The Hubble Hunter’s
Guide*
Lloyd Knox
UC Davis

https://arxiv.org/abs/1908.03663*with apologies to J. Gunion et al.

The Hubble constant / soundhorizon problem
From “The Hubble Hunter’s Guide” (LK+Millea 2019)

Also see Bernal, Verde & Riess (2016), andArendse et al. (2019)

SH0ES 2019 (Cepheids + Supernovae)(no assumption of LCDM)BOSS BAO + Pantheon SNe(no assumption of LCDM*)
Planck (Assumes LCDM)*assumes 5-parameter spline modelfor H(z) and zero mean curvature.
Also see Raveri et al. (2019).

Sound Horizon

The Hubble constant / sound horizon
problem and opportunity for theorists
Goal:
Model X
• restoresconcordance• is compelling andbeautiful• makes predictions…
• …that aresubsequently
confirmed*assumes 5-parameter spline modelfor H(z) and zero mean curvature.
Also see Raveri et al. (2019).

From “The Hubble Hunter’s Guide” (LK+Millea 2019)

Planck (Assumes Model X)

Sound HorizonChallenge to Meeting Our Goal
Precision cosmological data, mostly CMB measurements:

Please ignore CMB-S4 forecasts

J. HenningOutline•

How LCDM enables predictions of H0 and rs.

•

Solution categories from the Hubble Hunter’sGuide•

Solutions that raise H(z) prior to recombination••

Challenges they face•

ResultsSummary and Conclusions

https://arxiv.org/abs/1811.00537 and ApJ

Sounds Discordant: Classical Distance Ladder and ΛCDMbased Determinations of the Cosmological Sound Horizon

Kevin Aylor Mackenzie Joy Marius Millea Srini Raghunathan Kimmy Wu^LKThe Hubble Hunter’s Guide LK and Marius Millea
https://arxiv.org/abs/1908.03663

Einstein-Boltzmann Solver
MCMC

Determining H0 from CMB Data in 3 steps
Step 1: Calibrating a Standard RulerDecoupling of baryons and photons
adr = cs dt
Z td
Z addars =cs dt/a =cs 2a H(a)00
Need to know cs(a) and H(a) to calibrate the ruler.

Determining H0 from CMB Data
Step 1: Calibrating a Standard Ruler
rs =Z td
0cs dt/a =Z ad0da
cs 2a H(a)Need to know cs(a) and H(a) to calibrate the ruler.

2cs = @P/@⇢⇢b /⇢H (a) = 8⇡G/3(⇢ + ⇢⌫ + ⇢m )2

Determining H0 from CMB Data
Step 1: Calibrating a Standard Ruler
rs =Z td0cs dt/a =Z ad0da
cs 2a H(a)Need to know c_s(a) and H(a) to calibrate the ruler.

2cs = @P/@⇢

Pressure of plasma impacts peakmorphology (odd/even height modulation)

2H (a) = 8⇡G/3(⇢ + ⇢⌫ + ⇢m )“Radiation Driving” effect (Hu & White 1997)

Determining H0 from CMB Data
Step 2: Use the Ruler to Infer Distance
Measure thiscalculate thisrs✓sDA (z = 1100)
Infer thisStep 3:DA (z) =Z zdz 0 /H(z 0 )0To get the right DA, only thing left in the model to adjust is
the cosmological constant. With that done, we have H(z).

Outline•

How LCDM enables predictions of H0 and rs.

•

Solution categories from the Hubble Hunter’sGuide•

Solutions that raise H(z) prior to recombination••

Challenges they face•

Results

Summary and Conclusions

https://arxiv.org/abs/1908.03663

The Hubble Hunter’s Guide*
Solution Categories

Post-recombination

High rs

Low rsPre-recombination

1) H(z) wiggles
2) Axion brightening
3) New physics impacting(some) Cepheids

1) Confusion sowing2) Post-recombination
evolution of BAO feature

1) Confusion sowing
2) Sound speed reduction
3) Reduction of conformal
time to recombination*with apologies to J. Gunion et al.

