Type Ia Supernovae, Dark Energy, and the Hubble Constant · Wikipedia: “He proposed the theory of the expansion of the universe, widely misattributed to Edwin Hubble.[3][4] He was

Alex Filippenko University of California, Berkeley

Type Ia Supernovae, Dark Energy, and the Hubble Constant

Vatican Observatory, 9 May 2017

Lemaître Workshop: Black Holes, Gravitational Waves, Spacetime Singularities

Wikipedia: “He proposed the theory of the expansion of the universe, widely misattributed to Edwin Hubble.[3][4] He was the first to derive what is now known as Hubble's law and made the first estimation of what is now called the Hubble constant, which he published in 1927, two years before Hubble's article.[5][6][7][8] Lemaître also proposed what became known as the Big Bang theory of the origin of the universe, which he called his ‘hypothesis of the primeval atom’ or the ‘Cosmic Egg.’[9]”

Georges Lemaître

(1894 − 1966)

Vesto Slipher Edwin Hubble

(NASA/STScI/G. Bacon)

1917 (1922, 1923) 1929

log z (redshift)

Hubble’s law, v = H0d (v = cz)

log

d (d

ista

nce)

Observed low-redshift Hubble diagram (ideal):

Scale factor  

t0  (now)  

a(t)  

Low  (ΩM=0.3)  

Dense  (ΩM  >  1)  

Empty  (ΩM=0)  

Medium    (ΩM=1)  

Time t  

(ΩM  =  ρave/ρcrit)  

Dense    

(ΩM>1)  

t0  (now)  Age  

t  

RedshiC  z=0  a(t0)  

RedshiC    z  =  1  

Lookback    Gmes  for    

the  various  models  at  fixed  redshiC  

Note:  1  +  z  =  a(t0)/a(t)          z  =  redshiC  

0 0.3 1

>1

log

dist

ance

log z (redshift)

ΩM Observer’s version:

Determining the Hubble Diagram •  Redshift: easy to measure from galaxy spectrum •  Distance:

“Luminosity distance” dL

f = flux (erg/s-cm2) L = luminosity (erg/s)

•  Measure f, “know” L – NOT SO EASY ! – Need a “standard candle”

L

4π dL2

f =

Light Curve of Typical Cepheid

M31 (Andromeda)

Edwin Hubble

A03-93; SN 1998bu animation

(Peter Challis)

Spectra of Sne – Ia, II

Also discuss (but don’t show) Ib, Ic, IIb

a

An explosion resulting from the thermonuclear runaway of a white dwarf near M(Chandrasekhar)

5110

White Dwarf

An explosion resulting from the thermonuclear detonation of a White Dwarf Star

Type Ia Supernova

03W-220, merger of 2 WDs.

But not many WD-WD pairs known, that are close enough to merge in a relatively short time (some SN Ia come from 0.5-1 billion year old stars).

So consider sub-Chandra explosions (Next Slide) – but these have problems, too.

Thermonuclear runaway of some sort, in any case.

Type Ia Supernova

Calibrating the Nearly Standard Candle •  Phillips (1993), Riess

+ (1995), Hamuy+ (1995): established L vs. light-curve shape correlation with ~ 10 nearby SNe Ia

•  Use it to standardize other SNe Ia

•  Measured colors give reddening and extinction

•  Accurately calibrate individual SNe!

MLCS: Multi-color Light-Curve Shape (Riess et al.)

Absolute light curves of SN Ia in galaxies of

known distance Luminous

SNe Ia have slower light

curves!

σ = 0.44 mag

σ = 0.15 mag!

∝ log dL

∝ log dL

(Riess et al. 1995, 1996)

SN 1994d

S. Perlmutter, G. Aldering, S. Deustua, S. Fabbro, G. Goldhaber, D. Groom,A. Kim, M. Kim, R. Knop, P. Nugent, (LBL & CfPA)N. Walton (Isaac Newton Group)A. Fruchter, N. Panagia (STSci)A. Goobar (Univ of Stockholm)R. Pain (IN2P3, Paris)I. Hook, C. Lidman (ESO)M. DellaValle (Univ of Padova)R. Ellis (CalTech)R. McMahon (IofA, Cambridge)B. Schaefer (Yale)P. Ruiz-Lapuente (Univ of Barcelona)H. Newberg (Fermilab)C. Pennypacker

