The Inflationary Model of the Big Bang

1. The Inflationary Model of the Big Bang Quantum Field Theory Presentation Peter Williams 1st December 2005

2. Outline • Introduction • The standard Big Bang model • Limitations of the model • The Inflationary Big Bang model • requirements • Field potential • Vacuum states • Evolution during inflation

3. The Big Bang • Proposed to have occurred ~ 15 billion years ago • bringing the universe into existence • Penzias & Wilson (1962) discovered an isotropic background microwave signal • found to have a 2.7 K black body signature • remnant signal of the Big Bang explosion • COBE supports the theory with further observations of the microwave background

4. Standard Big Bang Model

5. Limitations • Standard model only goes as far back as 1 second after the initial Big Bang • All parameters from that point considered as initial conditions • Three main inconsistencies with observations • Horizon problem • Flatness problem (W = r/rc = 1 ?) • Smoothness problem • Need a model to account for earlier times and to overcome problems

6. Horizon Problem • Two distant regions of microwave background have similar temperatures • But they are too far apart to be causally connected

7. Flatness Problem • Why is space so flat ? • i.e. 0.1 < W < 2.0 • Initial condition of BB model unsatisfactory • at t = 1 s, W = 1 to within 1:1015 • Initial condition assumed, not explained

8. Smoothness Problem • Microwave background smooth on large scale • Deviations from homogeneity seen • accounts for galaxies, clusters, etc. • Treated as an initial condition • the model needs to explain the features

9. Early Inflationary Models • Landau & Starobinsky (1979) • based on theories of anomalies in quantum gravity • does not account for how inflation starts • Guth (1981) • exponential expansion at some early stage of the universe • results in phase transitions and supercooling • renounced due to inhomogeneities • Linde (1982) • results of Guth not used • uses chaotic fluctuations and checks for inflation

10. Inflationary Big Bang

11. Immediate Consequences • Inflation immediately popular by solving many standard problems • horizon problem solved leading to an early universe in equilibrium • driven rapidly to 1 (balloon analogy) • Negative pressure required for inflation • Phase transition • Symmetry breaking

12. Mechanisms Behind Inflation • Best candidate is QFT • a theory of matter at high energies • Construct a Lagrangian for a scalar field • Apply the action • Find the equation of motion • should be Klein-Gordon in form • Find the energy density potential • a function of the scalar field

13. ‘Old’ Inflation • Lagrangian: • Potential: a b

14. Mechanism • Initial condition (t = 10-34 s) • zero scalar field, non-zero potential • stable equilibrium • ‘false vacuum’ • Negative pressure causes inflation • Needs to reach true vacuum • Tunneling must occur to do so

15. Result • Advantages • universe does inflate • initial conditions of standard BB not required • in fact, they are produced • problems of standard BB solved (most of them!) • Potential energy → mass = PARTICLES! • Disadvantages • field must tunnel through potential • ‘Bubble nucleation’ occurs • bubbles of true vacuum expand in a sea of false vaccum • leads to inhomogeneous universe • microwave background is smooth on the large scale

16. ‘New’ Inflation • Lagrangian: • Potential: s s

17. Mechanism • Initial condition (t = 10-34 s) • zero scalar field, non-zero potential • unstable equilibrium • ‘false vacuum’ • Negative pressure causes inflation • Quantum fluctuations perturb field toward true vacuum • ‘Slow rolling’ towards V(j) = 0

18. Result • All the advantages of the old model kept • Tunneling not required • Further complications such as the phase transitions not required • Universe now smoothed out • Many mini-universes produced as opposed to a singular model

19. Successes • The inflation model solves the left over problems of the standard model • Assumptions of standard model not required • Invocation of Higgs field • Gives insight into pre-inflation era • Creates particles

20. Further Details • The potential well of the true vacuum leads to coherent oscillations • discussed in detail in literature • Linde produces ‘chaotic, self-reproducing inflationary universe’ • locally the universe is homogeneous • global complex structure • many universes linked by Planck-length sized tubes • Further models adopt super-symmetry and string-theory

21. Conclusions • Inflation not only substantiates, but furthers and improves the Big Bang model • It agrees well with observation • Successfully uses quantum field theory • evolution of scalar (Higgs) field • production of particles • Plays an important role in the research of new physics • Requires a field theory of gravity for further improvement

22. References • Börner G. (1988) The Early Universe, Springer-Verlag, Berlin, Germany • Bradenberger R.H. (1990) in Physics of the Early Universe, eds. Peacock J.A., Heavens A.F., Davies A.T., Edinburgh University Press, Edinburgh, UK, 281-360 • Guth A.H., Steinhardt P.J. (1984) SciAmer, 116-128 • Linde A. (1987) Physics Today, 40(9), 61-68 • Linde A. (1994) SciAmer, 48-55