Grand Summary The Concordance: 1998-2018 ASTR/PHYS 4080: - - PowerPoint PPT Presentation

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Grand Summary The Concordance: 1998-2018 ASTR/PHYS 4080: - - PowerPoint PPT Presentation

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Grand Summary The Concordance: 1998-2018 ASTR/PHYS 4080: Introduction to Cosmology Spring 2018: Week 15 1 Theory ASTR/PHYS 4080: Introduction to Cosmology Spring 2018: Week 15 2 Benchmark Model 2 Kt a e 0 log(a) 2/3 a t

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Spring 2018: Week 15 ASTR/PHYS 4080: Introduction to Cosmology

Grand Summary

The Concordance: 1998-2018

1

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Spring 2018: Week 15 ASTR/PHYS 4080: Introduction to Cosmology

Theory

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Benchmark Model

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−10 −8 −6 −4 −2 −6 −4 −2 2 log(H0t) log(a)

trm tmΛ t0 a∝t

1/2

a∝t

2/3

a∝e

Kt

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Spring 2018: Week 15 ASTR/PHYS 4080: Introduction to Cosmology

Early Universe Timescales

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strong force freeze out weak force freeze out

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Spring 2018: Week 15 ASTR/PHYS 4080: Introduction to Cosmology

Early Universe (Fundamental) Scales

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lp ≡ ✓G~ c3 ◆1/2 = 1.6 × 10−33cm tp ≡ ✓G~ c5 ◆1/2 = 5.4 × 10−44s Mp ≡ ✓~c G ◆1/2 = 2.2 × 10−5g Ep = Mpc2 = ✓~c5 G ◆1/2 = 1.2 × 1028eV = 1.2 × 1019GeV Tp = Ep/k = 1.4 × 1032K

Planck time: Planck units: Planck temperature: Planck length: Planck mass: Planck energy:

c = k = ~ = G = 1

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Key Relations

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Curvature

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How can we measure the curvature of spacetime?

= Radius of Curvature = area of triangle

Only possible geometries that are homogeneous/isotropic

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Lengths of Geodesics (3D, polar coords)

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<OR>

straight lines in a given geometry flat or Euclidean space: elliptical or spherical space: hyperbolic space:

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{

Minkowski & Robertson-Walker Metrics

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metrics define the distance between events in spacetime Minkowski (no gravity: metric in SR) Robertson-Walker (with gravity, if spacetime is homogeneous & isotropic) light travels along null geodesics, i.e.: cosmological proper time or cosmic time comoving coordinates

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Only 1 Constituent in a Flat Spacetime

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Matter + Lambda + Curvature

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Early Universe Timescales

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Inflation - quark soup - neutron capture - nucleosynthesis - recomb/decoup kT: 150 MeV 10 MeV 0.07 MeV 3760/2970K baryogenesis photon-baryon ratio

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neutron-proton ratio

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Nuclear Binding Energy

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release energy expect nucleosynthesis to result in all atoms becoming iron does not happen - why not?

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BBN

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Recombination

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(minus for bosons, plus for fermions) g —> 2 (for non-nucleons, gH=4) chemical potential of photons = 0 Saha Equation

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Surface of Last Scattering

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Reionization

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Observation

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Olber’s Paradox (1823)

Resolution?

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Cosmological Principle

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The universe is isotropic on very large

  • scales. (>100Mpc).

Radio sources from NVSS (Condon et al. 2003)

Copernican Principle => homogeneous & isotropic (Cosmological Principle)

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Near perfect BB everywhere on the sky

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dT/T ~ 10-3

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Abundances from Nucleosynthesis

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Creation process depends on relative abundances at any given time, so have to calculate computationally Nucleosynthesis doesn’t run to completion like in stars — rapidly dropping temperature cuts it off and “freezes” abundance pattern Exact yields depend most on baryon- to-photon ratio: (determines temperature of nucleosynthesis)

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Practical Distance Measures

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Luminosity Distance Angular Diameter Distance

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Practical Distance Measures

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How distances are affected by underlying cosmology

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Luminosity Distance Angular Diameter Distance

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Practical Distance Measures

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Getting distances to the nebulae

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2 Mpc 1000 km/s

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Practical Distance Measures

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CMB provides a giant triangle of known size!

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Acoustic peaks

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causal contact initial conditions first peak third peak second peak etc peaks size scale of a DM potential well where baryon collapse reaches turnaround due to its pressure

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Baryonic Matter

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By the time of the Big Bang and thereafter, normal matter is the subdominant form of matter in the universe, with some other form of matter (non-baryonic dark matter) making up the majority of non-relativistic matter in the universe Could be primordial black holes that were made before this time (i.e., not from stars).

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Dark Matter in Galaxies

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Detecting MACHOs via gravitational lensing

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b b b d d xd

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Temperature of the Dark Matter

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Hot Warm Cold velocity of particles compared to the speed of light relativistic at time of collapse (like neutrinos): hot non-relativistic at time of collapse (like WIMPs): cold fast motions wipe out initial

  • verdensities on small

scales: “free-streaming”

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Power spectrum of density fluctuations

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Power spectrum defined to be the mean squared amplitude of the Fourier components: Gaussian field: each component uncorrelated and random, drawn from the Gaussian distribution Inflation predicts this (random quantum fluctuations) and a power law power spectrum (with n=1)

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Acoustic peaks

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causal contact initial conditions first peak third peak second peak etc peaks First peak: spatially flat Second peak: existence of “dark baryons” Third peak: amount of dark matter Damping tail: photons can cross entire grav. fluct., wipes out signal damping tail

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Baryon Acoustic Oscillations

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Eisenstein+ 2005 To measure, use galaxies to trace the signature of these oscillations The number of galaxies should be correlated with each other on scales comparable to the sound horizon of the largest acoustic peaks (~150 Mpc comoving) The number of galaxies within a given volume is

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Open Questions

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  • Is the inflationary hypothesis -- which determines the "initial conditions" that control practically

everything we can now observe in the universe -- generally accurate?

  • If the inflationary hypothesis is generally correct, did inflation occur in such a way that the universe we

now observe is only one of countless "bubble universes" that could have arisen out of the same process?

  • How many forms of dark matter are really present in the universe, what is the relative percentage of

each, and how has the dark matter affected the observable structure of the universe?

  • What is the true cause of the accelerating expansion we seem to observe now, and is it likely to

continue indefinitely into the future?

  • What is the true dimensionality of spacetime, and how did the apparent three dimensions of space

and one of time (along with any other "hidden" dimensions) come to be as we see them?

  • Are the laws of physics, in particular the "fundamental constants", truly the same everywhere and at

every time in the observable universe, or do they vary in some slight but predictable way?

  • Is the topology of the observable universe truly infinite, or is it finite in such a way that we could in

principle observe our own section of the universe if we could only see "far" enough?

from http://www.openquestions.com/oq-cosmo.htm#questions