D.3 Cosmology

Question 1

What is red shifted light?

Answer 1

Light from distant galaxies is received on Earth at a wavelength that is longer than that emitted.

Question 2

How does the doppler effect explain red shifted light?

Answer 2

The galaxies are moving as from us so the universe is expanding.

Question 3

What does the universe expanding suggest about the previous universe?

Answer 3

That it was once smaller and had a beginning, The Big Bang which marks the beginning of time and space and the creation of all energy and matter. It happened everywhere in the universe which was then a point. At the early sages of the life of the universe the temperature would have been very high as the universe expanded it called down.

Question 4

What is Einstein’s interpretation of the red shift?

Answer 4

Space expands giving the illusion of galaxies moving away from one another. As space expands the wavelength of the photons emitted form distant galaxies also stretched by the time it gets to us, R is the scale factor of the universe, hence we measure a longer red shifted wavelength.

Question 5

What is the equation for the red shift?

Answer 5

Z = lambda/lambda0

where lambda0 is the emitted wavelength and lambda is the received wavelength.

Question 6

What does Hubble’s law suggest?

Answer 6

Distant galaxies move away form each other with a speed that is proportional to their separation v = Hod Hubble’s law only applies to distant galaxies.

Question 7

What is the graph of Hubble’s law?

Answer 7

The graph is a straight line passing through the origin, the axis are speed versus distance and the slope of the fray is Ho.

Question 8

What is the present accepted value of the Hubble constant?

Answer 8

Ho = 68kms-1Mpc-1

Question 9

How is the speed of a receding galaxy obtained?

Answer 9

Using the doppler formula
z = deltalambda/lamda0 = v/c

this can only be used or small red shift up yo about 0.2

Question 10

How do you derive the equation for Hubble time?

Answer 10

v = d/T where T is the present age of the universe.

Thus d/T = Hod giving a value of T = 1/Ho which is about 14 billion years.

Question 11

Why is Hubble time an overestimate of the age of the universe?

Answer 11

The expansion speed was greater at the beginning, so hubble time is only an upper bound on the age of the universe.

Question 12

What is the cosmic scale factor?

Answer 12

As the universe expands the physical distance between any two point increase, the scale factor R is used to quantify this. This factor varies with time.

Question 13

What is the ratio of the physical distance d between the two points given and their separation d0 in the past?

Answer 13

d/d0 = R/R0 where R is the scale factor now and R0 is the scale factor in the past.

Question 14

What is the actual value of the scale factor an indication of?

Answer 14

The size of the universe.

Question 15

How do we deduce the formula for the scale factor?

Answer 15

From z = delta lambda/lambda0 we deduce that z = (lambda - lambda 0)/ lambda 0 which equals (lambda/lambda 0) - 1 which in turns equals R/R0 -1

Question 16

What is cosmic microwave background radiation?

Answer 16

The best evidence for the big bang theory - it is black body radiation coming from all directions in the microwave region. It is the remnant of the radiation that filled the universe in its early stages when the temperature was very high. This means that in the past the peak wavelength was smaller and the temperature was very high, this is strong evidence for a hot big bang. As space stretched the initial wavelength also stretched to its present value.

Question 17

How is the temperature of the universe 3K and the peak wavelength 1.07 mm shown by an equation?

Answer 17

lambda0 x T = 2.9 x 10-3mK
T = 2.9 x 10-3/1.07mm
T = 2.7 K

Question 18

What was the evidence for the universe accelerating in its expansion?

Answer 18

Type Ia supernovae.

Question 19

What is a Type Ia supernova?

Answer 19

Occurs when a white dwarf that is part of a binary star system collected mass from its companion star thus increasing its own mass. Once the Chandrasekhar limit of 1.4 solar masses is exceeded the white dwarf explodes because of runaway nuclei fusion reactions that release large amounts of energy increasing its luminosity massively become a type Ia supernova.

Question 20

how does the luminosity vary for this type of supernova?

Answer 20

It peaks and drops off, they all have the same value of peak luminosity.

Question 21

How can we calculate the supernovas distance from earth?

Answer 21

We can observe the maximum apparent brightness b of such a supernova from
b = L/(4PiD^2) so we can directly calculate its distance form Earth. From its Doppler shift we can also determine the sped at which it is moving away.

Question 22

How does the supernova provide evidence for the universe accelerating?

Answer 22

They were dimmer than expected based on the big bang model, could be explained by assuming that they were actually further away so the universe is accelerating.