe, he proposed a change to the equations, something he would later famously call his "greatest blunder". That was the introduction of a cosmological constant, A, to the Friedmann equation (1) (a) (3 points) By referring to the Friedmann equation 1), derive an equation for a static Universe when k -0 (b) (8 points) Last week you derived an...
One of the reasons neutrons stopped forming in the earlier universe was the annihila- tion of...
One of the reasons neutrons stopped forming in the earlier universe was the annihila- tion of electron-positron pairs. When the temperature became too low, the electron- positron pairs could not be replaced by pair production. Since this then removed the supply of electrons that could combine with protons to form neutrons, the neutrons decayed into protons until the universe cooled down enough for the protons and neu- trons to combine to form deuterium nuclei. a. By setting the characteristic thermal...
Suppose the difference between matter and antimatter in the early universe were 1 part in 108 instead of 1 part in 109. (a.) Evaluate the temperature at which deuterium begins to form. (b.) At what ag...
Suppose the difference between matter and antimatter in the early universe were 1 part in 108 instead of 1 part in 109. (a.) Evaluate the temperature at which deuterium begins to form. (b.) At what age does this occur? (c.) Evaluate the temperature and the corresponding time of radiation decoupling (when hydrogen atoms form).
2. The present-day acceleration of the Universe could also be due to the existence of a false vac...
2. The present-day acceleration of the Universe could also be due to the existence of a false vacuum which will eventually decay. Assume that the energy of the false vacuum is εΛ 0.73 ε00, the energy of m atter is e,n,0 0.27 Eco, the Universe is flat, and e,0 5200 MeV m-3 a) What is the value of the Hubble parameter once completely dominates the expan- sion? Express it in units of km s-1 Mpc-1 and in units of to...
In a flat Universe that contains only a fluid with equation of state P = wpc,...
In a flat Universe that contains only a fluid with equation of state P = wpc, where w = -1/6, the evolution of the scale factor, R, with cosmic time, t, is given by R(t) = R, (1)", where R = R(to), and to is the present time: to = 3H, t = 0 corresponding to the Big Bang. The Hubble constant is H. = 67 kms-'Mpc-!. In this model of the Universe: 1. How does the Hubble parameter scale...
If. Good Handwriting!! Thank You
2. The Friedmann equation 2 0 2 Cl tells us how the reduced scale factor ä changes with time. From astro- nomical observations we know we are in a flat, matter-Lemaitre universe where S2c-0, ΩΤη-0.3089. Or-5 x 10-5( 0) and Ωυ-0.6911. a) Using the 'second form' of the Friedmann equation show, for the current epoch, äo > 0. Thus, the expansion of the universe is accelerating (b) Is there any future time (any possible à...
The Friedmann equation describes the evolution in the scale factor a of our universe. () = 8cp - Keny Use this equation to derive a formula for the critical density of the universe at the present day – the density at which the universe will have a flat geometry. Carefully explain the steps you take in your derivation. You may assume that the Hubble constant H. =
2. The acceleration equation We have derived in lectures the Friedmann and fluid equations, that describe the evolution of simple cosmologies. The Friedmann equation is usually given (adopting c 1) as where a(t) is the scale factor of the universe, p is the mass (energy) density, and k is constant. (a) (5 points) The simplest (although spectacularly uninteresting) cosmology has zero mass-energy, i.e. ρ 0. Solve the Friedmann equation under this condition to obtain an expression for at(t). Describe the...
2. Imagine a type of "phantom energy" with w<-1. (a) Write down the Friedmann equation for a flat universe containing matter and phantom energy 1/(3 ) (b) Show that the matter-phantom equality scale factor is amp = (1- 0) (c) In the phantom energy dominated epoch show that a → at a finite time trip-to = 200-311+wl This is called a "big rip". Hint: integrate over the time range from to to trip. (d) Current data is consistent with w...
Newtonian Cosmology 1. In class, we solved the Friedmann equation for the critical case, where the constant of integration was set to k 0; this resulted in the Einstein-de Sitter model, where a ox t2/3 Now, let us consider the closed case (k 1), where the universe starts with a Big Bang, reaches a maximum expansion, turns around, and eventually ends in a Big Crunch. For the closed model, it is convenient to write the Friedmann equation as follows: 8T...
3. The Cosmological constant When formulating general relativity, Einstein believed that the Universe was static. In order to arrange a static Universe, he proposed a change to the equations, something he would later famously call his "greatest blunder". That was the introduction of a cosmological constant, A, to the Friedmann equation (1) (a) (3 points) By referring to the Friedmann equation 1), derive an equation for a static Universe when k -0 (b) (8 points) Last week you derived an...
2. The present-day acceleration of the Universe could also be due to the existence of a false vacuum which will eventually decay. Assume that the energy of the false vacuum is εΛ 0.73 ε00, the energy of m atter is e,n,0 0.27 Eco, the Universe is flat, and e,0 5200 MeV m-3 a) What is the value of the Hubble parameter once completely dominates the expan- sion? Express it in units of km s-1 Mpc-1 and in units of to...
In a flat Universe that contains only a fluid with equation of state P = wpc, where w = -1/6, the evolution of the scale factor, R, with cosmic time, t, is given by R(t) = R, (1)", where R = R(to), and to is the present time: to = 3H, t = 0 corresponding to the Big Bang. The Hubble constant is H. = 67 kms-'Mpc-!. In this model of the Universe: 1. How does the Hubble parameter scale...
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