COSMOLOGY (THE BIG BANG)

• Mean distance from the Earth to the Sun

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• 150 million km

• Distance travelled by light in a vacuum in a time of one year

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• Distance = speed x time

= (3 x 10⁸) x (365 x 24 x 60 x 60)

= 9.46 x 10¹⁵ m

• A second of arc

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• 1 arcsecond = 1 / 3600^o

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• 60 arcseconds = 1 arcminute

• A minute of arc

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• 60 arcminutes = 1^o

The distance at which a radius of 1 AU subtends an angle of 1 arcsecond

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1 pc = 1 AU /  tan (1 arcsecond)

= (1.5 x 10¹¹) / tan (1 / 3600) 

= 3.1 x 10¹⁶ m

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If the point is at a distance of d pc, then the angle subtended by the radius is 1 / d arcsecond

A technique used to determine the distance to stars

......that are relatively close to the Earth (less than 100 pc)

............by comparing their apparent positions against distant stars

..................at times 6 months apart

Distance to nearby star in parsecs = 1 / parallax angle in arcseconds

The change in the frequency and wavelength of waves recieved from an object

......moving relative to an observer

............compared with what would be observed without relative motion

Waves recieved by B are compressed

Shorter wavelength

Higher frequency

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Waves recieved by A are stretched out

Longer wavelength 

Lower frequency

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Greater speed = greater effect

1. Absorption spectrum of a specific element determined in the laboratory

2. Same spectrum observed in light from a distant galaxy

3. Difference in observed wavelengths of absorption lines caused by relative motion between galaxy and Earth

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Blue-shifted

• Galaxy moving towards Earth
• Absorption lines move towards blue end of spectrum
• Shorter wavelength

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Red-shifted

• Galaxy moving away from Earth
• Absorption lines move towards red end of spectrum
• Longer wavelength

When speed of galaxy << speed of light

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Δλ / λ ≈ Δf / f ≈ v / c

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Δλ = change in wavelength recorded by observer

λ = source wavelength

Δf = change in frequency recorded by oberver

f = source frequency

v = magnitude of relative velocity between source and observer

c = speed of light through vacuum (3 x 10⁸ ms^-1)

The recessional speed of a galaxy is almost directly proportional to its distance from the Earth

• Straight line

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• Through the origin

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• Constant, positive gradient

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• Gradient = Hubble constant

v = H_od

H_o = 2.2 x 10^-18 s^-1 or 67.80 ± 0.77 kms^-1Mpc^-1

The fabric of space and time is expanding in all directions

......∴ any point, in any part of the Universe, is moving away from every other point in the Universe

............Greater distance between points = faster relative motion away from each other

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Light from more distant galaxies is more red-shifted

......∴ they are moving faster than those nearer to us

When viewed on a sufficiently large scale, the Universe is:

Homogeneous

• Matter distributed uniformly

Isotropic

• Looks the same in all directions
• Has no centre or edge

The laws of Physics are universal

At a moment in the past

......all the matter in the Universe was contained in a singularity (at a single point)

............(the beginning of space and time)

..................that expanded rapidly outwards

The microwave signal of uniform intensity detected from all directions of the sky, which fits the profile for a black body at a temperature of 2.7 K

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When Universe was young and extremely hot

......space saturated with high-energy gamma photons

............Expansion of Universe and thus space stretched their wavelength

..................Now observed as microwaves

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Universe extremely dense and hot when young

......Expansion of Universe and thus space reduced temperature to around 2.7 K

............Universe = black-body radiator

..................Peak wavelength ≈ 1 mm = in microwave region of EM spectrum

t = 1 / H_o

= 1 / (2.2 x 10^-18)

= 4.5 x 10¹⁷ s

≈ 14 billion years

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Inaccurate as expansion of Universe is accelerating

• Hypothetical form of energy

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• Fills all of space

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• Would explain the accelerating expansion of the Universe

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• 68.3% of the Universe

• Hypothetical form of matter

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• Spread throughout the galaxy

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• Neither emits nor absorbs light

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• Could explain the differences between the predicted and observed velocities of stars in galaxies

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• 26.8% of the Universe (matter = 4.9% of the Universe)

The Big Bang

• Time and space created
• Universe is a singularity- infinitely dense and hot

10^-35 s

• Universe expands rapidly
• Phase of incredible acceleration (inflation)
• No matter, only high-energy gamma photons
• 10²⁸ K

10^-6 s

• First fundamental particles gain mass

10^-3 s

• Quarks combine to form hadrons
• Pair production (high-energy gamma photons transform into particle-antiparticle pairs)
• Most of mass in Universe created by now