Cosmology

What are the three equations for Orbital motion?

1) F_centrifugal = F_Gravity

2) mV²/R = GMm/R²

3) V² = GM/R

What is the Friedmann equation and it’s derivation?

sS

What is the Planck Era, along with the temperature and time frame?

T>10³²K, t<10^-44s

Above the Planck temperature the four fundamental forces are assumed to operate on the same scale. General Relativity no longer provides an appropriate description of gravity and a theory of Quantum Gravity is needed. As we don’t yet have such a theory, we can’t say any more about this epoch.

What is the Quark Era, along with the temperature and time frame?

(10³² K > T > 10²⁸ K), (10^-44s < t < 10^-4 s)

This epoch begins when gravity separated from the other forces and can thenceforth be treated by GR. At the highest temperatures a GUT is required to describe the interaction of the quarks and leptons as the strong, weak and electromagnetic interactions are still unified. A process called “baryogenesis” is presumed to occur at a temperature around 10²⁸ K which results in a very small excess of quarks over anti quarks (3 parts in 10⁹). At this point the strong interaction separated from the weak and electromagnetic interactions, from that point on being described by QCD and the electroweak theory. At 10¹² K a phase transition is believed to occur with the quarks becoming bound into baryons and mesons, and their antiparticles.

What is the Lepton Era, along with the temperature and time frame?

(10¹²K > T > 10¹⁰K), (10^-4s < t < 1s)

During this epoch the Universe is full of leptons (e⁺/e^- ), hadrons (n/p) and neutrinos (𝑣/𝑣̅) all interacting through the weak and electromagnetic interactions. These interactions ensured that the plasma was in good thermodynamic equilibrium. Towards the end of this period the neutrinos (which don’t feel the electromagnetic interaction) decoupled as the weak interaction strength was falling very rapidly with decreasing temperature.

What is the Photon dominated era, along with the temperature and time frame?

10¹⁰ < T < 16,500K, 1s < t < 10¹¹s

As the temperature fell below the equivalent of 1MeV the photons were no longer able to create e⁺-e^- pairs and the electrons and positrons began annihilating, injecting more photons into the photon background. Between 10 K and 10 9 K primordial nucleosynthesis occurred and created the light elements (H, He, and Li).

What is the matter dominated era, along with the temperature and time frame?

16,500K > T > 2.725K, 10¹¹s < t < ~14 billion years

As the Universe expands, the radiation energy density falls off faster than the matter density and a point is reached where the expansion becomes dominated by matter. At T ~ 3000K atoms form creating neutral matter and the photons are free to propagate through the Universe. This is the last point at which matter and radiation interacted strongly. The matter starts to clump to form the structures that we see today. The radiation is stretched by the expansion with the black body spectrum cooling over time until it reaches the present temperature of 2.725K

What are the two ways to view Λ? (The cosmological constant)

• As an energy permeating the whole of space

• As a fluid filling all of space

Give all the R against t graphs for k = -1, 0, 1 and Λ < 0, Λ = 0, 0 < Λ < Λ_E, Λ = Λ_E, A > Λ_E?

GRaph