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Density Perturbations in an Inflationary Universe: 

Density Perturbations in an Inflationary Universe Guth andamp; Pi (1982) Bardeen, Steinhardt andamp; Turner (1983) Katie Mack

Density Perturbations in an Inflationary Universe: 

Density Perturbations in an Inflationary Universe Guth andamp; Pi (1982) Bardeen, Steinhardt andamp; Turner (1983) Katie Mack 1982: Michael Jackson releases Thriller

Outline of Talk: 

Outline of Talk Basics of inflation (summary of Sudeep’s talk) Varieties of inflationary models Guth’s original model New inflation Chaotic inflation Density Perturbations Inflationary Timeline Conclusion

Inflation: 

Inflation Proposed by Guth in 1981 to solve: Horizon problem Flatness problem Basic idea: universe undergoes exponential expansion in early history

Inflation: 

Inflation Horizon Problem Problem: correlated regions in CMB are outside each others’ horizons Solution: regions were expanded out of each others’ horizons (from Sudeep’s talk)

Inflation: 

Inflation Flatness Problem Problem: Total density parameter Ω improbably close to 1 (universe very close to flat) Solution: Exponential expansion flattens universe (from Sudeep’s talk)

Varieties of Inflationary Models: 

Varieties of Inflationary Models Guth’s original scenario Phase transition: Bubbles of true vacuum form in false vacuum background Bubbles coalesce to reheat universe Problem Space between bubbles expands exponentially -andgt; no coalescence Universe inflates forever ('graceful exit' problem)

Varieties of Inflationary Models: 

Varieties of Inflationary Models New Inflation (this scenario is used by Guth andamp; Pi and B,Sandamp;T) Coleman-Weinberg potential (chosen for super-symmetry breaking in GUT) Scalar field starts at local minimum (false vacuum) Local minimum is separated from global minimum (true vacuum) by temperature-dependent barrier Unstable equilibrium as T -andgt; 0 : field slowly rolls toward true vacuum state Whole universe can be contained in one bubble Reheating occurs when field oscillates about true minimum T andgt; 0 T = 0 V(φ) φ φ V(φ)

Varieties of Inflationary Models: 

Varieties of Inflationary Models New Inflation (this scenario is used by Guth andamp; Pi and B,Sandamp;T) Coleman-Weinberg potential (chosen for super-symmetry breaking in GUT) Scalar field starts at local minimum (false vacuum) Local minimum is separated from global minimum (true vacuum) by temperature-dependent barrier Unstable equilibrium as T -andgt; 0 : field slowly rolls toward true vacuum state Whole universe can be contained in one bubble Reheating occurs when field oscillates about true minimum T andgt; 0 T = 0 V(φ) φ φ V(φ) Problem: Gives incorrect magnitude of density perturbations

Coleman-Weinberg Potential: 

Coleman-Weinberg Potential

Varieties of Inflationary Models: 

Varieties of Inflationary Models Chaotic Inflation (currently favored model) Slow-roll of potential achieved with 'drag' term in equation of motion Powerlaw potential Production of particles (reheating) occurs as field oscillates about its minimum

Varieties of Inflationary Models: 

Varieties of Inflationary Models Chaotic Inflation (currently favored model) Slow-roll of potential achieved with 'drag' term in equation of motion Powerlaw potential Production of particles (reheating) occurs as field oscillates about its minimum Problem: Fine-tuning required for correct magnitude of density perturbations

Other Models: 

Other Models Hybrid inflation Multiple scalar fields, not necessarily all with consequences to dynamics Eternal inflation Universe infinitely reproduces new universes True vacuum is achieved in many different parts of the inflating universe that are not causally connected; this is a self-perpetuating process

Inflation and Density Perturbations: 

Inflation and Density Perturbations Inflation -andgt; nearly homogeneous universe …but if exactly homogeneous, no structure or CMB anisotropies Must be mechanism for density perturbations in inflation CMB anisotropy, LSS Superhorizon scales Nearly scale-free

Inflation and Density Perturbations: 

Inflation and Density Perturbations The short version: Quantum fluctuations before/during inflation Small, subhorizon fluctuations frozen in when universe expands and they cross the horizon Post-inflation, standard growth of perturbations (more discussion later)

Observing Density Perturbations: 

Observing Density Perturbations How do we measure primordial density perturbations? CMB anisotropy Sachs-Wolfe effect ΔT/T result of redshifting of photons coming out of gravitational potential wells Contrast in redshift -andgt; depth of potential wells -andgt; measure of δρ/ρ

Sachs-Wolfe Effect: 

Sachs-Wolfe Effect

Observing Density Perturbations: 

