Lessons on solving the Hubble tension
Cosmic Controversies Conference
ChicagoOctober 5, 2019

Francis-Yan Cyr-Racine
Assistant Professor
Department of Physics and Astronomy, University of New Mexico
w/ Christina Kreisch, Prateek Agrawal, David Pinner, Lisa Randall, Lloyd Knox

Approach: Discrepancy in the baryon
sound horizon

Knox & Millea (2019)

Francis-Yan Cyr-Racine - UNM

See also Arendse et al. (2019). Aylor et al. (2018),
Bernal et al. (2016), Verde et al. (2017)10/5/192

How to modify the Baryon-PhotonSound Horizon• Can either change the sound speed,or the Hubble rate at early times.

rs =Z ad0cs (a)
da 2a H(a)Can we change the
Hubble rate before
recombination without
ruining everything else?

Francis-Yan Cyr-Racine - UNM

cs = q13⇢b3(1 + 4⇢)X8⇡G
H 2 (a) =⇢i (a)
3i
10/5/193

Sound horizon probe: BAO
Eric Huff (JPL)BAO primarily measures 2“processed” versions of thebaryon-photon soundhorizon.
Line of sight:
Transverse:H(z)rsrs /DA (z)BAO measurements are invariant under the change H(z) ! f H(z)Francis-Yan Cyr-Racine - UNM

10/5/194

Canonical Neff alone doesn’t work…
• BAO and CMB prefers different trajectories in energy
density space.
• BAO likes scaling solution H(z) ! f H(z) , CMB doesn’t.

⌦c h2

0.128

CMB LCDM best fit
scaling

0.37

Leaves BAO~invariant

0.36
⌦DEh2

0.130

0.38

CMB best fit
scaling

0.132

0.126

0.35
0.34

0.124

0.33
0.122

Leaves BAO~invariant

0.32
0.120
3.1

3.2

3.3

Francis-Yan Cyr-Racine - UNM

3.4

Ne↵

3.5

3.6

3.7

3.8

0.31

3.1

3.2

3.3

3.4

Ne↵

3.510/5/19

3.6

3.7

3.8

5

properties, most notablyof their3)rγ =theΦ+ (1/ sum' of such new physics. In recent years, cosmology
31andnumber
the dots standterms. cosm
The Fotheir. e↵ective[?for?more? regular]. Can
ζin −dχ F− (χ) vided
(115)
pγ =
someofthemoststringent
constraintsontransformofeq.
(118)
followsfromthefirstand1 − 2Rν 2−1
canproperties,
inform us
about
other
aspectsofneutrilines of Table II, where n is set to 0 and 1, as
most notably the sum of their m%& 1Free-streaming neutrinos and the CMB$#Calculating pΦ from the last two equations is somewhat√O(ϕs−1 ) .
dγ (τ,numberk) = 2 pγ cosrγ π]. 3 Can
sin ϕs +their e↵ective[? ϕ?
cosmologeasier than from eq. (107).
s −?
Now we have all the analytic tools to analyze how neucan inform Ausnon-zero
aboutotherof toneutrino
2 phaseshiftaspects
with respect
the cos ϕstrinos aﬀect CMB perturbations. The evolution of metricFlations
isgenerated
wheneverr≠0.
Byeq. 11(119γperturbations without neutrinos is given by eqs. (108–234
can happen for adiabatic perturbations if only some109). Then the photon density Green’s function follows
p W
turbations
faster than the sound speed ifrom eqs. (112, 115) as
GF photon
2 fluid,g 2propagate
andthus
are able to ⇥generate
metricpe7== 1.16637(1)10 11MeVz = 5 ¥ 102$(√ #3
beyond the acoustic horizon. This is the ca(~c) bations
8 m(R →0)
-4-2W
3 θ √13 − |χ| −d¯γ ν= −3ζinthe neutrino perturbations,
150 Geff = 10 MeV
2 propagating
22 with
5 the(116)$)#of light, Fig.
3 a). ⌫ F ⌫WF ⌫Baryon-photon acoustic wave− 21 δD |χ| − √1 Free.
The values of pγ and rγ in eq. (118) are calcu
3streaming
2 2 C. With
2 5its resultsin O(Rν ) order in Appendix
/nGT/
GW
⌫
F
⌫
F T⌫ asand (C7), the mode (120) can be presented
neutrinos
Its Fourier transform (93) leads to the photondensity
Fourier modes in the radiation era:
propagate
100dγ (τ, k) = 3ζin (1 + ∆γ ) cos (ϕs + δϕ) + O(ϕs−1 ) ,*+faster than⌫,dec
2 sin ϕswheredγ(Rν →0) (τ, k) = −3ζin− cos ϕs , (117)baryonϕs
T ≃ − 0.2683R= 1.48+MeV
photon∆γ ⌫,decO(Rν2 ) ,√νwith ϕs = kτ / 3. In particular, without neutrinos thesound wave
50
photon density modes oscillate under the acoustic horiδϕ ≃ 0.1912 πRν + O(Rν2 ) .
⌫Self-Interacting
HSIL
Neutrinoszon (ϕs ≫ 1) as a pure ϕs cosine.
⌫Photons(wo/standardneutrinos)Photons
Hwê SIneutrinosL⇢⌫ 4 a),⌫our theoretical predic
As demonstrated in Fig.
The predictions
for boththe phase and the amplitude
R=' 0.403⌫
are in excellent agreement withnumerical calculaof the photon
mode oscillations diﬀer when the gravity
Standard
Neutrinos⇢ + ⇢⌫

