Inflation and Fundamental Physics

1. Inflation and Fundamental Physics What do cosmological measurements say about the very early universe? C.P. Burgess with M. Cicoli, M.Gomez-Reino,G.Tasinato, F.Quevedo and I.Zavala

2. Outline • Inflation • Why is it so widely believed to have happened? • What can we expect to learn? • String inflation • Why build models only a mother could love? • What can we expect to learn? Inflation

3. Outline • Inflation • Why is it so widely believed to have happened? • What can we expect to learn? • String inflation • Why build models only a mother could love? • What can we expect to learn? Inflation

4. Inflation • Who says it took place? • What might one hope to learn if so? Inflation

5. Inflation WMAP Concordance cosmology provides a great description of the wealth of cosmological data. • Who says it took place? • What might one hope to learn if so? Inflation

6. Inflation NCSA simulation Evidence supports the picture that structure forms from the collapse of an initially uniform distribution. • Who says it took place? • What might one hope to learn if so? Inflation

7. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Inflation

8. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Radiation domination: Matter domination: Inflation

9. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Inflation

10. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Initially very homogeneous Inflation

11. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Initially very homogeneous Inflation

12. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? fluctuations freeze once larger than H-1, so the problem is while so the product aH decreases with t Inflation

13. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? fluctuations freeze once larger than H-1, so the problem is while so the product aH decreases with t Inflation

14. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Possible solution: extrapolation into the past is wrong eg: if the universe bounced Inflation

15. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Possible solution: extrapolation into the past is wrong but: how do you get a bounce? Inflation

16. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Possible solution: extrapolation into the past is wrong or: if the expansion accelerated Inflation

17. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Possible solution: extrapolation into the past is wrong require aH to grow by ~ e60 Inflation

18. Inflation Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Possible solution: extrapolation into the past is wrong but: why should it start? Or end? Inflation

19. Inflation courtesy A. Linde Concordance model works well, if the universe starts off in just the right way: Initially very flat: Initially very homogeneous: surprise given speed of expansion seem to be no primordial defects • Who says it took place? • What might one hope to learn if so? Possible solution: extrapolation into the past is wrong and must it end everywhere? Inflation

20. Inflation A. Guth Archetype: if p = - r then Friedmann eq implies much like dark energy (but with a larger H) • Who says it took place? • What might one hope to learn if so? Inflation

21. Inflation A. Guth; A. Linde; A. Albrecht & P. Steinhardt How to achievep = - r ? For a single homogeneous scalar field so homogeneous slow roll can make things work • Who says it took place? • What might one hope to learn if so? Inflation

22. Inflation Lyth So Hubble scale is approximately constant provided are small • Who says it took place? • What might one hope to learn if so? Inflation

23. Inflation For exampleV = (1/2) m2f2 (large-field model) then positive and ~ e are small for large f. (Must then have m not too large.) Also, inflation ends as f is driven to smaller values. • Who says it took place? • What might one hope to learn if so? Inflation

24. Inflation Large-field variationV = V0 – A exp (-l f) then negative and >> e are small for large f (and V is bounded in this region) • Who says it took place? • What might one hope to learn if so? Inflation

25. Inflation For exampleV = V0 - (1/2) m2f2 then negative, bigger than e are small for small f and m . • Who says it took place? • What might one hope to learn if so? Inflation

26. Inflation • Who says it took place? • What might one hope to learn if so? Inflation

27. Inflation Mukhanov; Hawking; Linde; Guth & Pi; Steinhardt; … Bonus: besides providing a framework within which primordial seeds of CMB fluctuations can be explained, inflation also provides a mechanism: primordial quantum fluctuations. • Who says it took place? • What might one hope to learn if so? Inflation

28. Inflation CMB and large-scale structure sample density correlations • Who says it took place? • What might one hope to learn if so? Inflation

29. Inflation Separating primordial from late-time fluctuations primordial part transfer function • Who says it took place? • What might one hope to learn if so? Inflation

30. Inflation Separating primordial from late-time fluctuations • Who says it took place? • What might one hope to learn if so? Structure growth requires k/a > H and the universe is matter dominated. k-4 suppression because modes with k/a = H during rad. dom. must await mat. dom. Inflation

31. Inflation Evidence is that primordial fluctuations are simple with index and As chosen to ensure • Who says it took place? • What might one hope to learn if so? Inflation