Observing Density Perturbations 1982: only upper limit on CMB anisotropy (pre-COBE) δρ/ρ andlt; 10^-4 at present horizon scale COBE -andgt; δρ/ρ~10^-5 Harrison-Zel’dovich spectrum scale-independent: P(k) ~ k (or P(k) = kn where n ~ 1)

Observing Density Perturbations: 

Observing Density Perturbations Growth the same on all scales before horizon crossing Turnover in spectrum indicates horizon size at matter-radiation equality

Not Quite Scale-Independent : 

Not Quite Scale-Independent Inflation predicts nearly (but not quite) scale-independent fluctuations P(k) ~ kn , n≠1 (more on this later)

Timeline of Density Perturbation Production: 

Timeline of Density Perturbation Production Inflation begins -andgt; exponential expansion Quantum fluctuations frozen in Fluctuations in scalar field -andgt; time delay Post inflation: scales re-enter horizon, normal evolution of perturbations

1) Inflation begins: 

1) Inflation begins Scalar field φ slowly rolling down potential -andgt; exponential expansion Quantum fluctuations δφ in scalar field on horizon scale Analogy to Hawking radiation Zero-point fluctuations in the scalar field with wavelengths of order the Hubble radius Attributed to Hawking temperature (H/2π) associated with event horizon

1) Inflation begins: 

1) Inflation begins Scalar field φ slowly rolling down potential -andgt; exponential expansion Quantum fluctuations δφ in scalar field on horizon scale Analogy to Hawking radiation Zero-point fluctuations in the scalar field with wavelengths of order the Hubble radius Attributed to Hawking temperature (H/2π) associated with event horizon horizon shrinks, isolating particles

2) Fluctuations frozen in: 

2) Fluctuations frozen in Fluctuations produced when proper length scale comparable to Hubble Radius 1/H (horizon scale) Fluctuations 'frozen in' by expansion as they are carried outside the horizon horizon scale

2) Fluctuations frozen in: 

2) Fluctuations frozen in Fluctuations produced when proper length scale comparable to Hubble Radius 1/H (horizon scale) Fluctuations 'frozen in' by expansion as they are carried outside the horizon

2) Fluctuations frozen in: 

2) Fluctuations frozen in Fluctuations produced when proper length scale comparable to Hubble Radius 1/H (horizon scale) Fluctuations 'frozen in' by expansion as they are carried outside the horizon

2) Fluctuations frozen in: 

2) Fluctuations frozen in Fluctuations produced when proper length scale comparable to Hubble Radius 1/H (horizon scale) Fluctuations 'frozen in' by expansion as they are carried outside the horizon

2) Fluctuations frozen in: 

2) Fluctuations frozen in Fluctuations produced when proper length scale comparable to Hubble Radius 1/H (horizon scale) Fluctuations 'frozen in' by expansion as they are carried outside the horizon

3) Time delay: 

3) Time delay Perturbations δφ -andgt; different end times for inflation in different locations Regions in which inflation ends later become larger – density is 'diluted' Early end to inflation =andgt; underdensity Late end to inflation =andgt; overdensity φ φ t t δφ δt

4) Inflation Ends: 

4) Inflation Ends Horizon begins to grow again (with respect to space) Scales re-enter horizon Normal evolution of perturbations occurs as perturbations become causally connected

Slide31: 

start end now smooth patch on CMB horizon Horizon crossing in comoving coordinates start end horizon crossing Horizon crossing in physical coordinates

Scale near-independence: 

Scale near-independence Why are the primordial perturbations 'nearly' scale independent? δρ/ρ |H = fractional perturbation amplitude on a given scale upon re-entering the horizon δρ/ρ |H ~ HΔφ/(dφ/dt) (dφ/dt) will be different at different times as the field rolls down the potential (it increases with time) Δφ ~ H, and while H is nearly constant during inflation, it does grow slowly with time =andgt; Slight scale dependence

Density Perturbation Magnitude Estimate: 

Density Perturbation Magnitude Estimate Using the Coleman-Weinberg potential of New Inflation, both authors find δρ/ρ ~ 10 on scale of current horizon What went wrong? Choice of potential (was chosen for supersymmetry breaking) – could be fixed with implausible amount of fine-tuning of parameters (level of 10^-12) Current method: choose functional form of potential, normalize with δρ/ρ ~ 10^-5 Generally phenomenological – potential is not determined from first principles

Conclusions and Current Work: 

Conclusions and Current Work Inflationary models succeed in creating nearly scale-free density perturbations which can grow to create structure in the universe …But getting the magnitude of the perturbations right requires scaling the potential accordingly No conclusion yet on correct functional form of inflationary potential However, scale-independence is well constrained with CMB, Lyman-alpha forest measurements