Inflation Daniel Baumann

Transcription

1 Inflation Daniel Baumann University of Amsterdam Florence, Sept 2017

2 Cosmological structures formed by the gravitational collapse of primordial density perturbations. gravity 380,000 yrs 13.8 billion yrs What generated the initial fluctuations?

3 A Remarkable Fact The fluctuations were created before the hot Big Bang: 140 Planck [2015] TE Correlation superhorizon Multipole

4 Rapid Expansion or Slow Contraction? bounce inflation

5 Quantum Fluctuations during Inflation Any massless field experiences quantum fluctuations during inflation: Inflation stretches these to macroscopic scales. Two massless fields are guaranteed to exist during inflation: d`2 = e 2Ht [(1 + ) ij + h ij ]dx i dx j h ij expansion H(t) const scalar isotropic stretching tensor anisotropic stretching

6 Primordial Spectra recombination it inflation predicts 4 1 H h 2 i = 2 H 8 2 Mpl observed { } { hot big bang 2 2 H hh2ij i = 2 2 Mpl adiabatic Gaussian superhorizon scale-invariant required to show that 2 H H

7 Open Questions Did inflation really occur? Extraordinary claims require extraordinary evidence. What was the physical mechanism of inflation? What is the energy scale of inflation? How did inflation begin? How did it end? How did the universe reheat? Was the origin of perturbations quantum or classical? Opportunity to learn deep facts about the early universe from future observations.

8 In this talk, I will review the theoretical foundations of inflation and discuss future observational tests.

9 Theoretical Foundations

10 A Benchmark It is useful to define a standard model Single-clock inflation single-field slow-roll inflation (t, ~x) h ij (t, ~x) H(t) and then try to kill it.

11 Energy Scales The model is characterized by three energy scales: M pl f H

12 Energy Scales The model is characterized by three energy scales: (freeze-out) subhorizon superhorizon H

13 Energy Scales The model is characterized by three energy scales: (quantum gravity) M pl =10 18 GeV H

14 Energy Scales The model is characterized by three energy scales: M pl background slow-roll (symmetry breaking) f (M 2 pl Ḣ )1/4 = 1/2 Goldstone fluctuations curvature perturbations H

15 Energy Scales The model is characterized by three energy scales: f = 58H 2 = H f H measured

16 Energy Scales The model is characterized by three energy scales: M pl > 10 4 H 2 h = H M pl =? unknown H

17 Ultraviolet Completion The UV completion of inflation requires new scales between the Planck scale and the Hubble scale: M pl M s M KK M H M susy The inflationary dynamics is sensitive to those scales.

18 Cosmological Collider A detection of B-modes would suggest a large inflation scale H GeV This is both a challenge and an opportunity. The inflationary background is sensitive to high scales. Lyth [1996] The inflationary perturbations can be affected by high scales. Chen and Wang [2009] DB and Green [2011] Arkani-Hamed and Maldacena [2015]

19 Observational Tests

20 Current Constraints The data is starting to become really interesting 0.25 N=50 N= tensor-toscalar ratio Convex Concave Keck Array + BICEP2 [2015] scalar spectral index

21 Current Constraints The data is starting to become really interesting 0.25 N=50 N= Convex Concave Keck Array + BICEP2 [2015] broken scale invariance n s =0.960 ± 0.007

22 Current Constraints The data is starting to become really interesting 0.25 N=50 N= bound on tensors r< Convex Concave Keck Array + BICEP2 [2015]

23 Current Constraints The data is starting to become really interesting N=50 N=60 ruled out 0.15 Convex Concave favoured Keck Array + BICEP2 [2015] Starobinsky [1980] Bezrukov and Shaposhnikov [2007] Kallosh, Linde and Roest [2013]

24 Future Optimism There has been great experimental progress in recent years: post-bicep pre-bicep But, the era of B-mode cosmology is only beginning: ground balloon future BICEP2 Keck Array BICEP3 SPTpol ACTpol ABS PolarBear Simons Array C-BASS QUIJOTE B-Machine CLASS EBEX Spider Piper LiteBird CMB Stage IV COrE

25 Future Optimism What should we do after a B-mode detection? Check for consistency: Gaussian scale-invariant {superhorizon parity-invariant Look for additional signatures of high-scale physics: Non-Gaussianity Non-minimal Tensors

26 Non-Gaussianity N-point functions in single-clock inflation are strongly constrained by symmetries. Their soft limits vanish k 3 k 2 lim k 1!0 k 1 k N 0 The signal in the soft limit acts as a particle detector.