32. Inflation ns = 1 is special (Harrison-Zeldovich) d T/T tracks Newtonian potential so with then is scale invariant if ns = 1. • Who says it took place? • What might one hope to learn if so? Inflation

33. Inflation Mukhanov; Hawking; Linde; Guth & Pi; Steinhardt; … What is predicted by single-field models? Must propagate initial df at horizon exit to determine d F at late times, but why should df be nonzero? Although classical fluctuations are damped during inflation, they are replenished by quantum fluctuations so df ~ H/2p • Who says it took place? • What might one hope to learn if so? Inflation

34. Inflation Can compute linear fluctuations in inflaton and metric and evolve forward using quantum fluctuations as the initial condition at horizon exit. • Who says it took place? • What might one hope to learn if so? Tensor modes evolve independently. Scalar mixes with Newtonian potential by an amount controlled by df/dt Inflation

35. Inflation Mukhanov For single field there is a simple integral for modes with k/a < H • Who says it took place? • What might one hope to learn if so? Primordial fluctuations can be robustly evolved when outside the Hubble scale Inflation

36. Inflation For two regions with F approximately constant • Who says it took place? • What might one hope to learn if so? Ff varies inversely with e if initial region is inflating. Inflation

37. Inflation In this way one finds standard single-field formulae Scalar perturbations Tensor perturbations • Who says it took place? • What might one hope to learn if so? In principle 3 parameters (H, e, h) give 4 observables. Inflation

38. Inflation In this way one finds standard single-field formulae Scalar perturbations Tensor perturbations • Who says it took place? • What might one hope to learn if so? Conventional to define r = QT/QF (= 16 e = -8 nT.) Inflation

39. Inflation In this way one finds standard single-field formulae Scalar perturbations Tensor perturbations • Who says it took place? • What might one hope to learn if so? Conventional to define r = QT/QF (= 16 e = -8 nT.) Inflation

40. Inflation • Who says it took place? • What might one hope to learn if so? In particular, d T/ T ~ 10-5 implies So if e and h are similar in size then V should be very large relative to other particle physics scales. (Measurement of tensor modes would remove the assumption that e and h are similar Also, large-field models tend to give larger tensor modes Inflation

41. Inflation The good news: Predictive* and good agreement with observations: Close to HZ spectrum (precisely constant H gives scale invariant result) Gaussian fluctuations (ie <f f f f> not independent of <f f>) because slow roll implies weak inflaton self-couplings Evolution to present relatively model-independent • Who says it took place? • What might one hope to learn if so? and possibly more if tensor fluctuations are obseved Inflation

42. Inflation *Less predictive with more complicated models eg: Additional scalar fields: Should there be other light fields besides the inflaton during inflation then there are more than 3 parameters and predictions can change. In particular, z is no longer conserved, so can obtain more complicated post-inflationary evolution. (Can also remain simple, such as if in thermal equilibrium.) Interactions can be stronger, so can obtain observable non-gaussianity. • Who says it took place? • What might one hope to learn if so? Inflation

43. Inflation Linde *Less predictive with more complicated models eg: Additional scalar fields: Should there be other light fields besides the inflaton during inflation then more than 3 parameters and predictions can change. In particular, interactions can be stronger and z is no longer conserved, so can obtain observable non-gaussianity. • Who says it took place? • What might one hope to learn if so? For example: hybrid inflation Inflation

44. Inflation The bad news: Homogeneous slow roll is usually not generic, and can be sensitive to initial conditions; Very flat potentials have naturalness problems, and inflationary potentials are so flat they are sensitive to ‘planck slop’ (Mp suppressed interactions); Reheating not understood Predictions possible at all? (transplackia, multiverse) • Who says it took place? • What might one hope to learn if so? Inflation

45. Inflation Much of the bad news depends on the details of physics at the large energies relevant to the inflationary epoch: • Who says it took place? • What might one hope to learn if so? If the inflationary scale is so close to the gravity scale, won’t all of the new degrees of freedom at this scale completely change the picture? Inflation

46. Inflation The bottom line (part I): The great success of standard cosmology relies on relatively special initial conditions Very simple single-field inflationary models provide a simple description of these initial conditions Cosmological measurements provide limited information about very high energy physics Successful cosmologies rely on features that are unusual for physical theories (flat scalar potentials): what does this tell us? • Who says it took place? • What might one hope to learn if so? Inflation

47. fin Inflation