https://arxiv.org/abs/1908.03663

The Hubble Hunter’s Guide*
Categories of Solution

Post-recombination

High rs

Low rsDesmond, later
this session

Pre-recombination

1) H(z) wiggles
2) Axion brightening
3) New physics impacting(some) Cepheids

1) Confusion sowing2) Post-recombination
evolution of BAO feature

Marius Millea on Monday

1) Confusion sowing
2) Sound speed reduction
3) Reduction of conformal
time to recombination*with apologies to J. Gunion et al.

https://arxiv.org/abs/1908.03663

The Hubble Hunter’s Guide*
Categories of Solution

Post-recombination

High rs

Low rsDesmond, later
this session

Pre-recombination

1) H(z) wiggles
2) Axion brightening
3) New physics impacting(some) Cepheids

1) Confusion sowing2) Post-recombination
evolution of BAO feature

Marius Millea on Monday

1) Confusion sowing
2) Sound speed reduction
3) Reduction of conformal
time to recombination*with apologies to J. Gunion et al.

The Hubble constant / soundhorizon problem
Models that do notchange the matter content
we place in the ‘Confusion
Sowing’ category

From “The Hubble Hunter’s Guide” (LK+Millea 2019)

SH0ES 2019 (Cepheids + Supernovae)(no assumption of LCDM)BOSS BAO + Pantheon SNe(no assumption of LCDM*)

response toincreasing
matter density

Planck (Assumes LCDM)*assumes 5-parameter spline modelfor H(z) and zero mean curvature.
Also see Raveri et al. (2019).

Sound Horizon

https://arxiv.org/abs/1908.03663

The Hubble Hunter’s Guide*
Categories of Solution

Post-recombination

High rs

Low rsDesmond, later
this session

Pre-recombination

1) H(z) wiggles2) Axion brightening
3) New physics impacting(some) Cepheids

1) Confusion sowing2) Post-recombination
evolution of BAO feature

Marius Millea on Monday

1) Confusion sowing
2) Sound speed reduction
3) Reduction of conformal
time to recombination*with apologies to J. Gunion et al.

https://arxiv.org/abs/1908.03663

The Hubble Hunter’s Guide*
Categories of Solution

Post-recombination

High rs

Low rsDesmond, later
this session

Pre-recombination

1) H(z) wiggles
2) Axion brightening
3) New physics impacting(some) Cepheids

1) Confusion sowing2) Post-recombination
evolution of BAO feature

Marius Millea on Monday

1) Confusion sowing
2) Sound speed reduction
3) Reduction of conformal
time to recombination*with apologies to J. Gunion et al.

The Hubble Hunter’s Guide
Categories of Solution

Reduction of conformal time to recombination& Slosar (2019)
A) High-temperature recombination Chiang
Hart & Chluba (2018)B) Photon cooling/conversionC) Increasing H(z) with additional components:
1. Light Relics
2. Early/Acoustic Dark Energy

The Hubble Hunter’s Guide
Categories of Solution

Reduction of conformal time to recombination
A) High-temperature recombination Chiang & Slosar (2019)
Hart & Chluba (2018)B) Photon cooling/conversionC) Increasing H(z) with additional components:
1. Light Relics
2. Early/Acoustic Dark Energy

H0 Solutions: State of the Art
Light Relics
Self interacting
Lancaster, Cyr-Racine, LK, Pan (2017)
Kreisch et al. (2019)

Dark matterinteracting
Buen-Abad et al. (2018)
Pan, Kaplinghat, LK (2018)

See talk by
Francis-Yan
Cyr-Racine21

H0 Solutions: State of the Art
Scalar Fields
Light Relics
Self interacting

V ( ) / (1Lancaster, Cyr-Racine, LK, Pan (2017)
Kreisch et al. (2019)cos )3“Early Dark Energy”

Dark matterinteracting
Buen-Abad et al. (2018)
Pan, Kaplinghat, LK (2018)

See talk by
Francis-Yan
Cyr-Racine“Acoustic Dark Energy”
Poulin et al. (2019), Agrawal et al. (2019), Alexander and
McDonough (2019), Lin et al. (2019), Smith et al. (2019),
22

Outline•

How LCDM enables predictions of H0 and rs.

