Fingerprints of the early universe. Hiranya Peiris University College London

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1 Fingerprints of the early universe Hiranya Peiris University College London

2 Outline

3 Outline The primordial power spectrum Inferences from the CMB with inflationary priors

4 Outline The primordial power spectrum Inferences from the CMB with inflationary priors Beyond the standard model Is the cut sky CMB anomalous?

5 Cosmic History / Cosmic Mystery Fractional Energy Density!tot = 1(k=0) 10!42 s 10!33 s 10!22 s 10!16 s 10!12 s 1 sec 380 kyr 14 Gyr ~10 15 GeV Time ~1 MeV ~0.2 ev Planck Energy GUT symmetry Generation of primordial perturbations T=100 TeV (ILC X 100) nucleosynthesis Cosmic Microwave Background Emitted carries signature of acoustic oscillations and potentially primordial gravitational waves present energy density dark energy (73%) dark matter (23.6%) baryons (4.4%) non-linear growth of perturbations: signature on CMB through weak gravitational lensing Figure: J. McMahon, adapted by HVP

6 ΛCDM : The Standard Model of Cosmology Homogeneous background 60 K Perturbations Ω b, Ω c, Ω Λ,H 0, τ A s,n s,r atoms 4% cold dark matter 23% dark energy 73% nearly scale-invariant adiabatic Gaussian Λ? CDM? ORIGIN??

7 Inflation A period of accelerated expansion ds 2 = dt 2 + e 2Ht dx 2 H const Solves: horizon problem flatness problem monopole problem i.e. explains why the Universe is so large, so flat, and so empty Predicts: scalar fluctuations in the CMB temperature nearly scale-invariant approximately Gaussian (?)? primordial tensor fluctuations (gravitational waves)

8 Inflation Implemented as a slowly-rolling scalar field evolving in a potential: V (φ) Inflation H const Standard expansion H 2 = (ȧ a = 8πG 3 ) 2 expansion rate [ ] 1 2 φ 2 + V (φ) density Energy converted into radiation φ φ +3H φ + V =0 friction overdot = d/dt

9 Inflation Solves the flatness/horizon problems if the early universe inflates by factor ~ Cosmological perturbations arise from quantum fluctuations, evolve classically. P φ (k) h ( ) 2 P R h H 2π 4π 2 P h 2 h π 2 ( H 4 ( H m Pl φ 2 ) 2 k=ah ) 2 k=ah scalar tensor

10 Inflation Solves the flatness/horizon problems if the early universe inflates by factor ~ Cosmological perturbations arise from quantum fluctuations, evolve classically. P φ (k) h ( ) 2 P R h H 2π 4π 2 P h 2 h π 2 ( H 4 ( H m Pl φ 2 ) 2 k=ah ) 2 k=ah scalar tensor Don t know the dynamics of inflation: parameterize weakly scale-dependent functions with a few numbers to pin down observationally. P R (k) A s k k 0 ns 1 P h (k) A t k k 0 nt r = P h(k 0 ) P R (k 0 )

11 Reminder: the primordial power spectrum & the CMB P (k) n S < 1 k CMB physics power P (k) CMB physics n S > 1 k large scales small scales

12 Slow roll inflation consistent with WMAP+ Superhorizon, adiabatic fluctuations - T and E anticorrelated at superhorizon scales Flatness tested to 1%. Gaussianity tested to 0.1%. nearly scale-invariant fluctuations - red tilt indicated at ~3 " Spergel, Verde, Peiris et al. (2003), Komatsu et al. (2003), Peiris et al. (2003), Spergel et al (WMAP Collaboration) (2006), Dunkley et al & Komatsu et al (WMAP Collaboration) (2008)

13 What is the physics of inflation? V (φ) Why did the field start here? Where did this function come from? Why is the potential so flat? Inflation consists of taking a few numbers that we don t understand and replacing it with a function that we don t understand David Schramm φ How do we convert the field energy completely into particles?

