Cosmology Lecture 06

The Bright Side, continued

$matrix}"): {\displaystyle \begin{matrix} Gauge\ Bosons & spin & charge & mass \\ \gamma & 1 & 0 & 0 & (carries\ electroweak\ force) \\ w^\pm & 1 & \pm 1 & 80.4 GeV & (carries\ electroweak\ force) \\ Z^0 & 1 & 0 & 91.2 GeV & (carries\ electroweak\ force) \\ gluons & 1 & 0 & don’t\ know & (carries\ strong\ force) \\ Higgs & 0 & 0 & >114.4GeV \\ graviton & 2 & 0 & 0 \\ \end{matrix} \,\!$
${\displaystyle {\begin{matrix}Baryons&quark\ content&charge&mass&lifetime\\proton&uud&+1&938.07003MeV&\geq 10^{32}yrs\\neutron&udd&0&939.56536MeV&885.7sec\\\Lambda &uds&0&1.11GeV&10^{-10}sec\\\Sigma ^{+,0,-}&uus,uds,dds&+1,0,1&1.2GeV&10^{-10},10^{-19}\\\Xi ^{0}&uss&0&1.3GeV&10^{-10}\\\Xi ^{-}&dss&-1&1.3GeV&10^{-10}\\\Omega ^{-}&sss&-1&1.67GeV&?\\\end{matrix}}\,\!}$
${\displaystyle {\begin{matrix}Mesons(q{\bar {q}},\ Spin\ 0)&charge&quark&mass&lifetime\\\Pi ^{\pm }&\pm 1&u{\bar {d}},d{\bar {u}}&140MeV&10^{-8}s\\\Pi ^{0}&0&u{\bar {u}},d{\bar {d}}&135MeV&10^{-16}s\\K^{\pm }&\pm 1&u{\bar {s}},{\bar {u}}s&494MeV&10^{-8}s\\(Spin\ 1)\\J,\Psi &0&c{\bar {c}}&3.1GeV&10^{-20}\\\Upsilon &0&b{\bar {b}}&9.5GeV&10^{-20}\\\end{matrix}}\,\!}$
${\displaystyle {\begin{matrix}Fundamental\ Interactions&Gravity&Weak&EM&Strong\\Classical&Newton/Einstein&-&Maxwell&-\\Quantum&?&V-A\ Theory(flawed)&QED,Gauge&QCD[SU(3)]\\\end{matrix}}\,\!}$

Useful Scales/Conversion tricks

In particle physics, ${\displaystyle E\sim {1 \over length}}$, because ${\displaystyle \hbar c=1}$ (which had units ${\displaystyle E \over cm}$). In condensed matter physics, ${\displaystyle E\sim T}$.

The Planck mass is the mass scale at which the effect of gravity and quantum effects are comparable. We can get an estimate of the Planck mass by setting the Schwarzschild radius (${\displaystyle R_{sch}={2Gm \over c^{2}}}$) equal to the Compton wavelength of a particle (${\displaystyle \lambda ={hc \over mc^{2}}={2\pi \hbar c \over mc^{2}}}$). Dropping our constants (2’s, ${\displaystyle \pi }$’s), we get:

${\displaystyle {Gm_{planck} \over c^{2}}\sim {\hbar c \over m_{planck}c^{2}}\,\!}$
${\displaystyle m_{planck}={\sqrt {\hbar c \over G}}\approx 1.2\cdot 10^{19}{GeV \over c^{2}}\,\!}$

Another number of interest is the energy density in ${\displaystyle \Lambda }$. We know

${\displaystyle \Omega _{0,\Lambda }\equiv {\rho _{\Lambda } \over \rho _{crit}}\approx 0.7\sim 1\,\!}$
{\displaystyle {\begin{aligned}\rho _{\Lambda }\sim \rho _{crit}&=1.88\cdot 10^{-29}h^{2}{g \over cm^{3}}\\&=1.054\cdot 10^{-5}h^{2}{GeV \over cm^{3}}\end{aligned}}\,\!}

Converting ${\displaystyle {GeV \over cm^{3}}}$ to ${\displaystyle GeV^{4}}$, we get:

${\displaystyle \rho _{\Lambda }\sim \rho _{crit}\sim 10^{-46}GeV^{4}\,\!}$
${\displaystyle {\rho _{\Lambda } \over m_{planck}^{4}}\approx 10^{-122}=worst\ number\ in\ physics\,\!}$