Interface of high-energy particle physics with cosmology and astrophysics: ultra-high-energy cosmic rays, extensive air showers, astrophysical neutrinos (IceCube), gamma-ray astronomy (HESS, CTA, Fermi-LAT), dark-matter direct detection…
astroparticle-physics
Cosmic-ray primary spectrum: dN/dE ∝ E^{−2.7} below knee, E^{−3.0} above
All-particle cosmic-ray differential flux follows a broken power-law. Below the 'knee' (~3·10¹⁵ eV = 3 PeV), dN/dE ∝ E^{−2.7}: galactic…
GZK cutoff: E_th = (m_Δ² − m_p²)/(4·E_CMB) ≈ 5·10¹⁹ eV via p + γ_CMB → Δ⁺ → pπ⁰
Greisen-Zatsepin-Kuzmin (1966) cutoff: ultra-high-energy protons travelling through the CMB photon bath (T = 2.725 K, typical ω ≈ 6·10⁻⁴…
Heitler EAS toy: N_max = E₀/E_c, X_max = X₀·log₂(E₀/E_c) for EM cascade
Heitler's toy model (1954) for electromagnetic extensive air showers: after each splitting length X₀ = ln(2)·X_r (one radiation length…
Neutrino astronomy (IceCube): diffuse astrophysical νₑ,ν_μ,ν_τ at TeV-PeV
IceCube (2013+) detects astrophysical neutrinos at TeV-PeV energies via Cherenkov light from secondary muons (tracks) and…
Dark-matter direct detection: WIMP nuclear recoil, rate R ∝ ρ_χ·σ·⟨v⟩/m_χ
WIMPs from the galactic halo (local density ρ_χ ≈ 0.3-0.4 GeV/cm³, v̄ ≈ 220 km/s Maxwell-Boltzmann) scatter elastically off target nuclei…
Axion haloscope: resonant cavity → microwave photon via B·a coupling
Sikivie-style axion haloscope (1983): halo dark-matter axions a with mass m_a ~ μeV convert into microwave photons of the same frequency ν…
Fermi 2nd-order + 1st-order DSA: power-law spectrum from diffusion-advection FP
Fermi diffusive-shock-acceleration (DSA) framework — the canonical astrophysical mechanism for producing non-thermal power-law particle…
Liouville: cosmic-ray phase-space density f(x,p) conserved along trajectories
Liouville phase-space framework — the Hamiltonian-mechanics basis for cosmic-ray propagation theory and phase-space conservation (Liouville…
Blandford-McKee GRB fireball: self-similar Γ²(R) ~ E/(ρc²R^(3-k)) blast wave
Blandford-McKee framework — the canonical relativistic self-similar solution for an ultrarelativistic blast wave expanding into a uniform…
Fermi DSA: s = 1 - log(P_esc)/log(β_ratio); s=2 for strong r=4 shock
Sympy-exact symbolic witness of the Fermi-DSA spectral-index formula and its strong-shock limit. Setup: P_esc, β_ratio, r sp-symbols…
Liouville: Jacobian det(∂(q,p)/∂(q₀,p₀))=1 for SHO Hamiltonian flow; df/dt=0
Sympy-exact symbolic witness of Liouville's phase-space-volume theorem using the harmonic-oscillator Hamiltonian flow as minimal example. …
Blandford-McKee: Γ²(R) = 17E/(8πρc²R³); R_dec ~ E^(1/3); Γ²(2R)/Γ²(R) = 1/8
Sympy-exact symbolic witness of the Blandford-McKee self-similar blast-wave scaling. Setup: E, ρ, c, R sp-symbols positive. Uniform-ISM…
DM rotation curves (Rubin 1978)
Vera Rubin 1978 flat galactic rotation curves v(r) ~ const at large r imply spherical halo M(r) ~ r; first compelling DM evidence; modern…
Bullet cluster (Clowe 2006)
Clowe 2006 1E0657-558 bullet-cluster: weak-lensing mass offset from X-ray gas peak; kinematically-segregated DM during merger; rules out…
CMB Planck 2018 cosmological parameters
Planck 2018: H0 = 67.4 +/- 0.5 km/s/Mpc, Omega_m = 0.315, Omega_b h^2 = 0.022; tension with local SH0ES H0 = 73.0 +/- 1.0 = Hubble-tension…
Primordial GW (LiteBIRD prospects)
BICEP-Keck 2021 r < 0.036 95% CL; LiteBIRD 2030 target r ~ 10^-3 from B-mode CMB polarization; would measure inflation-energy-scale.
Axion haloscope (Sikivie 1983)
Sikivie 1983: axion-photon coupling g_agg in B-field cavity gives detectable RF signal at m_a c^2; ADMX 2018-2024 excluded m_a 2.66-3.31…
Inflation (Guth 1981 / Linde-Albrecht-Steinhardt 1982)
Guth 1981 + Linde 1982 + Albrecht-Steinhardt 1982: exponential expansion solves horizon + flatness + monopole; slow-roll potential V(phi)…
Hess (1912)
V Hess 1912 (Nobel 1936) cosmic-ray balloon-flights; modern modern foundational text + AMS-02 ISS + Pierre-Auger ground-array UHECR.
GZK cutoff (1966)
K Greisen-Zatsepin-Kuzmin 1966 GZK 5×10^19 eV; modern modern Pierre-Auger 2008 + ARA + GRAND + 2024 photo-pion-suppression confirmed.
Auger shower (1938)
P Auger 1938 extensive-air-shower; modern modern foundational text + 1991 Fly's Eye 'Oh-My-God' 3×10^20 eV + Telescope-Array.
IceCube (2013)
IceCube 2013 first PeV-astrophysical-neutrino + 2017 TXS 0506+056 blazar-association; modern modern KM3NeT + Pacific-Trident + IceCube-Gen2.
Direct DM (Goodman-Witten 1985)
M Goodman-E Witten 1985 dark-matter-recoil; modern modern XENONnT + LUX-ZEPLIN + DarkSide-50 + 2024 SI-WIMP exclusion 10^-49 cm².
Fermi-LAT (2018)
Fermi-LAT 2018 + 2024 dwarf-spheroidal indirect-DM + galactic-center-excess; modern modern HESS + CTA + DAMPE + 2024 KM3NeT.