The High Redshift Universe Reprise Planck time Particle physics stuff Inflation Element creation All in first 1000 seconds Bit of a snooze for the next 400000 years Atoms form from the ions and electrons => microwave background Dark ages 0.5Gyr before first stars (z~15)
Inflation Liddle chapter 13 Outline Problems with standard big bang model Inflation as a solution Beyond inflation: the very early universe
Problems with big bang Breaks into 3 broad categories (Liddle) and some minor ones Flatness why is Ω 0 ~ 1? Horizon why is CMB smooth across the sky? Relics from the past where are the heavy relic particles? Where do the fluctuations come from? Where does the photon-to-baryon ratio come from? What happens before Planck time (ie origin)?
Flatness Friedmann equation: can be written as: Rewrite:
Flatness Ω total = Ω stuff + Ω Λ Observationally Ω total ~ 1±0.1 Matter dominated: a t 2/3 and H 1/t Radiation dominated: a t 1/2 and H 1/t Ω total 1 t 2/3 a (matter) Ω total 1 t a 2 (radiation) Both => Ω total 1 grows with time
Flatness Ω total 1 a (matter) Ω total 1 a 2 (radiation) Ω total ~ 1±0.1 Recombination, Ω total 1 ~ 0.001 Matter-radiation equality, Ω total 1 ~ 0.000004 Nucleosynthesis, Ω total 1 ~ 10-14 So if Ω total 1 ~ 0.1 now must have been <10-60 in the very early universe Called a fine-tuning problem
Horizons CMB looks same in all directions. CMB formed at decoupling when horizon ~ 1-2 degrees now on sky => Patches larger than 1-2 degrees should not be in thermal equilibrium So why is CMB temperature same all over sky?
Funny particles All unification models for particle physics predict the presence of heavy particles that should be present in the early universe. Magnetic monopoles, supersymmetric heavy particle (photinos etc) Their mass scales with the energy at which unification occurs Would make universe matter dominated in very early stages And we don t see any
Fluctuations There is no route within standard big bang to create fluctuations of the right size to match observed structure and CMB, nor to make them roughly homogeneous
Baryogenesis Chapter A4 of Liddle discusses this topic In very early universe, when k B T >> m p c 2 : p + p <=> 2γ We assume the photon-to-baryon ratio comes from the point where this reaction froze out and protons and anti-protons annihilated. So why are we left with any protons?
Origin of the Universe Why did it start? What happened before the Planck time?
Solution (?): Inflation Inflation defined as any point when universe is accelerating a > 0 => acceleration equation gives p < ρc 2 /3 Note, p = ρc 2 /3, gives back same behaviour as free expansion Cosmological constant satisfies condition
Particle Physics Cause of inflation believed to be due to symmetry breaking in particle physics. Happens at energy of grand unification ~ 10 15 GeV
Particle Physics As temperature drops equilibrium stops (just like weak interaction or recombination) Particle physics predicts a unified force that behaves like cosmological constant as symmetry breaks down. Ends when fully broken Original inflation viewed this as a transition from a a false vacuum (high energy symmetric state) to a true vacuum at lower potential energy. The energy difference is injected into the universe to cause the expansion, and create all the particles we see.
Inflation: Flatness Inflation: ah increases with time Ω total 1 => 0
Inflation: Particles All particles in very early universe inflated away Density of particles drops to zero The energy deposited into universe at end of inflation ( reheating ) restarts particle production, giving the stuff we actually see around us
Inflation: Fluctuations The visible universe formed from tiny, ~quantum, space Initially has quantum fluctuations Particles created & destroyed allowed by Heisenberg uncertainty principle Inflation magnifies these differences (duration < t in Heisenberg) We re made from these initial quantum fluctuations
Cosmological Constant Consider Λ
Cosmological Constant 10 15 Gev ~ 10-36 seconds H GUT = (Λ/3) ~ 1/t GUT Suppose inflation lasts from 10-36 to 10-34 seconds a final ~ a GUT exp(h GUT (10-34 10-36 )) a final ~ a GUT exp(99) ~ 10 43 a GUT Clearly solves flatness problem since in this case Ω 1 a 2 ~ 10 86
Inflation: Horizons Only consider case of Λ:
Inflation: Horizons Cosmological constant => ~ constant horizon size Visible universe shrinks compared to what we could see before since universe itself expands => Regions that used to be in causal contact become disconnected Solves horizon problem
Inflation: Remaining problems No working Grand Unified Theory (GUT) model as yet Doesn t explain baryogenesis Doesn t explain origin
Dark Energy Early universe: inflation from break down of GUTs. Energy scale ~ 10 16 GeV Late universe: dark energy from what? Energy scale ~ k B T ~ 10-3 ev No known cause in terms of current particle physics. Would require an unsuspected low energy field breaking symmetry
Classical breakdown Early enough in universe classical physics must breakdown when? Planck had suggested only need c, G and h to define fundamental scales Later realised these form only combination that can be important for early universe Only one possible combination:
Planck time and earlier Planck time ~ 10-44 s and length ~ 10-35 m Earlier than inflation Need theory of quantum gravity (superstrings? M- branes? ) Nobel prize up for grabs if you can solve this one! Proper theory needed to make most of the standard model problems go away, and explain what causes inflation, and why it works out just right
Big Bang success or failure? Everything in standard big bang model back as far as nucleosynthesis appears to work Everything beyond that is speculative and requires better physical models for behaviour at very high energies So mostly yes with large caveats Still better than any of the alternatives for the late universe
Summary Standard model can t explain flatness of universe isotropy on super horizon scales at recombination lack of relic particles origin of CMB fluctuations Inflation naturally solves all of these at the cost of invoking plausible but unproven physics Makes it hard to understand dark energy if both it and inflation have common cause
Summary Classical physics should breakdown completely before Planck time We have no theory for creation of universe, or for what physics occurs before Planck time
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