INFLATION. - EARLY EXPONENTIAL PHASE OF GROWTH OF SCALE FACTOR (after T ~ TGUT ~ GeV)

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1 INFLATION - EARLY EXPONENTIAL PHASE OF GROWTH OF SCALE FACTOR (after T ~ TGUT ~ GeV) -Phenomenologically similar to Universe with a dominant cosmological constant, however inflation needs to end while exponential scale factor growth in a Λ-dominated phase does not need to end (de Sitter solution of Friedmann eqs.) - After inflation the Universe evolves as in standard Big Bang model (baryogenesis, nucleosynthesis, recombination etc.. take place in the usual way). Not one but many inflationary models (no quantum theory of gravity yet). Common aspect is the assumption that inflation is generated via energy release from a scalar field (inflaton) that initially dominates energy density of the Universe, but differ in the way inflationary growth is realized via the scalar field dynamics. A scalar field φ initially in a false vacuum state (V(φ) > 0) decays to true vacuum (V(φ) = 0) via spontaneous symmetry breaking (SBB). Idea analogous to SBB of Higgs field to give masses to bosons and leptons. After inflation energy density of matter and radiation (~ 1/a 3 with a grown exponentially) nearly zero but temperature can be high because of energy release by inflaton ( reheating ). Reheating necessary otherwise temperature too low for creation of particles of standard models (this also implies inflation needs to have an end). Rehating realized as inflaton undergoes phase transition from false to true vacuum.

2 PROBLEMS THAT INFLATION SOLVES: 1 HORIZON PROBLEM Observable Universe homogeneous and isotropic on large scale: CMB shows nearly uniform temperature on the entire sky, implies different regions causally connected, i.e. they were able to reach thermal equilibrium by exchanging photons (electronphoton scattering). However particle horizon of fundamental observer today smaller than scale of observed CMB homogeneity if we assume standard cosmology! (particle horizon = largest comoving distance from which signal can be received today by observer) -! need way to inflate particle horizon some time before surface of last scattering to enforce causal connection and explain homogeneity of CMB (does not matter if regions of the sky cannot be in causal contact today). 2 FLATNESS PROBLEM Small deviations from critical density today imply Universe had to be flat at Planck time -! fine tuning of ICs (or else if it is exactly unity today was always so but this is special IC) Need way to show that early Universe is flat almost from the start no matter what was its IC.

3 3 MONOPOLE PROBLEM Grand unified theories (GUT) predict magnetic monopoles (massive particles with net magnetic charge) as a result of SBB at T GUT ~ GeV (details depend on GUT model). Because they are produced so early and freeze-out so early the predicted energy density in monopoles today is Ω mp ~ 5 x >> energy density of matter, radiation and Λ today, contrary to all evidence of a flat Universe --! need way to dilute them readily. 4 Structure Formation Problem (if gravitational instability is the correct theory for structure formation, i.e. gravity amplifies small perturbations/inhomogeneities in the initial conditions) The largest gravitationally bound structures, galaxy clusters, have sizes of ~ 10 Mpc and gravitational binding energies per unit mass Ε/c 2 ~ 10-5.Parts of a cluster needed to be in causal contact at some point which can happen only when the horizon grows large enough, only at z < But at this redshift there is no way in to achieve these high binding energies (related to typical energy density of matter background that has decreased significantly already). Note: particle horizon increases with time hence the constraint in redshift. --! need a way to start the perturbations much earlier but inflate them fast so that they acquire a much larger scale very early and yet they are still causally connected (related to inflating particle horizon)

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5 INFLATIONARY MODELS -Different inflationary models characterized by choice of V(f) and by its eventual coupling to thermal bath (no such coupling in chaotic inflation). -Inflaton decay to true vacuum (V(phi) = 0) describes a phase transition when temperature coupling present (inflation and then transition to true vacuum occur as a function of temperature). -In different models phase transition can be first order or higher order. If phase transition first order phase transition via quantum tunneling, change of V(phi) discontinous -! from slow-roll condition inflation has to end immediately after tunneling (field does not roll towards true vacuum, rather abrupt change) -Old inflationary model (Guth 1981) is first order. True vacuum phase appears via nucleation of bubbles in sea of false vacuum that expands exponentially. -- Loss of energy within bubbles (V(f) has decayed to true vacuum) compensated by increase of energy at bubble walls (surface tension, sharp boundary of bubbles reflects first order of transition). -- Energy released when bubbles collide ( reheating ), which accelerates decay to True vacuum -- Inflation ends when bubble s volume filling factor is unity (V(f) in True vacuum state everywhere. But a long enough inflation needs slow bubble nucleation and few collisions, fairly natural condition in exponentially expanding background

6 Old inflation New inflation Veff = V (φ) + ½ λ ο T 2 φ 2 reheating given by damped oscillations of inflation when it reaches true vacuum minimum Field initially in equilibrium with radiation at temperature T >> Tc. Inflation begins when T <~ Tc, ρ ~ V. Initially <φ>=0, at false minimum, i.e. inflaton begins to dominate energy density. In (a) quantum tunneling needed because potential develops maximum,in (b) not needed (smoother potential change, higher order transition)

7 -- Graceful exit problem: in order to reheat enough and avoid leftover dishomogeneities (CMB uniform!) need high collision rate between bubbles (high rate of nucleation via tunneling), but this means inflation is short-lived -! Cannot get enough e-foldings to explain horizon problem+ enough rehating at the same time! Otherwise with low-enough tunneling rate inflation continues longer, but then never back to homogeneous Hot Big Bang model! New inflation Solves graceful exit problem by postulating (smooth) second order phase transition, i.e. mapping of V(φ) as a function of T(t) continuous function. Consequences: -No quantum tunneling needed because no maxima develop in V(φ) -Decay to true vacuum continuous in all domain >> bubble size in old inflation so guarantees horizon problem solved plus homogeneous state after inflation guaranteed (observable Universe within single domain!). -Reheating to temperature T ~ Ti (temperature of radiation at the onset of inflation) via decay of φ to photons and other particles). But fine tuning + conceptual problems: Realised with: V(φ) = ½ λ (φ 2 σ 2 ) 2 (Coleman-Weinberg potential) -- Requires φ= + σ to reach true vacuum and φi << σ to have enough e-foldings (slow-roll for as long as possible), while thermal fluctuations of φ due to coupling with radiaton field imply they are of order ~ σ initially. -- Slow-roll conditions (on second derivative of V) imply σ >> m pl, unnatural condition

8 Possible way-out: Chaotic inflation (Linde 1986 also stochastic/ethernal inflation when initial quantum fluctuations of φ taken into account) -No phase transition, no initial thermal bath hence no coupling with it or any other component of matter/energy -Only scalar field that slow rolls, with V(φ) = ½ mφ 2 - Initial stochastic distribution of φ values,inflation only occurs where false vacuum distant enough from true vacuum --! multi-verse, i.e. many domains as in new inflation but set in ICs rather than result of phase transition, so natural to start at Planck time -Our Universe arises in one of those domains that have successful inflation (i.e. domain inflates beyond Hubble radius). No inhomogeneity problem in single domain But problem even here -- need mass scale of the potential m << m pl at Planck time, implied by requiring enough e-foldings -! Condition not natural! Also, what about monopole problem, if inflation starts too early might also finish too early (t pl << t GUT ), another inconsistency/fine tuning?