•Solution categories from the Hubble Hunter’sGuide•

Solutions that raise H(z) prior to recombination••

Challenges they face•

Results

Summary and Conclusions

Hubble Hunter’s Guide (LK + Millea)

Additional componentsmust be important in thisinterval if they are toreduce the sound horizon(Aylor et al. 2019)

CMB is very sensitive to that epoch

01021
31
4251
scale factor at recombination divided
by scale factor at horizon crossing

Summary of Current Measurements (+CMB-S4 Forecasts)
CMB-S4 Science Book

J. HenningChallenges•

Not altering rd/rs too much.

•Not altering the gravitational driving of theacoustic oscillations too much.

HO Tension

HO0 in.
3 in.
6 in.
9 in.

HO under tension

0 in.
3 in.
6 in.
9 in.

321Oscillation Amplitude Boost Factor

Amplitude Boost vs. Weight
Reduction

020406080

100

percentage weight reduction at low point in oscillation

23(3in —> 9 in.)1

Oscillation Amplitude Boost Factor

Amplitude Boost vs. Weight
Reduction

020406080

100

percentage weight reduction at low point in oscillation

23(3in —> 9 in.)1

Oscillation Amplitude Boost Factor

Amplitude Boost vs. Weight
Reduction

020406080

100

percentage weight reduction at low point in oscillation

23(3in —> 9 in.)

1Oscillation Amplitude Boost FactorAmplitude Boost vs. Weight
Reduction

020

40

60

80

100

percentage weight reduction at low point in oscillation

HO under tension

0 in.
3 in.
6 in.
9 in.

HO under tension

InitialEquilibrium

0 in.
3 in.
6 in.
9 in.

HO under tension
start with bottomof weight here

InitialEquilibrium

0 in.
3 in.
6 in.
9 in.

matter domination
start
here

range of oscillation —>(because grav potential is constantduring matter domination)

radiationInitial
domination
Equilibrium

range of oscillation —>(because grav potential nearly allgone after 1st compression)

0 in.
start
here
3 in.
6 in.
9 in.

if no photon diffusion

if no photon diffusion

The “potential envelope” of Hu & White (1997)

if no photon diffusion

The “potential envelope” of Hu & White (1997)

if no photon diffusion

01021
31
4251
scale factor at recombination divided
by scale factor at horizon crossingDespite the challenges…

V ( ) / (1Smith, Poulin & Amin (2019)cos )nSome Scalar Field Results
Dataset = Planck 2015 T+E+phi + SHOES + BAO + Pantheon
LCDM

cADE

Lin, Benvenuto, Hu & Raveri (2019)
Smith, Poulin & Amin (2019)Some Scalar Field Results
Dataset = Planck 2015 T+E+phi + SHOES + BAO + Pantheon
LCDMcADE

Lin, Benvenuto, Hu & Raveri (2019)
Smith, Poulin & Amin (2019)

The Hubble constant / sound horizon
problem and opportunity for theorists
Goal:
Model X
restoresconcordance• is compelling andX
beautiful• makes predictions
that are testable

From “The Hubble Hunter’s Guide” (LK+Millea 2019)•*assumes 5-parameter spline modelfor H(z) and zero mean curvature.
Also see Raveri et al. (2019).

Planck (Assumes Model X)

Sound Horizon

Summary and Conclusions•Two related, yet distinct, discrepancies: LCDM predicts low H0 and high rs.

•LCDM prediction of high rs is robust.

•LCDM prediction of a low H0 is robust given BAO + SNe data. (Does notdepend on any one dataset.)•

Best way to reduce sound horizon seems to be by increasing the expansion
rate in the ~decade of scale factor evolution just prior to recombination.

•Some models are achieving some degree of success in accommodating ahigh H0 and low rs.

•We’re in an exploratory phase, trying to understand what the data want, andtrying to deliver it with a palatable particle physics model.

•Predictions are being made that are testable in the relatively near future withdata to come from ACT, SPT, SO, and CMB-S4. See Jo Dunkley’s talk.

•Tension across angular scale internal to CMB data may be an important clue.