14 The duration of inflation log (length scale) radiation matter Constraint: Comoving Hubble Radius at onset of inflation > Comoving Hubble Radius today. N H = ln ( arh a H ) Standard expansion Solves cosmological problems if radius of universe expands by e-folds during inflation aeq atoday log (scale factor)

15 The duration of inflation log (length scale) H -1 current horizon radiation matter Standard expansion Constraint: Comoving Hubble Radius at onset of inflation > Comoving Hubble Radius today. N H = ln ( arh a H ) Solves cosmological problems if radius of universe expands by e-folds during inflation aeq log (scale factor) atoday

16 The duration of inflation log (length scale) H -1 Inflation current horizon radiation matter Standard expansion Constraint: Comoving Hubble Radius at onset of inflation > Comoving Hubble Radius today. N H = ln ( arh a H ) Solves cosmological problems if radius of universe expands by e-folds during inflation ah arh aeq log (scale factor) atoday

17 The duration of inflation log (length scale) H -1 Inflation current horizon galaxy radiation matter Standard expansion Constraint: Comoving Hubble Radius at onset of inflation > Comoving Hubble Radius today. N H = ln ( arh a H ) Solves cosmological problems if radius of universe expands by e-folds during inflation ah arh aeq log (scale factor) atoday

18 Connecting measurements to an inflationary model log (length scale) pivot scale k0 radiation matter Observable parameters are a function of scale! e.g. ns[k(nefold)] k0 Inflation Standard expansion ak0 arh aeq log (scale factor) atoday

19 Connecting measurements to an inflationary model log (length scale) k0 pivot scale k0 matter radiation matter Reheat temperature can vary from GUT scale (10 15 GeV) to nucleosynthesis scale (1 MeV)! Resulting uncertainty in predictions at a given pivot : N efold 14 r r 1 n 0.02 Inflation Standard expansion ak0 aend arh aeq log (scale factor) atoday

20 e-fold priors Connection equation in a universe that inflated, reheated, and passed through matter-radiation equality: k N(k) = ln Mpc ln Hreh m Pl 2 3 ln Hend m Pl + ln Hk m Pl weaker N(k) > 15 T reh > 10 MeV T reh > 10 TeV H reh = H end minimal guarantees thermalized neutrino sector reheating occurs well above EW scale instant reheating stronger

21 Reheating uncertainties 0.20 gravitational wave amplitude r Natural Hilltop Monomial scalar spectral index ns Inflection Figure: R. Easther

22 Reheating uncertainties (worst case) gravitational wave amplitude r scalar spectral index ns Figure: R. Easther

23 Fingerprinting the very early universe Physical model priors Exact (numerical) computation of observables (MODECODE) Bayesian parameter estimation with data with R. Easther, M. Mortonson, M. Bridges

24 ModeCode with R. Easther, M. Mortonson

25 ModeCode: accuracy Analytic solution for power law inflation Accuracy better than 0.01% Figure: Mortonson, Peiris, Easther (arxiv: )

26 Example: natural inflation V (φ) =Λ 4 cos(φ/f) Grey: WMAP7+ general reheat Flat priors on log f, log! Red: WMAP7 + instant reheat Figure: Mortonson, Peiris, Easther (arxiv: )

27 Example: hilltop inflation V (φ) =Λ 4 λ 4 φ4 Grey: WMAP7+ general reheat Flat priors on log ", log! Red: WMAP7 + instant reheat Figure: Mortonson, Peiris, Easther (arxiv: )

28 priors vs constraints natural hilltop Flat priors on log f, log!, log " Grey: WMAP7+ general reheat Black: Monte Carlo-ing the priors Figure: Mortonson, Peiris, Easther (arxiv: )

29 Inverting empirical constraints quadratic inflation WMAP7+ general reheat Sort of works for single parameter models Relation not uniquely invertible for 2+ parameter models Figure: Mortonson, Peiris, Easther (arxiv: )

30 Marginalized Reheating Uncertainty Grey: WMAP7+ general reheat Red: WMAP7 + instant reheat Figure: Mortonson, Peiris, Easther (arxiv: )

31 Planck Extract essentially all information in primary CMB temperature anisotropy; big advance in polarization measurements. Have a full sky in the can!