• Brian Schmidt (ANU)• Nick Suntzeff, Bob Schommer, Chris Smith (CTIO)• Mark Phillips (Carnegie)• Bruno Leibundgut and Jason Spyromilio (ESO)• Bob Kirshner, Peter Challis, Tom Matheson (Harvard)• Alex Filippenko, WeidongLi, Saurabh Jha(Berkeley)• Peter Garnavich, Stephen Holland (Notre Dame)• Chris Stubbs (UW)• John Tonry, Brian Barris (University of Hawaii)• Adam Reiss (Space Telescope)• Alejandro Clocchiatti (Catolica Chile)• Jesper Sollerman(Stockholm)

Cerro Tololo Inter-American Observatory, Chile

(CTIO)

Searching by Subtraction

W. M. Keck Observatory, Hawaii (two 10-meter telescopes)

Low-z and High-z SN IaKeck LRIS, 1 hour

3 HST supernovae

•  Fainter than expected. •  So faint that they are farther than they could

have been, if Universe decelerating or expanding with constant speed.

•  Therefore, Universe must have accelerated. •  Cosmic antigravity! •  Let me explain in more detail

0 0.3 1

>1

ΩΜ < 0 ?! lo

g di

stan

ce

log z (redshift)

ΩM

Hubble’s law, v = H0d (v = cz)

Observer’s version:

Cosmological Const. Other galaxy

Milky Way galaxy

0 0.3 1

>1

Λ > 0 ?! lo

g di

stan

ce

log z (redshift)

ΩM

Hubble’s law, v = H0d (v = cz)

Observer’s version:

Pre-1998 data:

Riess et al. (1998) – blue dots

Perlmutter et al. (1999) – red dots

High-z data: fainter than flat or low-ΩM Univ.

∝ log dL

∝ [Δ (log dL)]

Pre-1998 data: Riess et al. (1998) Perlmutter et al. (1999)

A nonzero cosmological constant!?

High-z Team, Sep. 1998

SCP, June 1999

THE  ACCELERATING  UNIVERSE  (1998)  

et al. (AVF, …)

(SDSS, other LSS studies, and measurements of clusters: large majority agree that ΩM = 0.3 ± 0.1)

CMB sky if different geometries

(2000/ 2001)

Clusters, large-scale structure: ΩM = 0.3 ± 0.1

Concor-dance: (ΩM, ΩΛ = (0.3, 0.7)

LSS

(CMB)

WMAP CMB Map of the Early Universe, t = 380,000 years old

SN Ia + LSS: ΩM = 0.28, ΩΛ = 0.72

Precision comparable to CMB + LSS

Riess et al. (2004), using all published high-z SN Ia data.

ΩΜ = 1 ruled out at very many σ!

Probing the era of deceleration

Scale factor

t0 (now)

a(t)

Low (ΩM=0.3)

Dense (ΩM > 1)

Empty(ΩM=0)

Medium (ΩM=1)

Time t

Note: 1+z = a(t0) / a(t) z = redshift

"Cosmic Antigravity"

(ΩΛ > 0)

(ΩM = ρave/ρcrit)

(Riess et al. 2007)

(mag

) ∝

log

d L

He retained the cosmological constant after Einstein & de Sitter (1932) had renounced it. Advocated a model with Λ in which the expansion initially decelerates and later accelerates (Lemaître 1934)! Among other things, this might remove a conflict between the known ages of stars and the expansion age of the Universe.

Georges Lemaître

(1894 − 1966)

Evolution of Universe: simulation (A. Kravtsov)

(Expansion removed)

Simulated 3D flight through Universe (V. Springel)

(Expansion removed)

Dark%energy%%70%%

Ordinary%ma1er%5%%

Dark%ma1er%%25%%

A5er%Planck%Average Composition of the Universe

(atoms)

(nonbaryonic)

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Multimedia

Studies of Universe’s Expansion Win Physics Nobel

Johns Hopkins University; University Of California At Berkeley; Australian National University

From left, Adam Riess, Saul Perlmutter and Brian Schmidt shared the Nobel Prize in physics awarded Tuesday.

By DENNIS OVERBYEPublished: October 4, 2011

Three astronomers won the Nobel Prize in Physics on Tuesday fordiscovering that the universe is apparently being blown apart by amysterious force that cosmologists now call dark energy, a findingthat has thrown the fate of the universe and indeed the nature ofphysics into doubt.

