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Description
Flashcards by Lucy Clements, updated more than 1 year ago
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Created by Lucy Clements
over 1 year ago
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| Question | Answer |
| Cosmological Principle | The universe is on average: -Isotropic : same in all directions -Homogenous: same at all points |
| What is the scale factor, a? What equation is it the constant of proportionality for? | It relates positions at time t to positions at today time t_0 By r(t)=a(t)r(t_0) |
| What is Hubbles Law? (Define all letters) | v=Hr+v_pec Where, v is velocity r is position H is Hubble parameter v_pec is random motion |
| What is the equation for the Hubble parameter? What is it today? What does it represent? | H_0 = 100hkms^-1Mpc^-1 The relative expansion rate of the universe |
| What are comoving coordinates? - Definition -Equation -coordinates today | Comoving coordinates, x, are carried along with the expansion of the Universe Today a_0=1 so comoving and physical coordinates coincide |
| Red shift equations | For nearby, z=v/c For distant: Relation to a: 1+z=1/a |
| Friedmann Equation (define each term) | a=scale factor G=Newtons constant ρ=energy density k=curvature λ=cosmological constant |
| Fluid Equation - explain each term | 1st term: dilution due to the expansion 2nd term: loss of energy due to pressure doing work as volume increases |
| Acceleration Equation | Expansion accelerates if positive |
| Equation of state | w=gamma-1 |
| Matter: Definition Pressure Equation of state | Non-relativistic: baryons+dark matter P=rho*kt/mu where mu=mean mass 3kt=mu<v^2> So p=0 , w=0 |
| Radiation: Definition Pressure Equation of state | Relativistic: photons + neutrinos K.E exerts P=(rho*c^2)/3 so w=1/3 |
| Dark energy: Definition Pressure Equation of state | Has negative pressure but rho>0 So P=-rho*c^2 So w=-1 |
| Matter domination: density, a, and H expansion? | a..<0 so expansion decelerating |
| Radiation domination: density, a, and H expansion? | a..<0 so expansion decelerating Expands slower due to pressure providing deceleration |
| Cosmological domination a expansion? | Expansion is accelerating since a..>0 |
| Deceleration parameter | If q>0 then universe is decelerating |
| Geometry = Flat k? Infinite? Angles of a triangle? Circle circumference? Parallel lines? | k = 0 Infinite Angles of a triangle= 180 Circle circumference= 2*pi*r Parallel lines stay parallel |
| Geometry = Closed k? Infinite? Angles of a triangle? Circle circumference? Parallel lines? | k > 0 Finite Angles of a triangle > 180 Circle circumference < 2*pi*r Parallel lines intersect |
| Geometry = Open k? Infinite? Angles of a triangle? Circle circumference? Parallel lines? | k < 0 Infinite Angles of a triangle < 180 Circle circumference > 2*pi*r Parallel lines diverge |
| Critical density | The density required for universe to be flat and k=0 Density of galaxies is order of magnitude=p_c |
| Density parameter | |
| Cosmological density parameter | |
| Sum of density parameters | |
| What happens at late times? (0 cosmological) If k=0? If k>0? If k<0? | Matter eventually dominates since decays less rapidly than radiation density k=0 - density->0 so H->0 so expansion->0 k>0 - universe recollapses when H=0 k<0 - H never 0, k dominates so a is directly proportional to t - expands forever |
| What happens at late times? (non-zero cosmological) | Cosmological dominates and universe expands exponentially |
| Sketch parametric solutions for closed universe a(theta), t(theta), a(t) | |
| Sketch parametric solutions for open universe a(psi), t(psi, a(t) | |
| General solution to friedmann equation and curvature density parameter | curvature density= - kc^2/(H_0)^2 |
| Log density against log a | |
| Expansion of the universe graph | |
| Inflation time | 10^-34s |
| Nucleosynthesis time | (1-100)s |
| Time of matter-radiation equality | 10^12 s |
| Decoupling time | 10^13 s |
| Time of cosmological constant domination | 10Gyr |
| Today (time) | 13Gyr |
| Physical equation for density | rho=mN/V for N particles of mass m in volume V |
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