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Cosmology > Section 1-2 > Flashcards

Section 1-2 Flashcards

1
Q

The universe we see and measure is

A

inhomogeneous and anisotropic on almost every scale

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2
Q

The spatial distribution of galaxies is not

A

uniform

galaxies appear to be clustered

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3
Q

We see evidence of galaxy clustering in the

A

projected distribution of galaxies on the sky

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4
Q

Hubble - Lemaitre’s law says that

A

distant galaxies recede from us with speeds that increase linearly with distance

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5
Q

Redshift survey

A

accurate maps of the galaxy distribution on large scales using the measured redshift to indicate the relative separation of galaxies

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6
Q

Redshift surveys reveal

A

patterns in the galaxy distribution that we see galaxy clusters, sheets and filamentary structure, and voids

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7
Q

A feature that suggests the universe is not homogeneous or isotropic

A

The Sloan Great Wall

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8
Q

On small scales galaxies are grouped together in

A

clusters

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9
Q

Within galaxy clusters, galaxies may have a peculiar motion, or speed, that differs slightly from

A

their recession velocity given by the Hubble-Lemaitre law.

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10
Q

The peculiar motion is caused by

A

their gravitational interaction with the other cluster members. The effects of this are most pronounced for galaxies that are reasonably close and have therefore relatively low recession velocities.

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11
Q

The distribution of galaxy clusters is

A

non-uniform

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12
Q

Galaxy clusters are themselves

A

clustered

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13
Q

Superclusters

A

Galaxy clusters that are organised into larger-scale structures

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14
Q

The two most commonly used variable star distance indicators are

A

RR Lyrae Stars and Cepheid variable Stars

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15
Q

For the closest galaxies the Hubble-Lemaitre expansion law is

A

distorted by peculiar motions due to the pull of nearby galaxies.

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16
Q

Hubble’s constant measures

A

the expansion rate of the Universe

Hubble reached the wrong expansion rate due to underestimating the distances to his calibrating galaxies.

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17
Q

Hubble’s constant value is widely accepted as

A

70kms^-1 Mpc^-1

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18
Q

The standard model for the origin and evolution of the Universe is called the

A

Hot Big Bang

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19
Q

The Universe began

A

13.7 billion years ago and has been expanding ever since

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20
Q

The Cosmological Principle

A

The Universe is homogenous (no matter where you are in it) and isotropic (no matter what direction). The universe looks the same.

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21
Q

The Cosmological Principle states there are no

A

‘special places’ in the Universe such as a centre or an edge.

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22
Q

Only space between _ is expanding

A

galaxies

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23
Q

Gravitationally bound systems do not

A

expand

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24
Q

The sizes of galaxies themselves

A

do not change, only the distances between them

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25
Q

Galaxies can be thought of as local disturbances in an

A

otherwise perfectly homogenous and isotropic universe.

26
Q

cosmic scale factor a(t)

A

a dimension-less number that can describe the size of the evolution of the Universe

27
Q

a(t) measures the

A

characteristic size of the Universe at time t. More specifically, it allows one to determine by how far galaxies have been carried apart by the expansion of the underlying space.

28
Q

The present day factor of the scale factor is

A

a(t₀) = a₀

29
Q

The proper distance between two galaxies at time t is their

A

actual seperation

30
Q

co - moving separation of two galaxies

A

is their separation expressed in terms of a coordinate system which expands along the background space.

31
Q

Galaxies co-moving separation is

A

not changed

32
Q

Cosmological redshifts are not

A

due to the motions of distant objects, but are the result of the stretching of the wavelength of their light as it propagates through expanding space.

33
Q

Hubble’s constant measures the rate of change of the

A

scale factor a(t): it is not a constant in time, but a constant in space at any given time

34
Q

Hubble time

A

τ, is a timescale for the expansion of the Universe. This simple treatment ignores the effect of gravity, which will slow down the expansion so that H(t) was larger in the past.

35
Q

proper distance formula

A

r(t) = a(t) x s

36
Q

how does the expansion of the universe affect the wavelength of light emitted by a distant object

A

the wavelength is stretched by the expansion of the universe

37
Q

redshift formula

A

z = (λobs - λem) / λem

38
Q

Hubble-Lemaitre law formula

A

Vrec = Ho * d

39
Q

Hubble-Lamaitre law distorted by peculiar motions

A

Vobs = Ho * d + Vpec

40
Q

λobs / λem =

A

a₀ / a(t)

41
Q

1 + z =

A

a₀ / a(t)

42
Q

v = dr/dt =

A

d/dt (as) = ȧ*s = ȧ/a * (as) = ȧ/a * r

43
Q

H(t) =

A

ȧ/a

44
Q

present day value of Hubble constant formula

A

Ho = (ȧ/a)t=to

45
Q

age of the universe

A

τ = 9.8h⁻¹ x10⁹ yr

46
Q

luminosity distance

A

d²lum ≡ L/S

accounting for redshift
=>
dlum = a₀r₀ (1+z)

47
Q

relating angular and luminosity distances via

A

ddiam = a₀r₀ / 1+z = dlum / (1+z)²

48
Q

what is used to estimate luminosity distances

A

the 3-band near-infrared photometry of 2MASS

49
Q

4 things that support a homogeneous and isotropic universe

A

1) Hubble-Lemaitre law has been verified over a large range of scales and its accuracy supports

2) The CMBR is isotropic to a very high accuracy, and it has a very large energy density

Standard hot Big Bang models naturally incorporate the CMBR

3) By adjusting only the baryon density, given the standard model for expansion, one obtains an accurate prediction for the abundances of several light elements and their isotopes which is in agreement

4) All measurements give consistent values for the age of the universe of 13.7x10^9 y

50
Q

The number of objects observed from any given point within a solid angle at radii smaller than r is

A

N = no 4/3πr³*Ω/4π

51
Q

The number of objects of a given luminosity L and a flux larger than F is

A

N(>F) = const*no L³/² F-³/²Ω

52
Q

If not all galaxies have same luminosity L N(>F) =

A

constnoF-³/²Ω 0 ∫∞ f(L)L³/²dL

53
Q

we obtain the number of object of a given luminosity L and an apparent magnitude smaller than m

A

logN(< m) = const + 3/5 m+logΩ

54
Q

Robertson - Walker metric

A

ds² = -c²dt² + a²(t) [(dr²/1-kr²) + r²(d² + sin²θ d²ϕ)]

55
Q

The total number of sources out to some distance ro is,

A

N(ro) = n(to)ao³ 0 ∫ ro (r²dr/√1-kr²)

56
Q

Olber’s Paradox

A

“why is the sky dark at night”

If the Universe is infinite in extent and eternal, with stars roughly uniformly distributed throughout space, then every line of sight will intercept a star, so that the whole night sky should be as bright as the surface of a star

57
Q

Resolution of Olber’s Paradox

A
  1. Stars have finite lifetimes, and can’t fill their portion of space with light forever
  2. The speed of light is finite, so only stars within a finite distance can be observed, i.e. the light from the most distant sources has not had time to reach us,
  3. Above all, the Universe almost certainly has a finite age.
58
Q

dlum derivation

A

photons lose energy ∝ (1+z)

photons arrive less frequently, also ∝ (1+z)

S = L/a0^2r0^2(1+a)^2

dlum = a0r0(1+z)

59
Q

ddiam derivation

A

ddiam = l/sinθ = l/θ

l = ds = r0a(te)dθ

dθ = 1/r0a(te) = 1(1+z)/a0r0

dlum/(1+z^2) = a0/1+z

60
Q

graph for d diam

A

see notes

Cosmology (7 decks)

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