The astronomers are Saul Perlmutter,52, of the Lawrence Berkeley NationalLaboratory and the University ofCalifornia, Berkeley; Brian P. Schmidt,44, of the Australian NationalUniversity in Canberra; and Adam G.Riess, 41, of the Space TelescopeScience Institute and Johns HopkinsUniversity in Baltimore.

“I’m stunned,” Dr. Riess said by e-mail, after learning of hisprize by reading about it on The New York Times’s Website.

The three men led two competing teams of astronomerswho were trying to use the exploding stars known as Type1a supernovae as cosmic lighthouses to limn the expansionof the universe. The goal of both groups was to measurehow fast the cosmos, which has been expanding since itsfiery birth in the Big Bang 13.7 billion years ago, was

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TimesCast | Nobel Nod to DarkEnergy

Saul Perlmutter on DarkEnergy

Nobel in Physics Goes to Perlmutter, Schmidt and Riess - NYT... http://www.nytimes.com/2011/10/05/science/space/05nobel.htm...

1 of 4 10/4/11 6:40 PM

2011 Nobel Prize in Physics

Dec. 8, pm: High-z Team celebratory lunch

The 2015 Breakthrough Prize in Fundamental Physics

Since “dark energy” seems real…

what is it?

CMB (WMAP, Planck)

SN Ia

LSS

+ ISW, X-ray Clusters

Λ, the Cosmological Constant? •  Not good quantitative

agreement with theo-retical expectations!

•  Way too small (ΩΛ ≈ 0.7), and “Why now?”

•  “A bone in the throat.” – Steven Weinberg

Define w = P/(ρc2) •  Equation-of-state parameter •  ρ ∝ (volume)−(1+w)

w = 0 for normal nonrelativistic matter w = 1/3 for photons w = −1 for Λ w ≠ −1 for “quintessence,” etc. (rolling

scalar field, etc.; −1/3 for cosmic strings). In GR, gravitational acceleration ∝ −(ρc2 + 3P). If w < −1/3, the Universe accelerates!

Difference in apparent SN brightness vs. z ΩΛ = 0.70, flat universe

(mag)

Redshift z 0.01 Redshift z 0.1 1.0

Betoule et al. (2014) SDSS-II + SNLS joint analysis

∝ lo

g d L

(Planck+WP: Planck CMB temperature fluctuations, WMAP CMB polarization. JLA: SNLS-SDSS joint SN Ia light-curve analysis. BAO: baryon acoustic osc.)

(Betoule et al. 2014)

Time-dependent w? Assume w(a) = w0 + wa(1−a), where a = 1/(1+z) is a scale factor (Linder 2003). For Λ: w0 = −1 and wa = 0

(Betoule et al. 2014)

The Most Recent Surprise

The current rate of expansion still

might be too high!

Planck satellite map of the early Universe, t = 380,000 years old

Planck team, 2015, power spectrum

CMB: Measure θs; know rs (rs = sound horizon length) The angular diameter distance is

defined as DA = rs/θs .

(z* = redshift of CMB = 1079)

Planck Data: Predict Current Expansion Rate (H0)

• H0 = 66.93 ± 0.62 km/s/Mpc (67.8 ± 0.9 km/s/Mpc)

• Previous direct measurements: H0 = (70−75) ± (4−7) km/s/Mpc

• Possible conflict, but not clear: error bars large and uncertain

Planck team, 2015 paper

SH0ES (Riess et al. 2005, 2009a,b, 2011, 2014, 2016; see also Macri

Hoffman+ 2016, Macri+ 2017) •  Goal: Measure current value of H0 to ± 1%,

through direct parallaxes of Galactic Cepheids, Cepheid calibration of SN Ia host galaxies, and SN Ia Hubble diagram.

•  Latest results: Riess et al. (2016):

SN 1994d

With Cepheids and SNe Ia, we (Riess+ 2016) Measured Current H0

• H0 = 73.24 ± 1.74 km/s/Mpc • Planck: H0 = 67.8 ± 0.9 (66.93 ±

0.62), ~3σ from Cepheid/SN Ia •  There may be a conflict! • We have smaller uncertainties

than before, and we think we understand them very well.

Possible explanations • Relaxing constraints;

e.g., flatness? • Evolving dark energy

equation of state? (but data suggest w ~ -1)

• >3 neutrino species? ("dark radiation")

Technique errors? New physics? (GR wrong? Weird DM?) Need independent methods to overcome systematics.