Baryon-photon perturbations interact with all
p relativistic species
through their gravitational coupling G = 2 g = 1.16637(1) ⇥ 10(~c)

8 m

M150

dg HrLdn,g HrL/n G T /G T

10050Photons Hwê standard neutrinosL0T= 1.48 MeVR =⇢' 0.403⇢ +⇢One0.0050assumption that is rarely challenged isNe↵ ' 3.046
forof cosmological-1
streaming
natureneutrinos (fr @h MpcDtions,see [? ? Bashinsky? ? ?&? Seljak? ]).(2004)
Within the standa
FIG. 2. Snapshot of neutrino and photon density fluctuations in configuration space at a fixed redshift. The
black dot-dashed& Sigurdson
0 (2014)assumption
thatisrarely
challenge
line showsCyr-Racine
the standard free-streaming
neutrino
fluctuation while the green dashed line displays the One
correspondingphoton
Follinal. (2015) since SM neutrino
density fluctuation. The solid blue and red dotted lines show the density fluctuation of self-interacting
neutrinos
and thethisassumption
isetjustified
corresponding photon perturbation, respectively. These two lines0.0010
lie on top of one another sincebothneutrinos andphotons0.00150.00200.0050Baumann,
Green,Meyers & Wallisch(2016)
streaming
natureof0.0030
cosmologicalneutrino
behave as tightly-coupled fluids at the epoch shown here. The di↵erence between the green dashed and pected
the red dottedlines
tohavedecoupledfromtheprimeval
plas
Choi,
Chiang&Loverde(2018)
readily illustrates the phase shift and amplitude suppression of the photon fluctuation associated with free-streaming neutrinos.
0.00100.0015Here we have adopted a Planck cosmology [3].