32 Example: quadratic inflation + Planck Flat prior on log m 2 ns(realization) ~ 0.963, r(realization) ~0.14 Grey: WMAP7+ general reheat Blue: Planck + general reheat Apply MODECODE to Planck Simulation by Efstathiou+Gratton

33 Example: natural inflation + Planck V (φ) =Λ 4 cos(φ/f) Grey: WMAP7+ general reheat Flat priors on log f, log! Blue: Planck + general reheat Apply MODECODE to Planck Simulation by Efstathiou+Gratton

34 Example: hilltop inflation + Planck delta chisq ~ 75 worse than quadratic / natural inflation V (φ) =Λ 4 λ 4 φ4 Grey: WMAP7+ general reheat Flat priors on log ", log! Blue: Planck + general reheat Apply MODECODE to Planck Simulation by Efstathiou+Gratton

35 Outline The primordial power spectrum Inferences from the CMB with inflationary priors Beyond the standard model Is the cut sky CMB anomalous?

36 Testing Fundamental Cosmological Assumptions N ecliptic hemisphere l=2 S ecliptic hemisphere l=3 Asymmetry? Alignment?

37 Is the CMB sky statistically isotropic? Isotropy anomalies identified in WMAP temperature field. e.g. hemispherical asymmetry N ecliptic S ecliptic South (ecliptic) has more power than North. Eriksen et al. 2004: P-value ~1% in isotropic universe.

38 Is the CMB sky statistically isotropic? Isotropy anomalies identified in WMAP temperature field. e.g. e.g. quadrupole-octupole alignment Quadrupole and octupole are planar and mutually aligned (de Oliveira Costa et al. 2003) WMAP7: P-value ~ in isotropic universe.

39 Isotropy anomalies seem related to local directions SD GD GD SD

40 p(a B)! p(b A) 100% 0.01% A = I am a scientist criminal B = I am a CMB murderer cosmologist

41 p(a B)! p(b A)?? 0.01% A = The standard model is basically correct B = CMB anomalies ( some subset of the CMB data which we don t like the look of )

42 a posteriori

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44 TTTHHHTHHHHTTTHTHTHTTHHTHHHTTHTHHTHHHHHTHHTTHTHTHTTHTHHT TTHHTTHTHHTTHTTHHTTTTHHTHHHTTTHHHHHTHHTTTHTHHTTHHTHTHHTT HHHHTHHHHHHHHTHTHHHTHTTTTHHHTHTTTHTTHTHHTHTTTHHTTTTHHHTT HTTTTTTHTTHTHHHHHTHHHHTTTTTTTTTTHTTTHHHTHHHHTTTTTTTHHTHT TTHHHTHTHTTTTHHHHHHHHHHHTTHTTTHHTHHTTTHHTTHHHHHHTHTTHTTT HTTHHTTTTTTHHTTHHHTTTHTHTTTHTTHHTHTHTHTHHHTTHHTHHHHHTHHH HHHTHHTHHHHTHTHTHHHHTHTHHTTHHHTTTTHTHHHHTTHTHTTTTTHHHHTT HTTHTTTHTHTHHTTTHTHHTTHHTTTHTHHTTTHTTTHHHTHTHTHTHHHTTHTH Chain of 11 HTTTHHHHHHTHTTTHHHTHTTHTTTHTTHTHHTHTHHHHHHHHHHHTTHHHHTTHHHHHHHHHHHH HHTTHHTHHHTTTHHHTHHTHTHTHTTTTTHTHTHHHTTHTHHHHHHTHTHTHHTT 0.1% = 1 in 2 10 THHHHTHTTTHTTTHHTHTTHHTTHTTHHTHHTHTHHHHHHTTHTTTTHTHTTTTH THHTHHTTTTTHTHHHHHTTHHHTTHTTHHTHTHHHHHHTTHTTHTTTTTHHTHTT HTTHTHHTTHTHHTHTHHTTTHTHHTTHHHHTHTHHTTTTTTTTHTTTHTTHHHHT TTTTTHHTTHTHTHHHTTTTHTTTTHHTHHHHTTTHTTHHHTHTHTTTHTTTTTHH THHHTHTHHTHHTHHHTTHTTHHTTHTTTHTTHTHHTHTTTHHTTHTTHHHTHTHT HHTTTHHHTTHHTHTTHTTHTHHTTHTTTTTHHTTHTHHTTTTHHHTTTHTTTTHT HTHTHHTHTHHTHHHHHTTHHHTTTTTHTHHTTHTHHTTHHTTTHTTTHTTTTHTT TTHTHHHTHHHTHHHHHHHHHHTHTTTHTHTHHHHHHTHHHHTHTTTTTHTTTTHH TTHTTHTTTTTHHTHTTHTTHTHHTTHTHHTHTHHTTTHTHHTTHHHHTHTHHTTT TTTTTHTTTHTTHHHHTTTTTTHHTTHTHTHHHTTTTHTTTTHHTHHHHTTTHTTH HHTHHTHHTHTHHHHHHTTHTTTTHTHTTTTHTHHTHHTTTTTHTHHHHHTTHHHT Figure: A. Pontzen THTTHHTHTHHHHHHTTHTTHTTTTTHHTHTTHTTHTHHTTHTHHTHTHHTTTHTH