Measurements of H0

Planck 2015: 66.93 ± 0.62 (0.9%)

73.24 ± 1.74 (2.4%) Riess et al. 2016

H0LiCOW: H0 Lenses in COSMOGRAIL’s Wellspring

Bonvil et al. (2017) and 4 other papers: use measured time delays in distinct images of gravitationally lensed QSOs

length - length

Q2237+030

•  QSOs are powered by accretion into SMBH •  Light emitted from quasars changes in time (“flickers”)

Strongly lensed quasars (QSOs)

The H0LiCOW QSO Sample

Current Expansion Rate (H0) • H0LiCOW: H0 = 72.8 ± 2.4 km/s/

Mpc (Bonvin et al. 2017; 3 lenses) • H0 = 73.24 ± 1.74 km/s/Mpc (Riess

et al. 2016; SNe Ia + Cepheids) • Planck: H0 = 67.8 ± 0.9 (66.9 ± 0.6) • A new, very light, fundamental

subatomic particle (neutrino?) exists?! “Dark radiation”?!

?!

Stay tuned!

•  Vatican Observatory (invitation to speak) •  National Science Foundation (NSF) •  Nat. Aeronautics & Space Adm. (NASA) •  US Department of Energy •  AutoScope Corporation •  TABASGO Foundation (Wayne Rosing) •  Sylvia and Jim Katzman Foundation •  Gary and Cynthia Bengier •  Christopher R. Redlich Fund •  Richard and Rhoda Goldman Fund

Thank You!

Addison, Huang, Watts, Bennett, Halpern, Hinshaw, Weiland 2016, ApJ, 818, 132

4 G. E. Addison et al.

0.020

0.022

⌦bh

2

0.11

0.12

0.13

⌦ch

2

0.001

0.002

0.003

✓ MC

+1.039

3.0

3.1

log(

1010

As)

0.95

1.00

1.05

ns

60

65

70

H0

0.06 0.07 0.08 0.09

⌧

0.3

0.4

⌦m

0.06 0.07 0.08 0.09

⌧

0.80

0.85

�8

0.06 0.07 0.08 0.09

⌧

1.75

1.80

1.85

1.90

1.95

109

Ase

�2⌧

Planck TT 2015 2 ` < 1000 Planck TT 2015 1000 ` 2508

Figure 2. Marginalized 68.3% confidence ⇤CDM parameter constraints from fits to the ` < 1000 and ` � 1000 Planck TT spectra. Herewe replace the prior on ⌧ with fixed values of 0.06, 0.07, 0.08, and 0.09, to more clearly assess the e↵ect ⌧ has on other parameters in thesefits. Aside from the strong correlation with As, which arises because the TT spectrum amplitude scales as Ase�2⌧ , dependence on ⌧ isfairly weak. Tension at the > 2� level is apparent in ⌦ch2 and derived parameters, including H0, ⌦m, and �8.

rameters to the best-fit values inferred from the fit to thewhole Planck multipole range rather than allowing themto vary separately in the ` < 1000 and ` � 1000 fits.This helps break degeneracies between foreground and⇤CDM parameters and leads to small shifts in ⇤CDMparameter agreement, with the tension in ⌦ch

2 decreas-ing to 2.3� for ⌧ = 0.07± 0.02, for example. The best-fit�2 is, however, worse by 3.1 and 4.8 for the ` < 1000and ` � 1000 fits, respectively, reflecting the fact thatthe ` < 1000 and ` � 1000 data mildly prefer di↵erentforeground parameters. Overall the choice of foregroundparameters does not significantly impact our conclusions.

3.1. Comparing temperature and lensing spectra

Planck Collaboration XIII (2015) found that allowing anon-physical enhancement of the lensing e↵ect in the TTpower spectrum, parametrized by the amplitude param-eter AL, was e↵ective at relieving the tension betweenthe low and high multipole Planck TT constraints. Forthe range of scales covered by Planck, the main e↵ectof increasing AL is to slightly smooth out the acousticpeaks. If ⇤CDM parameters are fixed, a 20% change inAL suppresses the fourth and higher peaks by around0.5% and raises troughs by around 1%, for example.

