1. Inflation and Fundamental Physics
What do cosmological measurements
say about the very early universe?
C.P. Burgess
Frequently, presenters must deliver material of a technical nature to an audience unfamiliar with the topic or vocabulary. The material may be complex or heavy with detail. To present technical material effectively, use the following guidelines from Dale Carnegie Training®.
Consider the amount of time available and prepare to organize your material. Narrow your topic. Divide your presentation into clear segments. Follow a logical progression. Maintain your focus throughout. Close the presentation with a summary, repetition of the key steps, or a logical conclusion.
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with M. Cicoli, M.Gomez-Reino,G.Tasinato, F.Quevedo and I.Zavala

2. Outline Inflation String 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?
UniverseNet
Inflation

3. Outline Inflation String 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?
UniverseNet
Inflation

4. Inflation Who says it took place? What might one hope to learn if so?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

5. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

6. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

7. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

8. Inflation Who says it took place? What might one hope to learn if so?
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:
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

9. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

10. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

11. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

12. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

13. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

14. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
eg: if the universe bounced
UniverseNet
Inflation

15. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
but: how do you get a bounce?
UniverseNet
Inflation

16. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
or: if the expansion accelerated
UniverseNet
Inflation

17. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
require aH to grow by ~ e60
UniverseNet
Inflation

18. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
but: why should it start? Or end?
UniverseNet
Inflation

19. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
and must it end everywhere?
UniverseNet
Inflation

20. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

21. Inflation Who says it took place? What might one hope to learn if so?
A. Guth; A. Linde; A. Albrecht & P. Steinhardt
How to achieve p = - 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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

22. Inflation Who says it took place? What might one hope to learn if so?
Lyth
So Hubble scale
is approximately constant provided
are small
Who says it took place?
What might one hope to learn if so?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

23. Inflation Who says it took place? What might one hope to learn if so?
For example V = (1/2) m2 f2 (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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

24. Inflation Who says it took place? What might one hope to learn if so?
Large-field variation V = 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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

25. Inflation Who says it took place? What might one hope to learn if so?
For example V = V0 - (1/2) m2 f2
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

26. Inflation Who says it took place? What might one hope to learn if so?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

27. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

28. Inflation Who says it took place? What might one hope to learn if so?
CMB and large-scale structure sample density correlations
Who says it took place?
What might one hope to learn if so?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

29. Inflation Who says it took place? What might one hope to learn if so?
Separating primordial from late-time fluctuations
primordial part transfer function
Who says it took place?
What might one hope to learn if so?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

30. Inflation Who says it took place? What might one hope to learn if so?
Separating primordial from late-time fluctuations
Who says it took place?
What might one hope to learn if so?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
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.
UniverseNet
Inflation

31. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

32. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

33. Inflation Who says it took place? What might one hope to learn if so?
Mukhanov; Hawking; Linde; Guth & Pi; Steinhardt; …
What is predicted by single-field models?
Must propagate initial d f at horizon exit to determine d F at late times, but why should d f be nonzero? Although classical fluctuations are damped during inflation, they are replenished by quantum fluctuations so d f ~ H/2p
Who says it took place?
What might one hope to learn if so?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

34. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
Tensor modes evolve independently. Scalar mixes with Newtonian potential by an amount controlled by df/dt
UniverseNet
Inflation

35. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
Primordial fluctuations can be robustly evolved when outside the Hubble scale
UniverseNet
Inflation

36. Inflation Who says it took place? What might one hope to learn if so?
For two regions with F approximately constant
Who says it took place?
What might one hope to learn if so?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
Ff varies inversely with e if initial region is inflating.
UniverseNet
Inflation

37. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
In principle 3 parameters (H, e, h) give 4 observables.
UniverseNet
Inflation

38. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
Conventional to define r = QT/QF (= 16 e = -8 nT.)
UniverseNet
Inflation

39. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
Conventional to define r = QT/QF (= 16 e = -8 nT.)
UniverseNet
Inflation

40. Inflation Who says it took place? What might one hope to learn if so?
In particular, d T/ T ~ 10-5 implies
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
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
UniverseNet
Inflation

41. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
and possibly more if tensor fluctuations are obseved
UniverseNet
Inflation

42. Inflation Who says it took place? What might one hope to learn if so?
*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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

43. Inflation Who says it took place? What might one hope to learn if so?
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
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

44. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

45. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
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?
UniverseNet
Inflation

46. Inflation Who says it took place? What might one hope to learn if so?
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?
Start with the picture of how scales evolve during and after inflation;
Describe the inflaton-metric system in its original and Mukhanov form;
Describe the squeezing of the Mukhanov vacuum into the Bunch-Davies vacuum
UniverseNet
Inflation

47. fin
UniverseNet
Inflation