Francis-Yan Cyr-Racine - UNM
neutrinos solely couple to CMB photons via the gravitational potentials, which themselves depend on integrals

0.00200.0030

tions,
see-1[?MpcD? ? ? ? ? ? ]). Within the star @h
10/5/19

ond term becomes vanishingly small and c2vis ! 1/3. Thisillustrates that modeling nonstandard neutrino physics

6neutrino-electron
residual Since
that[23]drives
difference
antineutrinos.
CMB(see Ref.
for a review).
Ge↵ in Eq. (1)interacis
how well neu
calculatingtions to heat the neutrinos.
Byassume
momentum-independent,
we willthis interaction
processes involving elec⌫ tem+—photonrisingtherelativelyȧable to track
are “integrating
trinosfrom
arisesout”
aparticle
withmassm
neutrinos, v+e*+ v+e
˙DM + ✓DM c2 k 2 DM k 2 =✓of neutrino
theDM
followprocess
able to ato
we are coupling
perature,
anda perturbative
neutrinos
g :attering and annihilation
decoupling.
nos can only thermalize
1 in
1 we↵ write the phase-space dis
WithL these facts
2 mind,2+v„orv, +v,Interaction:v, +v„~v,New
Unknownm+(g⌫↵ ⌫ + h.c.),
(3)
phen
2
2
and scattering processes
8⇡G
2
H =
⇢tot
nd their matrix-elements
where2⌫↵ are two-component left-handedq neutrinos,↵3P
Seee.g.
Cherry,Friedland&Shoemaker(2014),are displayed in Table I and are flavor⌫
andthe {othersubscriptparticle) indioutqoin(j “phen”
neutrino orlepton)(outgoing indices
Ng & Beacom (2014), Blinov et al. (2019)
for p and r neutrinos is cates that we will use this Lagrangian for our phenomenois explained
our notation
logicalanalysis. In Eq. (3) we have assumed that is a 1
νν>>parHig. 1.
real scalar e↵
without loss⌫of essential generality.
In2⌫ +qIMFP=2p. q-space distribution funcLow Energy
ticular,our conclusions remain una↵ected-p'j
ifI 2 =-~p-p'is a CPal to that of the electron-q' =-~p.
oddν or complex scalar. We focus on a scalar
mediatorqνs have both neutral- andhere for clarity; introducing a new vector force instead,2
We shall assume that the/M 2⌫ = g⌫withfor example, follows the same reasoning butGcomes
speciesvery smalln Cyr-Racine
additional, stronger constraints
discussed in more detail&are
Sigurdson⌫
νqP's(2014)
and is expected for allOne
assumption
thatis rarely
below. We also
explicitly
allowforgenericg ↵ chaparticle)(other incomingcouplings(incoming neutrino)al. (2015)that etthe
phase-spaceliesOldengott
streaming
naturecosmologicalbetween di↵erent neutrino
species,and of
discuss
implica- neLancaster, Cyr-Racine, etνInteraction
interactheir antiparticles
es al.and
four-momentaof
1. stronger
The labelingFIG.
of di↵erent
choicesofseeg ↵ [?
below.
tions,? ? ? ?for? neutrino? ]). Within(2017)
4-Fermiontions
than Fermi
constant
the etv„andthattions, cf. Tables I and II, and our definitions of the Mandelstam
Oldengottal.ν(2017)v, distrithis assumption is justified since SM
Cyr-Racine,track thevariables s,⌫t, and u. F
we needt Kreisch,
only &F

self-interaction, leading to G .
Beyond Free-streaming
following, weNeutrinos
focus on the case w
The key quantity characteriz
the neutrino sector is the therm
self-interaction cross section hthe order unity numerical factor
G / G , and T is the temp
bath. The X-mediated self-intertrino medium opaque with an owhere n is the number densit
the scale factor describing the ex
In this work, we focus our atten
G > Gpected, whereG is theFermtohavedecoupled
fromthe pri
φvery early
Universe atthe
a temperatur
is justified
to neglect
contrib
this assumption is not a priori drive
processes
to the neutrino opacity
I

Doré (2019)

Francis-Yan Cyr-Racine - UNM

10/5/197

Impact of self-interacting Neutrinos on CMB
Fixed
Fixed

0.10Pm⌫ = 0.06 eV
2b h , zeq ,0.06

C`,T T⇤CDM

0.02

C`,T TI ⌫⌘/C`,T T⇤CDM

0.14

0.06

⇣0.02

Planck 2015

0.10
0.140

⇤CDM (Ne↵ = 3.046)