In Figure 3 we show the e↵ect of fixing AL to valuesother than the physical value of unity on the ` < 1000and ` � 1000 parameter comparison, for ⌧ = 0.07± 0.02.For AL > 1 the parameters from ` � 1000 shift towardsthe ` < 1000 results, resulting in lower values of ⌦ch

2 andhigher values of H0. Planck Collaboration XIII (2015)found AL = 1.22±0.10 for plik combined with the low-` Planck joint temperature and polarization likelihood,although note that this fit was performed using PICOrather than CAMB, which uses a somewhat di↵erent ALdefinition.

Lensing also induces specific non-Gaussian signaturesin CMB maps that can be used to recover the lens-ing potential power spectrum (hereafter ‘�� spectrum’).Planck Collaboration XV (2015) report a measurementof the �� spectrum using temperature and polarizationdata with a combined significance of ⇠ 40�. The ��spectrum tightly constrains the parameter combination�8⌦0.25

m . We computed constraints on this same combi-nation from Planck TT data using a ⌧ = 0.07 ± 0.02prior:

�8⌦0.25m = 0.591 ± 0.021 (Planck 2015 ��),

= 0.583 ± 0.019 (Planck 2015 TT ` < 1000),

= 0.662 ± 0.020 (Planck 2015 TT ` � 1000).(1)

The ` < 1000 and ` � 1000 TT values di↵er by 2.9�,consistent with the di↵erence in ⌦ch

2 discussed above.The ` � 1000 and �� values are in tension at the 2.4�level (for fixed values of ⌧ in the range 0.06 to 0.09 wefind a 2.4 � 2.5� di↵erence). The ` < 1000 TT and ��values are consistent within 0.3�.

It is worth noting that while allowing AL > 1 doesrelieve tension between the low-` and high-` TT results,it does not alleviate the high-` TT tension with ��. ForAL = 1.2 (by the CAMB definition) we find �8⌦0.25

m =0.612 ± 0.019 from ` 1000, while the �� spectrumrequires �8⌦0.25

m = 0.541 ± 0.019. This is because the�� power roughly scales as AL(�8⌦0.25

m )2, so, for fixed��, increasing AL by 20% requires a ⇠ 10% decrease in�8⌦0.25

m . As shown in Figure 4, there is no value of ALthat produces agreement between these data.

The �� spectrum featured prominently in the Planck

claim that the true value of ⌧ is lower than the valueinferred by WMAP (Planck Collaboration XIII 2015).

4 G. E. Addison et al.

0.020

0.022

⌦bh

2

0.11

0.12

0.13

⌦ch

2

0.001

0.002

0.003

✓ MC

+1.039

3.0

3.1

log(

1010

As)

0.95

1.00

1.05

ns

60

65

70

H0

0.06 0.07 0.08 0.09

⌧

0.3

0.4

⌦m

0.06 0.07 0.08 0.09

⌧

0.80

0.85

�8

0.06 0.07 0.08 0.09

⌧

1.75

1.80

1.85

1.90

1.95

109

Ase

�2⌧

Planck TT 2015 2 ` < 1000 Planck TT 2015 1000 ` 2508

Figure 2. Marginalized 68.3% confidence ⇤CDM parameter constraints from fits to the ` < 1000 and ` � 1000 Planck TT spectra. Herewe replace the prior on ⌧ with fixed values of 0.06, 0.07, 0.08, and 0.09, to more clearly assess the e↵ect ⌧ has on other parameters in thesefits. Aside from the strong correlation with As, which arises because the TT spectrum amplitude scales as Ase�2⌧ , dependence on ⌧ isfairly weak. Tension at the > 2� level is apparent in ⌦ch2 and derived parameters, including H0, ⌦m, and �8.

rameters to the best-fit values inferred from the fit to thewhole Planck multipole range rather than allowing themto vary separately in the ` < 1000 and ` � 1000 fits.This helps break degeneracies between foreground and⇤CDM parameters and leads to small shifts in ⇤CDMparameter agreement, with the tension in ⌦ch

2 decreas-ing to 2.3� for ⌧ = 0.07± 0.02, for example. The best-fit�2 is, however, worse by 3.1 and 4.8 for the ` < 1000and ` � 1000 fits, respectively, reflecting the fact thatthe ` < 1000 and ` � 1000 data mildly prefer di↵erentforeground parameters. Overall the choice of foregroundparameters does not significantly impact our conclusions.

