Fingerprints of the early universe. Hiranya Peiris University College London

Fingerprints of the early universe Hiranya Peiris University College London

Outline

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

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

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

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??

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)

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

Inflation Solves the flatness/horizon problems if the early universe inflates by factor ~10 30. 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 )

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

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)

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 1945-1997 φ How do we convert the field energy completely into particles?

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 ) 50 60 Standard expansion Solves cosmological problems if radius of universe expands by 50-60 e-folds during inflation aeq atoday log (scale factor)

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 ) 50 60 Solves cosmological problems if radius of universe expands by 50-60 e-folds during inflation aeq log (scale factor) atoday

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 ) 50 60 Solves cosmological problems if radius of universe expands by 50-60 e-folds during inflation ah arh aeq log (scale factor) atoday

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 ) 50 60 Solves cosmological problems if radius of universe expands by 50-60 e-folds during inflation ah arh aeq log (scale factor) atoday

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

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

e-fold priors Connection equation in a universe that inflated, reheated, and passed through matter-radiation equality: k N(k) = ln Mpc 1 + 1 6 ln Hreh m Pl 2 3 ln Hend m Pl + ln Hk m Pl + 59.59. 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

Reheating uncertainties 0.20 gravitational wave amplitude r 0.15 0.10 0.05 Natural Hilltop Monomial 0.00 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 scalar spectral index ns Inflection Figure: R. Easther

Reheating uncertainties (worst case) gravitational wave amplitude r 0.20 0.15 0.10 0.05 0.00 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 scalar spectral index ns Figure: R. Easther

Fingerprinting the very early universe 0.20 0.15 0.10 0.05 0.00 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 Physical model priors Exact (numerical) computation of observables (MODECODE) Bayesian parameter estimation with data with R. Easther, M. Mortonson, M. Bridges

ModeCode http://zuserver2.star.ucl.ac.uk/~hiranya/modecode with R. Easther, M. Mortonson

ModeCode: accuracy Analytic solution for power law inflation Accuracy better than 0.01% Figure: Mortonson, Peiris, Easther (arxiv: 1007.4205)

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: 1007.4205)

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: 1007.4205)

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: 1007.4205)

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: 1007.4205)

Marginalized Reheating Uncertainty Grey: WMAP7+ general reheat Red: WMAP7 + instant reheat Figure: Mortonson, Peiris, Easther (arxiv: 1007.4205)

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

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

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

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

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

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

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.

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 ~0.0055 in isotropic universe.

Isotropy anomalies seem related to local directions SD GD GD SD

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

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 )

a posteriori

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C(!) = T1 T2

180 o S1/2 =! C(!) 2 cos! d! 60 o (Spergel+ 2003) C(!) (µk 2 ) 1000 800 600 400 200 0-200 -400 V W ILC (KQ75) ILC (full) WMAP5 C l WMAP pseudo-c l LCDM 0 20 40 60 80 100 120 140 160 180! (degrees) V W ILC (KQ75) ILC (full) WMAP5 C l WMAP pseudo-c l Copi+ 2009

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%

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%

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

1. Is ML-estimation reliable? Copi+ 2010, 1004.5602 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

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 (1004.2706, PRD, 2010)

Contamination Bianchi model Quad. modul. Picture 0.00 0.10 0.20 0.30 0.04 0.02 0.00 0.02 0.1 0.0 0.1 0.2 0.8 0.4 0.0 0.4 0.8 1.0 0.0 1.0 Designer 2.0 Bias /C PCL f sky =20% (2 +1) V / 2C QML f sky =20% 5 10 15 20 0.15 0.10 0.05 0.00 0.20 0.15 0.10 0.05 0.00 1.5 1.0 0.5 0.0 0.5 12.5 10.0 7.5 5.0 2.5 0.0 2 1 0 1 2 5 10 15 20 Pontzen & Peiris (1004.2706, PRD, 2010)

Feeney & Peiris (unpublished)

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

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%

0.8 large! small! Fractional error on PCL reconstruction C PCL l l full /C conc l 0.6 0.4 0.2 0.0 0.2 0.4 0.6 Shortfall of power 5 10 15 20 l PCL 1! variance full-sky ILC, 20% sky cut Pontzen & Peiris (1004.2706, PRD, 2010)

=5 Low, ~ planar quadrupole =7 + 35 µk =3 + 35 ILC7 =3, 5, 7 = =5 + =7 35 = 95 95 µk ILC7 =3, 5, 7 Pontzen & Peiris (1004.2706, PRD, 2010)

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

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"

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.

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 (1004.2706, PRD, 2010)

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 (1004.2706, PRD, 2010)

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