45 TTTHHHTHHHHTTTHTHTHTTHHTHHHTTHTHHTHHHHHTHHTTHTHTHTTHTHHT TTHHTTHTHHTTHTTHHTTTTHHTHHHTTTHHHHHTHHTTTHTHHTTHHTHTHHTT HHHHTHHHHHHHHTHTHHHTHTTTTHHHTHTTTHTTHTHHTHTTTHHTTTTHHHTT HTTTTTTHTTHTHHHHHTHHHHTTTTTTTTTTHTTTHHHTHHHHTTTTTTTHHTHT TTHHHTHTHTTTTHHHHHHHHHHHTTHTTTHHTHHTTTHHTTHHHHHHTHTTHTTT HTTHHTTTTTTHHTTHHHTTTHTHTTTHTTHHTHTHTHTHHHTTHHTHHHHHTHHH HHHTHHTHHHHTHTHTHHHHTHTHHTTHHHTTTTHTHHHHTTHTHTTTTTHHHHTT HTTHTTTHTHTHHTTTHTHHTTHHTTTHTHHTTTHTTTHHHTHTHTHTHHHTTHTH HTTTHHHHHHTHTTTHHHTHTTHTTTHTTHTHHTHTHHHHHHHHHHHTTHHHHTTHHHHHHHHHHHH HHTTHHTHHHTTTHHHTHHTHTHTHTTTTTHTHTHHHTTHTHHHHHHTHTHTHHTT THHHHTHTTTHTTTHHTHTTHHTTHTTHHTHHTHTHHHHHHTTHTTTTHTHTTTTH THHTHHTTTTTHTHHHHHTTHHHTTHTTHHTHTHHHHHHTTHTTHTTTTTHHTHTT HTTHTHHTTHTHHTHTHHTTTHTHHTTHHHHTHTHHTTTTTTTTHTTTHTTHHHHT Chain of 11 somewhere TTTTTHHTTHTHTHHHTTTTHTTTTHHTHHHHTTTHTTHHHTHTHTTTHTTTTTHH THHHTHTHHTHHTHHHTTHTTHHTTHTTTHTTHTHHTHTTTHHTTHTTHHHTHTHT within 1,000 trials HHTTTHHHTTHHTHTTHTTHTHHTTHTTTTTHHTTHTHHTTTTHHHTTTHTTTTHT HTHTHHTHTHHTHHHHHTTHHHTTTTTHTHHTTHTHHTTHHTTTHTTTHTTTTHTT TTHTHHHTHHHTHHHHHHHHHHTHTTTHTHTHHHHHHTHHHHTHTTTTTHTTTTHH TTHTTHTTTTTHHTHTTHTTHTHHTTHTHHTHTHHTTTHTHHTTHHHHTHTHHTTT TTTTTHTTTHTTHHHHTTTTTTHHTTHTHTHHHTTTTHTTTTHHTHHHHTTTHTTH HHTHHTHHTHTHHHHHHTTHTTTTHTHTTTTHTHHTHHTTTTTHTHHHHHTTHHHT Figure: A. Pontzen THTTHHTHTHHHHHHTTHTTHTTTTTHHTHTTHTTHTHHTTHTHHTHTHHTTTHTH