3.1. Comparing temperature and lensing spectra

Planck Collaboration XIII (2015) found that allowing anon-physical enhancement of the lensing e↵ect in the TTpower spectrum, parametrized by the amplitude param-eter AL, was e↵ective at relieving the tension betweenthe low and high multipole Planck TT constraints. Forthe range of scales covered by Planck, the main e↵ectof increasing AL is to slightly smooth out the acousticpeaks. If ⇤CDM parameters are fixed, a 20% change inAL suppresses the fourth and higher peaks by around0.5% and raises troughs by around 1%, for example.

In Figure 3 we show the e↵ect of fixing AL to valuesother than the physical value of unity on the ` < 1000and ` � 1000 parameter comparison, for ⌧ = 0.07± 0.02.For AL > 1 the parameters from ` � 1000 shift towardsthe ` < 1000 results, resulting in lower values of ⌦ch

2 andhigher values of H0. Planck Collaboration XIII (2015)found AL = 1.22±0.10 for plik combined with the low-` Planck joint temperature and polarization likelihood,although note that this fit was performed using PICOrather than CAMB, which uses a somewhat di↵erent ALdefinition.

Lensing also induces specific non-Gaussian signaturesin CMB maps that can be used to recover the lens-ing potential power spectrum (hereafter ‘�� spectrum’).Planck Collaboration XV (2015) report a measurementof the �� spectrum using temperature and polarizationdata with a combined significance of ⇠ 40�. The ��spectrum tightly constrains the parameter combination�8⌦0.25

m . We computed constraints on this same combi-nation from Planck TT data using a ⌧ = 0.07 ± 0.02prior:

�8⌦0.25m = 0.591 ± 0.021 (Planck 2015 ��),

= 0.583 ± 0.019 (Planck 2015 TT ` < 1000),

= 0.662 ± 0.020 (Planck 2015 TT ` � 1000).(1)

The ` < 1000 and ` � 1000 TT values di↵er by 2.9�,consistent with the di↵erence in ⌦ch

2 discussed above.The ` � 1000 and �� values are in tension at the 2.4�level (for fixed values of ⌧ in the range 0.06 to 0.09 wefind a 2.4 � 2.5� di↵erence). The ` < 1000 TT and ��values are consistent within 0.3�.

It is worth noting that while allowing AL > 1 doesrelieve tension between the low-` and high-` TT results,it does not alleviate the high-` TT tension with ��. ForAL = 1.2 (by the CAMB definition) we find �8⌦0.25

m =0.612 ± 0.019 from ` 1000, while the �� spectrumrequires �8⌦0.25

m = 0.541 ± 0.019. This is because the�� power roughly scales as AL(�8⌦0.25

m )2, so, for fixed��, increasing AL by 20% requires a ⇠ 10% decrease in�8⌦0.25

m . As shown in Figure 4, there is no value of ALthat produces agreement between these data.

The �� spectrum featured prominently in the Planck

claim that the true value of ⌧ is lower than the valueinferred by WMAP (Planck Collaboration XIII 2015).

4 G. E. Addison et al.

0.020

0.022

⌦bh

2

0.11

0.12

0.13

⌦ch

2

0.001

0.002

0.003

✓ MC

+1.039

3.0

3.1

log(

1010

As)

0.95

1.00

1.05

ns

60

65

70

H0

0.06 0.07 0.08 0.09

⌧

0.3

0.4

⌦m

0.06 0.07 0.08 0.09

⌧

0.80

0.85

�8

0.06 0.07 0.08 0.09

⌧

1.75

1.80

1.85

1.90

1.95

109

Ase

�2⌧

Planck TT 2015 2 ` < 1000 Planck TT 2015 1000 ` 2508

Figure 2. Marginalized 68.3% confidence ⇤CDM parameter constraints from fits to the ` < 1000 and ` � 1000 Planck TT spectra. Herewe replace the prior on ⌧ with fixed values of 0.06, 0.07, 0.08, and 0.09, to more clearly assess the e↵ect ⌧ has on other parameters in thesefits. Aside from the strong correlation with As, which arises because the TT spectrum amplitude scales as Ase�2⌧ , dependence on ⌧ isfairly weak. Tension at the > 2� level is apparent in ⌦ch2 and derived parameters, including H0, ⌦m, and �8.

rameters to the best-fit values inferred from the fit to thewhole Planck multipole range rather than allowing themto vary separately in the ` < 1000 and ` � 1000 fits.This helps break degeneracies between foreground and⇤CDM parameters and leads to small shifts in ⇤CDMparameter agreement, with the tension in ⌦ch

2 decreas-ing to 2.3� for ⌧ = 0.07± 0.02, for example. The best-fit�2 is, however, worse by 3.1 and 4.8 for the ` < 1000and ` � 1000 fits, respectively, reflecting the fact thatthe ` < 1000 and ` � 1000 data mildly prefer di↵erentforeground parameters. Overall the choice of foregroundparameters does not significantly impact our conclusions.

