Past exam of the particle Astrophysics course of the University of Cambridge / 2014 / Paper 1 / 3

Supersymmetry relates bosons and fermions whose spins differ by one-half. Broken supersymmetry can soften Higgs-mass sensitivity and improve gauge-coupling unification in suitable spectra; neither feature establishes that nature realizes it. Collider searches look for squarks/gluinos or electroweak superpartners through jets/leptons, missing transverse momentum and appropriate cascade-decay kinematics. Null searches constrain specified masses and branching fractions, with weaker reach for compressed or nonstandard spectra.

With conserved R-parity, superpartners are pair-produced and the lightest supersymmetric particle is stable. A neutral weakly coupled lightest state, such as a neutralino, can be a dark-matter candidate. Its thermal abundance follows annihilation freeze-out when $n_{\chi }⟨\sigma v⟩\sim H$; later expansion dilutes number density while leaving the comoving relic abundance approximately fixed. Coannihilation and resonances can change the result. Recoil searches and cosmic-ray/photon searches test complementary couplings.

Cosmology also constrains unstable long-lived relics through nucleosynthesis and reheating; not every supersymmetric spectrum gives the observed dark matter. R-parity is an additional assumption: supersymmetry by itself does not guarantee a stable neutral relic. Laboratory discovery and a matching cosmological abundance would both be needed.

Cosmic inflation is accelerated expansion with decreasing comoving Hubble radius, $\ddot{R}>0$ or ${ϵ}_H=-\dot{H}/H^2<1$. It can make the observed region causally connected before inflation and dilute spatial curvature or unwanted relics. A slowly rolling scalar has energy and pressure ${\rho }_{\varphi }={\dot{\varphi }}^2/2+V$, $P_{\varphi }={\dot{\varphi }}^2/2-V$ in natural units. Potential domination gives near-exponential expansion; ending inflation and reheating must create the hot radiation era.

For a canonical single scalar with reduced Planck mass $M_{\mathrm{Pl}}$,Quantum fluctuations stretched to cosmological scales seed density perturbations. Tests include the scalar spectral tilt, acoustic coherence, spatial curvature, non-Gaussianity and tensor-induced CMB B-mode polarization. Foregrounds and lensing must be separated from primordial tensors. A tensor non-detection does not exclude all inflation; tilt and tensor consistency predictions depend on the model. Approximate flatness and near-scale-invariant fluctuations support the framework but do not uniquely determine a potential or prove an exact de Sitter phase.

Baryogenesis dynamically creates a baryon–antibaryon imbalance rather than assuming it as an initial condition. Under the usual local relativistic assumptions, the Sakharov conditions are baryon-number violation, C and CP violation, and departure from thermal equilibrium. Without the last condition, inverse reactions and equilibrium constraints cancel a net asymmetry; CP-conjugate rates must differ in a channel with the required number violation.

In heavy-boson decay baryogenesis, heavy particles decay through baryon-violating channels with CP-asymmetric branching. Expansion makes decays/inverse decays fall out of equilibrium; washout reactions must then become ineffective. Inflation would dilute an earlier asymmetry, so the generation/reheating history matters.

In leptogenesis, out-of-equilibrium Majorana-neutrino decays first produce lepton number. Electroweak sphalerons violate $B+L$ while preserving $B-L$ and convert part of the surviving asymmetry to baryon number. In the minimal Standard Model chemical-equilibrium limit, $B=28(B-L)/79$; the coefficient depends on particle content and equilibrated interactions. Electroweak baryogenesis is another possibility if CP violation and a sufficiently strong nonequilibrium phase transition are supplied. The Standard Model's observed parameters do not by themselves furnish an adequate conventional electroweak scenario. Each proposal must quantitatively match the relic asymmetry and avoid washout.