Section 1

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Physics Fichas sobre Section 1, creado por Lucy Clements el 12/12/2022.
Lucy Clements
Fichas por Lucy Clements, actualizado hace más de 1 año
Lucy Clements
Creado por Lucy Clements hace casi 2 años
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Pregunta Respuesta
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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