Apps | Priority To Do | Notes | Tech-Followup | WaWf list | write.as notes | WriteFreely | Fediverse-Followup | CMB | Cosmology | Cosmology-Followup | Physics | Winlinks | e6430 | Cloudready | Linux | Android Dev | Python | Symbols | WebDev | Cipherlinks | Test |

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

\(D_A = \frac{r_s}{\theta_s}\)

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

MathJax is available in write.as blog posts only, not anonymous posts. great MathJax reference MathJax turns 3.0 online LaTeX editor; codingGround | 2nd LaTeX coding example |

MathJax tutorial and quick reference | mathjax.org | PhysicsForums Reference | LaTeX math | Free LaTeX book PDF format | Niko tweet on LaTeX spacing with a good PDF on it

Get LaTeX source from browser developer Elements tab: https://imgur.com/Th8Gj

When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are $$(x = {-b \pm \sqrt{b^2-4ac} \over 2a})$$ You can test this online using jsbin.com $$\left [ – \frac{\hbar^2}{2 m} \frac{\partial^2}{\partial x^2} + V \right ] \Psi = i \hbar \frac{\partial}{\partial t} \Psi$$ $$f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz$$ $$\hbar \frac{\partial}{\partial t} \Psi = \hat H\Psi$$ $$\lim_{x \to +\infty} \frac{3x^2 +7x^3}{x^2 +5x^4} = 3$$

$$\sigma = \sqrt{\frac{3x^2 +7x^3}{x^2 +5x^4}}$$

These examples use inline LaTeX. Note that write.as/writefreely does not work with $, you need to use \\( and \\) instead of $\H_0$ \(H_0\) \(\ddot a\) : \ddot a to put a double dot over a \(\vec a\) : to put a little arrow over a \(\bar a\) : \bar a to put an overbar over a \(\tilde a\) : \tilde a to put '~' over a \(\hat a\) : \hat a to put '^' over a \(\dot a\) : \dot a to put a single dot over a

\(\Lambda^\mu_\nu\)

\(\Lambda_\nu^\mu\)

\(\Lambda^\mu{}_\nu\)

According to Planck's law, the energy density inside a blackbody cavity for modes with frequency \(\nu\) \(\in\) \([\nu, \nu + \mathrm{d}\nu]\) is given by $$ \rho(\nu, T)\mathrm{d}\nu = \frac{8\pi\nu^2}{c^3}\frac{h\nu}{\exp\left(\frac{h\nu}{k T}\right) – 1}\mathrm{d}\nu $$ from: https://www.physicsforums.com/threads/radiance-and-energy-density-of-a-black-body.956343/

Hashtags: #physics

Tom Hartman's notes on quantum gravity and general relativity http://www.hartmanhep.net/index.php Recommended here

Brilliant.org: Quantum Objects | Linear Algebra | 3blue1brown Essence of Linear Algebra |

jrdt wiki

Thoroughly read this great Poor Man's CMB Primer series

Complexity and Gravity, Leonard Susskind video | Particles, Fields, and the Future of Physics, Sean Carroll video

EdX physics courses

“Time” replaced by quantum correlations, W. Wooters, https://link.springer.com/article/10.1007/BF02214098 | https://physics.williams.edu/profile/wwootter/

Open source textbooks: https://archive.org/details/opensource_textbooks

https://www.citehero.com/ (very good) | http://www.cite.me/ (meh)

Intro to QM: Quantum Entanglement

Time in fundamental physics, Ashtekar https://arxiv.org/abs/1312.6322

Hashtags: #physics

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

Planck 2013 results. XVI. Cosmological parameters | Nice wp article on measuring SNe distances |

WikiProject Astronomy/Cosmology | Cosmology Task Force | Physics | Science Directory | reddit Q&A |

Discovery of the hot Big Bang: What Happened in 1948 Past, Present and Future of Cosmic Microwave Background Observations: Implications for Cosmology

Astro2020 Science White Paper: A proposal to exploit galaxy-21cm synergies to shed light on the Epoch of Reionization https://arxiv.org/abs/1903.03628

3 cosmology lectures by Celine Boehm at Sept. 2017 European School of High Energy Physics (slides) https://t.co/bbl9reJMU3 https://t.co/dtn0oy08gi https://t.co/XcEIqpkksQ All ESHEP 2017 lectures: https://t.co/dHsZMwuOn5

Sound Waves from the Beginning of Time, PBS SpaceTime video on Baryon Acoustic Oscillation (BAO) Secrets of the Cosmic Microwave Background, PBS SpaceTime video | reddit post |

