CMB — Notes and Useful Info

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Sat, 03 Oct 2020 16:05:24 +0000

Note: keep this at top of blog list by updating it's date in post metadata. Blog Index 01: Articles Index and Hashtags Page 1 02: Apps 03: MathJax quirks/issues in Write.as 04: WSL 05: Search Test 06: Custom Javascript/CSS Coding 07: Text-Only Sites 08: DMV Tests 09: Nextcloud 16.04.1 Install on Debian 9 10: Nextcloud Docker Notes 11: Notes Page 2 12: Nextcloud Notes 13: WA WF Code Examples 14: Phone Tips 15: Cosmology-Followup 16: Blogs Posts 17: Fediverse Followup 18: Tech Followup 19: Priority To Do 20: write.as usage notes 21: WriteFreely info, setup, and config Page 3 22: Win1809 23: Science Projects Ideas 24: Git 25: MathJax and LaTeX 26: Latest Cosmology Results 27: WebDev 28: CyberSecurity links 29: Linux 30: e6430 31: Android Dev Page 4 32: Cloudready 33: Winlinks 34: Ideas for More Secure or Anonymous Payments Online 35: Python 36: Test Post 37: Physics Links 38: CMB 39: Cosmology

MathJax quirks/issues in Write.as

Mon, 24 Aug 2020 15:44:58 +0000

The Hubble constant is determined through obtaining the angular diameter distance to the last scattering surface. That's not a direct observable; instead it's inferred through trigonometry. We can directly measure the angular scale of the Baryon Acoustic oscillations in the CMB – it's the distance between troughs in the power spectrum. In the standard $\Lambda$CDM cosmological model, we also know the physical scale of the BAO feature, known as the sound horizon length. The angular diameter distance is then defined as

$D_A = \frac{r_s}{\theta_s}$

where the numerator is the known physical scale and the denominator is the measured angular scale. The angular diameter distance is a well-known function of the Hubble rate, and you can infer the Hubble rate from getting the angular diameter distance (assuming the only pertinent species of particles in the universe are dark matter, baryons, photons, neutrinos, and the cosmological constant). In particular, the equation is

$\int_0^{z^*}$

$D_A = \int_0^{z^*}$

$ D_A = \int_0^{z^*} $

$ D_A = \frac{1}{1+z^*} \frac{dz}{H(z)} $

$ D_A = \frac{1}{1+z^*} \int_0 \frac{dz}{H(z)} $ (works)

$D_A = \frac{1}{1+z^*} \int_0 \frac{dz}{H(z)}$ (works)

$D_A = \frac{1}{1+z^*} \int_0^z \frac{dz}{H(z)}$ (works) $D\_A = \frac{1}{1+z^*} \int_0^z \frac{dz}{H(z)}$

$D_A = \frac{1}{1+z^*} \int_0^{z^1} \frac{dz}{H(z)}$ (works) $D\_A = \frac{1}{1+z^1} \int_0^{z^1} \frac{dz}{H(z)}$

$D_A = \frac{1}{1+z^*} \int_0^{z*} \frac{dz}{H(z)}$ (works) $D\_A = \frac{1}{1+z^\*} \int_0^{z\*} \frac{dz}{H(z)}$

$D_A = \frac{1}{1+z^*} \int_0^{z^*} \frac{dz}{H(z)}$ (works) $D\_A = \frac{1}{1+z^\*} \int_0^{z^\*} \frac{dz}{H(z)}$

$D_A = \frac{1}{1+z^} \int_0^{z^} \frac{dz}{H(z)}$ (does not work) $D\_A = \frac{1}{1+z^*} \int_0^{z^*} \frac{dz}{H(z)}$

$ D_A = \frac{1}{1+z^} \int_0^{z^} \frac{dz}{H(z)} $ (does not work) \$ D\_A = \frac{1}{1+z^*} \int_0^{z^*} \frac{dz}{H(z)} \$

$H(z) = H_0 \sqrt{\Omega_m (1+z)^3 + \Omega_{rad} (1+z)^4 + \Omega_{\Lambda}}$

with $z^*$ is the redshift of the CMB (~1100), and the $\Omega$ density parameters corresponding to the known total matter density, radiation density, and vacuum energy density today, respectively.

Tags: #CMB #Cosmology #Physics

CMB

Sat, 22 Sep 2018 20:45:13 +0000

Verde et al., WMAP: Parameter Estimation Methodology | astro-ph/0302218 | Physics of the CMB great slides | [1504.06335] Physics of the Cosmic Microwave Background Radiation great review paper |

GitHub project: Tools for plotting CMB polarization power spectra

Spherical CMB map or 2D CMB map

Wayne Hu: graphic taking apart features in the power spectrum, slide 9 | CMB fluid approximation, slide 9+ |.

https://en.wikipedia.org/wiki/Cosmic_microwave_background (the refs, esp to Wayne Hu's work, are good)

Will the CMB ever recede outside our visibility: SE1 | SE2 | R1 | H1 | Doug Scott's answer to CMB questions | Ned Wright | S1 |

https://www.ast.cam.ac.uk/~pettini/Intro%20Cosmology/Lecture09.pdf Recombination was not an instantaneous process but proceeded relatively quickly nevertheless, with the fractional ionisation decreasing from X = 0.9 to X = 0.1 over a time interval ∆t ∼ 70,000 yr. With the number density of free electrons dropping rapidly, the time when photons and baryons decoupled follows soon, once the rate for Thomson scattering falls below the expansion rate H. Section 9.3, Photon Decoupling, pg 6 (These excellent notes cover the following epochs: Radiation-Matter Equality, Recombination, Photon Decoupling, Last Scattering.)

Physics of the cosmic microwave background anisotropy [1501.04288], by Martin Bucher | Anisotropy of the Cosmic Background Radiation and Cosmological Parameters, Bartelmann | Determining Cosmological Parameters from Anisotropies in the CMB |

Wayne Hu's writings: CMB, power spectrum, BAO, etc | Great graphic | BAO section | Lecture notes from introductory cosmology course: e.g., cosmic geometry |

https://www.reddit.com/r/AskPhysics/comments/8i79wf/why_do_we_believe_there_is_dark_matter/

The CMB, J. Kenney class 22 slides, very good

Halverson – Measuring the CMB Angular Power Spectrum with DASI.pdf (local PDF) | [astro-ph/0104489] DASI First Results: A Measurement of the Cosmic Microwave Background Angular Power Spectrum, 8 pages |

The simplicity of CMB physics – due to linearity – is mirrored in analysis by the apparent Gaussianity of both the signal and many sources of noise... The Gaussianity of the CMB is not shared by other cosmological systems since gravitational non-linearities turn an initially Gaussian distribution into a non-Gaussian one. http://background.uchicago.edu/~whu/araa/node32.html

most of the secondary anisotropies are not linear in nature and hence produce non-Gaussian signatures. Non-Gaussianity in the lensing and SZ signals will be important for their isolation. The same is true for contaminants such as galactic and extragalactic foregrounds. Finally the lack of an initial non-Gaussianity in the fluctuations is a testable prediction of the simplest inflationary models [Guth & Pi, 1985,Bardeen et al, 1983]. Consequently, non-Gaussianity in the CMB is currently a very active field of research. http://background.uchicago.edu/~whu/araa/node31.html

arXiv listing with abstracts of all Planck 2013, 2015, 2018 papers

Astro useful info

Hashtags: #CMB #Cosmology #physics