46 TTTHHHTHHHHTTTHTHTHTTHHTHHHTTHTHHTHHHHHTHHTTHTHTHTTHTHHT TTHHTTHTHHTTHTTHHTTTTHHTHHHTTTHHHHHTHHTTTHTHHTTHHTHTHHTT HHHHTHHHHHHHHTHTHHHTHTTTTHHHTHTTTHTTHTHHTHTTTHHTTTTHHHTT HTTTTTTHTTHTHHHHHTHHHHTTTTTTTTTTHTTTHHHTHHHHTTTTTTTHHTHT TTHHHTHTHTTTTHHHHHHHHHHHTTHTTTHHTHHTTTHHTTHHHHHHTHTTHTTT HTTHHTTTTTTHHTTHHHTTTHTHTTTHTTHHTHTHTHTHHHTTHHTHHHHHTHHH HHHTHHTHHHHTHTHTHHHHTHTHHTTHHHTTTTHTHHHHTTHTHTTTTTHHHHTT HTTHTTTHTHTHHTTTHTHHTTHHTTTHTHHTTTHTTTHHHTHTHTHTHHHTTHTH HTTTHHHHHHTHTTTHHHTHTTHTTTHTTHTHHTHTHHHHHHHHHHHTTHHHHTTHHHHHHHHHHHH HHTTHHTHHHTTTHHHTHHTHTHTHTTTTTHTHTHHHTTHTHHHHHHTHTHTHHTT THHHHTHTTTHTTTHHTHTTHHTTHTTHHTHHTHTHHHHHHTTHTTTTHTHTTTTH THHTHHTTTTTHTHHHHHTTHHHTTHTTHHTHTHHHHHHTTHTTHTTTTTHHTHTT HTTHTHHTTHTHHTHTHHTTTHTHHTTHHHHTHTHHTTTTTTTTHTTTHTTHHHHT Chain of 11 somewhere TTTTTHHTTHTHTHHHTTTTHTTTTHHTHHHHTTTHTTHHHTHTHTTTHTTTTTHH THHHTHTHHTHHTHHHTTHTTHHTTHTTTHTTHTHHTHTTTHHTTHTTHHHTHTHT within 1,000 trials HHTTTHHHTTHHTHTTHTTHTHHTTHTTTTTHHTTHTHHTTTTHHHTTTHTTTTHT HTHTHHTHTHHTHHHHHTTHHHTTTTTHTHHTTHTHHTTHHTTTHTTTHTTTTHTT 1 (99.9%) 1000 = 38% TTHTHHHTHHHTHHHHHHHHHHTHTTTHTHTHHHHHHTHHHHTHTTTTTHTTTTHH TTHTTHTTTTTHHTHTTHTTHTHHTTHTHHTHTHHTTTHTHHTTHHHHTHTHHTTT TTTTTHTTTHTTHHHHTTTTTTHHTTHTHTHHHTTTTHTTTTHHTHHHHTTTHTTH HHTHHTHHTHTHHHHHHTTHTTTTHTHTTTTHTHHTHHTTTTTHTHHHHHTTHHHT Figure: A. Pontzen THTTHHTHTHHHHHHTTHTTHTTTTTHHTHTTHTTHTHHTTHTHHTHTHHTTTHTH

47 C(!) = T1 T2

48 180 o S1/2 =! C(!) 2 cos! d! 60 o (Spergel+ 2003) C(!) (µk 2 ) V W ILC (KQ75) ILC (full) WMAP5 C l WMAP pseudo-c l LCDM ! (degrees) V W ILC (KQ75) ILC (full) WMAP5 C l WMAP pseudo-c l Copi+ 2009

49 180 o S1/2 =! C(!) 2 cos! d! 60 o (Spergel+ 2003) S1/2 cut ~ 1000 µk 4 <S1/2 cut >"CDM ~ 94,000 µk 4 p"cdm(#s1/2 cut ) ~ 0.03%