27 Non-Gaussianity If inflation occurred at a high scale (maybe as high as GeV), we have the opportunity to probe the particle spectrum at those energies: H M pl h ij GeV GeV These fields could tell us something about the microphysics of inflation. Chen and Wang [2009] DB and Green [2011] Arkani-Hamed and Maldacena [2015]

28 Non-Gaussianity The rapid expansion of the spacetime creates these massive particles: y. g. j h ij µ 1 µ J The decay of the particles produces distinct correlations. The signal depends on mass and spin on the particles.

29 Non-Gaussianity lim h ~ k L!0 kl ~ks ~ks i / cos apple M H ln kl k S P J (cos ) Oscillations in the squeezed limit measure the mass of the particle: Angular dependence in the squeezed limit measures the spin of the particle: (k3/k1) ks S(k1,k3,k3) ks kl 0 2 S(k1,k2,k3) k 1 /2k 3 k L /2k S θ [] [ ] Lee, DB and Pimentel [2016]

30 Non-minimal Tensors High-scale inflation is sensitive to gravitational corrections: L g = M 2 pl 2 apple R + f( ) W 2 M 2 s + g( ) W W M 2 s anomalous tensor tilt DB, Lee and Pimentel [2015] parity violation Lue, Wang and Kamionkowski [1998] + W 3 M 4 s + W 2 W M 4 s + tensor non-gaussianity Maldacena and Pimentel [2011] parity violation Soda, Kodama and Mozawa [2011] After a detection of B-modes it would be worth looking for non-minimal features in the tensor sector.

31 Quantum or Classical? Gaussian scale-invariant parity-invariant super-planckian fields Quantum fluctuations h ij =16 G ij Classical source non-gaussian non-scale-invariant parity violating sub-planckian fields e.g. SU(2) gauge fields Agrawal, Fujita and Komatsu [2017]

32 Conclusion

33 A B-mode detection would be a milestone towards a complete understanding of the origin of all structure in the universe inflation sec 380,000 yrs It would also give us the opportunity to probe physics at the highest energy scales.

34 There has been great experimental progress in recent years: post-bicep pre-bicep But, the era of B-mode cosmology is only beginning: ground balloon future BICEP2 Keck Array BICEP3 SPTpol ACTpol ABS CLASS PolarBear Simons Array C-BASS QUIJOTE B-Machine EBEX Spider Piper LiteBird PIXIE CMB Stage IV COrE

35 Thanks for your attention

36 Scalar Consistency Relation Consider the squeezed limit of the scalar bispectrum. At the freeze-out of the short modes, the long mode is classical and acts as a rescaling of the coordinates: lim k L!0 h ~kl ~ks ~ks i P (k L )P (k S ) = d ln[k3 P (k S )] d ln k S = (1 n s ) Maldacena [2003] Creminelli and Zaldarriaga [2004] unobservable A violation of this consistency relation signals: new particles non-inflationary perturbations Pajer, Schmidt and Zaldarriaga [2015] Chen and Wang [2009] DB and Green [2011] Arkani-Hamed and Maldacena [2015]

37 Tensor Consistency Relation A similar argument applies if the long mode is a tensor mode: lim k L!0 hh ~kl ~ks ~ks i P (k L )P (k S ) = ijk i Sk j S d ln P h (k S ) dk 2 S = ijˆki Sˆkj S [3 (1 n s)] This is even more robust than the scalar consistency relation, since it is hard to violate even with extra particles. A violation of this consistency relation signals: broken spatial symmetries exotic new particles non-inflationary perturbations Bordin et al [2016] Lee, DB and Pimentel [2016] Endlich, Nicolis and Wang [2012] Lee, DB and Pimentel [2016]

38 Lessons from the Past I did not continue with studying the CMB, because I had trouble imagining that such tiny disturbances to the CMB could be detected... Jim Peebles ns = ± I thought that it would take 1000 years to detect the logarithmic dependence of the power spectrum. Slava Mukhanov

39 Lessons from the Past We apologise to experimentalists for having no idea what is the mass of the Higgs boson and for not being sure of its couplings to other particles. For these reasons we do not want to encourage big experimental searches for the Higgs boson, Ellis, Gaillard and Nanopoulos Events Data S+B Fit B Fit Component Mass

40 Lessons from the Past I arrived at the interesting result that gravitational waves do not exist, Einstein, in a letter to Born