GitHub - yaojian95/yaojian95.github.io: Jian Yao's personal website

Welcome to my personal page. It stays at pikipiki.

The mostly recommended references for Cosmology can be found at Hannu's webpage, especially on CMB physics

Miscellaneous

The trace of the metric is always just $\delta_\mu^{\mu} = d$ , the number of spacetime dimensions.

The stress-energy tensor is defined as $T^{\mu \nu} \equiv \frac{2}{\sqrt{-g}} \frac{\delta S_{\mathrm{pp}}}{\delta g_{\mu \nu}}$

What do you mean by Solenoidal vector? In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field) is a vector field v with divergence zero at all points in the field: A common way of expressing this property is to say that the field has no sources or sinks.
Volume element

$g=det(g_{\mu\nu})\rightarrow det\left(g_{\tau\lambda}\frac{\partial x^{\tau}}{\partial x'^{\mu}}\frac{\partial x^{\lambda}}{\partial x'^{\nu}}\right)=g\,\cdot\,(|J|^{-1})^2=g'$

$d^4x\rightarrow det\left(\frac{\partial x'}{\partial x}\right)d^4x=|J|\,d^4x=d^4x'$

$d^4x\sqrt{-g}\quad\rightarrow\quad d^4x\sqrt{-g}|J|\cdot|J|^{-1}=d^4x\sqrt{-g}$

The Post-Newtonian formalism is nothing but a Taylor expansion in powers of 1/c.

$\begin{array}{l} L=-m c^{2}\left[1 \frac{\phi_{\mathrm{N}}}{c^{2}}-\frac{\phi_{\mathrm{N}}^{2}}{2 c^{4}} \frac{\phi_{1 \mathrm{PN}}}{c^{4}}-\frac{v_{i} \omega_{1 \mathrm{PN}}^{i}}{c^{4}} \right. \left.-\frac{1}{2} \frac{v^{2}}{c^{2}} \frac{\phi_{\mathrm{N}}}{c^{2}} \frac{v^{2}}{c^{2}} \mathcal{O}\left(\frac{1}{c^{6}}\right) \mathcal{O}\left(\frac{1}{c^{7}}\right)\right] m \end{array}$

\begin{array}{l}
L=-m c^{2}+\frac{1}{2} m v^{2}-m \phi_{\mathrm{N}}+\left(1 \mathrm{PN} \text { corrections of order } c^{-2}\right)+ \\
+\left(2 \mathrm{PN} \text { corrections of order } c^{-4}\right)+\left(2.5 \mathrm{PN} \text { corrections of order } c^{-5}\right)
\end{array}

ORCID

Name		Name	Last commit message	Last commit date
Latest commit History 67 Commits
Base.html		Base.html
CMB_physics.html		CMB_physics.html
CNAME		CNAME
Cl_today.jpg		Cl_today.jpg
Euler_equation.html		Euler_equation.html
Fisher-matrix-guide.pdf		Fisher-matrix-guide.pdf
Inflation.html		Inflation.html
Monopole_dipole.jpg		Monopole_dipole.jpg
Non_gaussianity.html		Non_gaussianity.html
Outreach.html		Outreach.html
Power_spectrum_estimation.html		Power_spectrum_estimation.html
README.md		README.md
Tools.html		Tools.html
_config.yml		_config.yml
better_r.jpg		better_r.jpg
brandenberger2008.pdf		brandenberger2008.pdf
delta.svg		delta.svg
logo.png		logo.png
lower_variance_purified_BB.jpg		lower_variance_purified_BB.jpg
map_making.html		map_making.html
myscripts.js		myscripts.js
peaks.svg		peaks.svg
styles.css		styles.css
suggested_papers.html		suggested_papers.html

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Welcome to my personal page. It stays at pikipiki.

The mostly recommended references for Cosmology can be found at Hannu's webpage, especially on CMB physics

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