50 C(θ) = 1 4π (2 + 1)C P (cos θ) C(!) Cl p ~ 5% C cut (!) C PCL l p ~ 0.03% C MLE (!) C MLE l p ~ 5%

51 The MLE for C(!) is fine. 1. Is ML-estimation reliable?

52 1. Is ML-estimation reliable? Copi+ 2010, isotropic cosmology. However, the pixel-based approach is clearly far more robust to assumptions about what lies behind the cut. We can only observe reliably the 75% of the sky that was not masked, and that is where the large-angle two-point-correlation is near-vanishing. Any attempt to reconstruct the full sky must make assump- = PCL is more reliable than QML

53 PCL assumption QML assumption We observe more large scale power than small scale power. The CMB cannot be uncorrelated. See Appendix A of Pontzen & Peiris ( , PRD, 2010)

Contamination Bianchi model Quad. modul.

0 0.1 0.2 0.8 0.4 0.0 0.4 0.8 1.0 0.0 1.

20 0.15 0.10 0.05 0.00 1.5 1.0 0.5 0.0 0.5 12.

54 Contamination Bianchi model Quad. modul. Picture Designer 2.0 Bias /C PCL f sky =20% (2 +1) V / 2C QML f sky =20% Pontzen & Peiris ( , PRD, 2010)

55 Feeney & Peiris (unpublished)

56 1. Is ML-estimation reliable? Copi+ 2010, isotropic cosmology. However, the pixel-based approach is clearly far more robust to assumptions about what lies behind the cut. We can only observe reliably the 75% of the sky that was not masked, and that is where the large-angle two-point-correlation is near-vanishing. Any attempt to reconstruct the full sky must make assump- = PCL is more reliable than QML?

57 The MLE for C(!) is fine. 1. Is ML-estimation reliable? Regardless, 2. is the cut sky C(!) telling us something about anisotropy?

58 C(θ) = 1 4π (2 + 1)C P (cos θ) C(!) Cl p ~ 5% C cut (!) C PCL l p ~ 0.03% C MLE (!) C MLE l p ~ 5%

59 0.8 large! small! Fractional error on PCL reconstruction C PCL l l full /C conc l Shortfall of power l PCL 1! variance full-sky ILC, 20% sky cut Pontzen & Peiris ( , PRD, 2010)

=5 Low, ~ planar quadrupole =7 + 35 µk =3 + 35 ILC7 =3, 5, 7 = =5 +

60 =5 Low, ~ planar quadrupole = µk = ILC7 =3, 5, 7 = =5 + =7 35 = µk ILC7 =3, 5, 7 Pontzen & Peiris ( , PRD, 2010)

61 Aligned power at the largest observable scales Movie: A. Pontzen

62 Aligned power at the largest observable scales Movie: A. Pontzen

63 S1/2 cut 180 o =! C cut (!) 2 cos! d! = " sll C PCL l C PCL l 60 o C 2 low C3 planarity C3 rough Galactic alignment C5 low C7 low ~2" p~15% p~21% ~2" ~2"

64 S1/2 cut 180 o =! C cut (!) 2 cos! d! = " sll C PCL l C PCL l 60 o C 2 low C3 planarity C3 rough Galactic alignment C5 low C7 low ~2" p~15% p~21% ~2" ~2" Only when a series of minor anomalies in our particular realization get combined in a particular way is frequentist alarm raised.

65 S1/2 cut 180 o =! C cut (!) 2 cos! d! = " sll C PCL l C PCL l 60 o Minimize variance subject to: fixed full sky Cl s small power on cut sky (l=3,5,7) Pontzen & Peiris ( , PRD, 2010)

66 The cut sky CMB is not anomalous Maximize likelihood of cut sky S statisic over all anisotropic* Gaussian models with zero mean. Designer Theory straw man (~ 6900 dof) only improves likelihood over LCDM (8 dof) by. ln L 5 *Covariance matrix of alms has complete freedom to be correlated in any way whatsoever, as long as matrix is positive definite. Pontzen & Peiris ( , PRD, 2010)

67 p(m2 D) p(m1 D) = < 50 very small p(d M2) p(m2)/p(d p(d M1) p(m1)/p(d D = S1/2 cut M1 = vanilla LCDM M2 = large scale power planar

Structures in the early Universe. Particle Astrophysics chapter 8 Lecture 4

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