Ge↵ = 10 2 MeV 2 , Ne↵ = 3.046⇤CDM (Ne↵ = 4.046)

Ge↵ = 10 2 MeV 2 , Ne↵ = 4.046

500

Kreisch, Cyr-Racine + (2019)

1000

P

1500

2000

2500

3000

FIG. 1: E↵ects ofm⌫ , Ge↵ , and Ne↵ on the phase and amp
PFrancis-Yan Cyr-Racine - UNM
10/5/198
di↵erent values of Ge↵ . Solid spectra correspond tomAnother possibility: Localized energyinjection• Need energy injection around matter-radiation equality.
0.12

Ne↵
Energy Injection

0.10

Karwal & Kamionkowski, 2016
Poulin et al. (2018,2019)
Agrawal, FYCR, Pinner, Randall(2019)
Lin et al. (2019)Smith, Poulin & Amin (2019)⇢inject/⇢totzdrag

zeq

0.08
0.06
0.04
0.02
100

101102103104z
Francis-Yan Cyr-Racine - UNM

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Planck 2018 model comparison
Interacting Neutrinos
Energy Injection
LCDM

Planck 2018 +BAO + Panth +
SH0ES

1

ns

0.98
0.96
0.94

H0 [km/s/Mpc]

0.92

R1974
72
70
68

0.86

80.84
0.82
0.8
137.5

142.5

rs [Mpc]
Francis-Yan Cyr-Racine - UNM

147.5

0.92 0.94 0.96 0.98 1.00

ns68

7072

74

H0 [km/s/Mpc]

0.80

0.82

0.84

0.86

8

10/5/1910

General lesson #1• The epoch between z = 103 and 104 seems to be key in addressing
the current tensions. Is matter-radiation more involved than wethink? Is this related to the ℓ𝓁 < 800 vs ℓ𝓁 > 800 discrepancy?
0.12

Neutrino
decoupling

Ne↵
Energy Injection

0.10⇢inject/⇢tot

zdrag

zeq

0.08
0.06
0.04
0.02
100

101

102

103

104

z
Francis-Yan Cyr-Racine - UNM

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11

General lesson #2• Adding energy before recombination always require a larger dark
matter density and a larger scalar spectral index.
Interacting Neutrinos
Energy Injection
LCDM

8 (⌦m /0.3)

0.5

0.88

10.96

S8 =

ns0.980.94

H0 [km/s/Mpc]

0.92

R1974

0.86
0.84
0.82
0.80.78

72

SH0ES(Riess et al. (2019))

Interacting Neutrinos
Energy Injection
LCDM

HSC (Hikage et al. (2018))

67.5

69.0

70.5

72.0

73.5

H0 [km/s/Mpc]

7068
0.114

0.126

⌦c h 20.138 0.92 0.94 0.96 0.98 1.00

Francis-Yan Cyr-Racine - UNM

ns68

70

7274

H0 [km/s/Mpc]
10/5/1912

General lesson #3: Finding a satisfactory
particle model is challenging

Blinov et al. (2019)
See also Ng & Beacom (2014) and Arcadi et al. (2018)
Francis-Yan Cyr-Racine - UNM

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13

General lesson #3: Finding a satisfactory
particle model is challenging• It appears highly nontrivial to obtain the right potential
shape (fine-tuning, breaking of perturbation theory,
sensitivity to UV corrections)Francis-Yan Cyr-Racine - UNM

10/5/19

14

Take Home Messages• As precision increases, cracks might be appearing
in the standard cosmological model.
• We have yet to identify a complete solution that ispalatable to both cosmologists and particle
physicists, but have found important clues about
what a successful model would look like.

Thank you!

Francis-Yan Cyr-Racine - UNM

10/5/19

15