Hubble Constant
2nd:
CMB --> Hubble constant
Wang Sen
How to derive H_0 from CMB

phidutial model -- calibrated in low z



https://www.physicsforums.com/threads/using-wmap-to-measure-the-hubbles-constant.552885/
Using WMAP to measure the Hubble's constant


https://arxiv.org/abs/1910.09881
Measuring the Hubble constant from the cooling of the CMB monopole

https://www.quora.com/How-is-Hubble-constant-calculated-from-Cosmic-Microwave-Background-Radiation-measurements





Baryon Acoustic Oscillation

scale factor a=1/(1+z), number density of photons
enerfy density, Stefan-Boltzmann law
T propto 1/a, propto (1+z)
--> T of recombination 3000K, --> z~1100

define sound speed, c_s = c/sqrt(3(1+R)), 光子扰动传播的速度
流体力学
R = 3\rho_b/4\rho_r

阻尼对波的传播速度有没有影响





1st:
Li Xiao
Supervisor Prof. Cai Zheng

It set the scale for all cosmological distance and times
It help to determine other cosmological parameter

Methods:
Gravitational Lensing
Type Ia SNe - Standard candle
and many more
(a review paper, )


history

2001 HST Key project, 10% uncertainty
2018 Plank collaboration: 67.4 \pm 0.5
2019 SHOES Project 74 \pm 1.42

Time delay cosmology
Lens equation

angular diameter distance is related to r, and thus H_0
D_d, D_s how to compute?

low z:
cz = H_0 d

high z:
integrate, H as a function of z
H(z) = sqrt{\Omega_M(1+z)^3+\Omega_{^}}/H_0  ,for flat univese

6 lens systems now are available (what's the z of lensing galaxies of those 6 systems, low z? )
	1% -- 40 lenses are needed


late-universe measurement


Explosion of carbon-oxygen white dwarf
peak luminosity is related to the shape of the light curve


2 methods:
Stretch method
Multicolor light curve shapes (MCLS)

sigma-tension


hubble tension - observational effect
examine potential alternatives to the standard ^CDM model