3.1. Comparing temperature and lensing spectra

Planck Collaboration XIII (2015) found that allowing anon-physical enhancement of the lensing e↵ect in the TTpower spectrum, parametrized by the amplitude param-eter AL, was e↵ective at relieving the tension betweenthe low and high multipole Planck TT constraints. Forthe range of scales covered by Planck, the main e↵ectof increasing AL is to slightly smooth out the acousticpeaks. If ⇤CDM parameters are fixed, a 20% change inAL suppresses the fourth and higher peaks by around0.5% and raises troughs by around 1%, for example.

In Figure 3 we show the e↵ect of fixing AL to valuesother than the physical value of unity on the ` < 1000and ` � 1000 parameter comparison, for ⌧ = 0.07± 0.02.For AL > 1 the parameters from ` � 1000 shift towardsthe ` < 1000 results, resulting in lower values of ⌦ch

2 andhigher values of H0. Planck Collaboration XIII (2015)found AL = 1.22±0.10 for plik combined with the low-` Planck joint temperature and polarization likelihood,although note that this fit was performed using PICOrather than CAMB, which uses a somewhat di↵erent ALdefinition.

Lensing also induces specific non-Gaussian signaturesin CMB maps that can be used to recover the lens-ing potential power spectrum (hereafter ‘�� spectrum’).Planck Collaboration XV (2015) report a measurementof the �� spectrum using temperature and polarizationdata with a combined significance of ⇠ 40�. The ��spectrum tightly constrains the parameter combination�8⌦0.25

m . We computed constraints on this same combi-nation from Planck TT data using a ⌧ = 0.07 ± 0.02prior:

�8⌦0.25m = 0.591 ± 0.021 (Planck 2015 ��),

= 0.583 ± 0.019 (Planck 2015 TT ` < 1000),

= 0.662 ± 0.020 (Planck 2015 TT ` � 1000).(1)

The ` < 1000 and ` � 1000 TT values di↵er by 2.9�,consistent with the di↵erence in ⌦ch

2 discussed above.The ` � 1000 and �� values are in tension at the 2.4�level (for fixed values of ⌧ in the range 0.06 to 0.09 wefind a 2.4 � 2.5� di↵erence). The ` < 1000 TT and ��values are consistent within 0.3�.

It is worth noting that while allowing AL > 1 doesrelieve tension between the low-` and high-` TT results,it does not alleviate the high-` TT tension with ��. ForAL = 1.2 (by the CAMB definition) we find �8⌦0.25

m =0.612 ± 0.019 from ` 1000, while the �� spectrumrequires �8⌦0.25

m = 0.541 ± 0.019. This is because the�� power roughly scales as AL(�8⌦0.25

m )2, so, for fixed��, increasing AL by 20% requires a ⇠ 10% decrease in�8⌦0.25

m . As shown in Figure 4, there is no value of ALthat produces agreement between these data.

The �� spectrum featured prominently in the Planck

claim that the true value of ⌧ is lower than the valueinferred by WMAP (Planck Collaboration XIII 2015).

H0

Evidence)for)a)systema3c)error)in)the)Planck)CMB)data?)

Claimed 2.5 σ Tension Between Halves of Planck CMB data, l>1000 vs l<1000 (WMAP)

Planck Team, arXiv: 1608.02487—”2.5 σ like 1.8 σ for 6 parameters”, but we measure H0 !

Current Status•  Dark energy exists, or GR wrong. •  Most data consistent with w0 = −1,

wa = 0: the cosmological constant! •  But it’s possible that dark energy is

growing stronger with time (or that there is a new form of relativistic particle: “dark radiation”).

•  The future looks hopeful! Larger homogeneous samples, improved techniques (e.g., Gaia parallaxes).

However…•  If dark energy really is Λ, we will

never know for sure. •  Cannot prove w0 = −1.0000000…

and wa = 0.0000000… •  Can only show w0 ≠ −1.0000000…

and wa ≠ 0.0000000… •  And, it becomes progressively

more expensive & time consuming to decrease the error bars.