The Distance Scale of the Universe; excellent! [astro-ph/0310571] A Map of the Universe This explains the “future visability limit”, which is also refered to in this Ethan Siegel article

[1812.06841] Inflation in Loop Quantum Cosmology, Ed Copeland et al

Megamaser Cosmology Project

Las Cumbres Observatory: Measuring the Age of the Universe | Magnitudes and Distance Measurement | Star in a Box: interactive app on lifecycle of stars |

John C. Brown, Astronomer Royal for Scotland | on wp | U Glasgow | what being an astronomer is like | known for Cold Thick-Target model |

Latest cosmology results page

Amplitude of Matter Fluctuations, σ8. The σ8 parameter is a measure of matter clumping in the LCDM model The amplitude of the primordial matter power spectrum is parameterized by σ8. This provides an important constraint on clustering of matter (CDM dominated) and the formation of structure.
Determining the cosmological parameters Ωm and σ8 from peculiar velocity and density-contrast data Another, albeit somewhat weaker, tension (compared to H0) exists between the values of the amplitude of galaxy clustering S8 σ8 and the matter fraction Ωm (S₈ − Ωm tension) in the Planck best fit model and those inferred from the latest surveys of large scale structure. [2004.09487] Adam Riess interview with Sean Carroll: this is not a quest to measure a number, this is a quest to do an end-to-end test of the universe and understand why it’s failing or we’re failing...there is this problem with the lumpiness of the universe as well...there’s another parameter, which often goes by the catchy name of Sigma 8 and it measures the clumpiness of matter. And so likewise in the early universe, because we know the state of the universe shortly after the Big Bang, and then we know how it dilutes due to expansion, we should be able to predict how clumpy it should be today. And then we have techniques which are also hard but are powerful in measuring how clumpy is, either by measuring this phenomenon called loop lensing, where we measure how clumps of matter distort the shapes, the apparent shapes of galaxies, or by measuring the motions of galaxies, extra motions due to not the expansion of space but matter, the clumpiness of matter, and those two at this point disagree with each other at… I guess the most recent number that I’ve seen is sort of 3 sigma from each of those, the lensing method and the peculiar velocity method. And in the same direction, that the late universe measurements are in a different direction in terms of size to the sigma 8 number as multiple early universe measurement.

IPython notebook tutorials covering NumPy, Matplotlib, SciPy. etc. and overview of the Python language itself. Matplotlib plotting | Precision data plotting in Python with Matplotlib | Do you often find a figure you made and have no idea what script you used to generate it? I just discovered the metadata keyword in matplotlib (plt.savefig). You can pass a dictionary including the “Creator” and the name of the script! [tweet]

ICRAR cosmology calculator | iCosmos | Ned Wright cosmology calculator |

Lambda-Tools | wp cosmology software | astrobites software refs | ASCL web resources and tools | LightCone7 Combo Tutorial – calculator for expansion history of universe |

Computing the Expansion History of the Universe, pdf |

CosmoloPy | nbinderkit |

Colossus html exported from ipynb notebooks | Colossus cosmology python astrophysics toolkit | Overview docs | LSS and DM Halo modules | Diemer 1712.04512 paper | -The easiest way to learn how to use Colossus is by following the tutorial notebooks. -You can learn more about Jupyter notebooks on the Jupyter website. * Cosmology <static/tutorialcosmology.html> * LSS: peaks in Gaussian random fields <static/tutoriallss_peaks.html> -The editable notebooks are located in the colossus/tutorials directory, the links below point to their html output: https://bitbucket.org/bdiemer/colossus/commits/f73536addcb083173bbbe3adb9021da45cac1bbe https://pypi.org/project/colossus/ from the WinPython command interpreter: pip install colossus

>python 
>>>from colossus.tests run import run_tests
Ran 87 tests in 17.344s

Astropy | Astrophysics source code library | astropy tutorials, Jupyter notebooks on github |

Cosmology Collaboration Wikis: https://cmb-s4.org/wiki/index.php/UChicago-2020:_Cosmology_with_CMB-S4 (MediaWiki) Planck Legacy Archive: https://wiki.cosmos.esa.int/planck-legacy-archive/index.php/Planck_Collaboration https://wiki.cosmos.esa.int/planck-legacy-archive/index.php/Main_Page (MediaWiki) NRAO: https://safe.nrao.edu/wiki/bin/view/Main/WebHome (public wiki, separate staff wiki) MCP: https://safe.nrao.edu/wiki/bin/view/Main/MegamaserCosmologyProject TASI: https://sites.google.com/a/colorado.edu/tasi-2018-wiki/home

Hashtags: #cosmology #physics