Oscillating scalar fields andthe Hubble tension: asolution with novel featuresrtical/solid) and log10 zc (horizontal/dashed) as a function of the axion mass,e contours for n = 2 and the black for n = 3. Since H0 = 100h km/s/Mpc =tential that helps to resolve the Hubble tension ranges between 10 28 eV .

0.10

9H 2 (zc ),⇥i ) n .

fEDE(7)ermines zc .
al at zc , theeld at zc is

0.08
0.06

n = 2,
n = 2,
n = 3,
n = 3,

i = 3.1
i = 0.1
i = 3.1
i = 0.10.040.02(8)at fEDE (zc )y, the ratestate oncew ⌘ (nt discussed
DE (zc ), theof the backpeed of theoscillation
re we plotand ⇥ , in0.00
101102103

104105106z1908.06995, submitted PRD

Figure 2. The evolution of the fraction of the total energy
density in the EDE as a function of redshift for zc = 104 and
fEDE (zc ) = 0.1. Note that as the initial field displacement
becomes larger the asymmetry of fEDE (z) and oscillation frequency of the background field increases.

Tristan L. Smith (Swarthmore College)B.

With Vivian Poulin (Univ. Montpellier)
Mustafa Amin (Rice U)
Linear Perturbations

2• Hard to modify
late-time expansion
Poulin++ 1803.02474
Knox and Millea 1908.03663• Modifications ofearly-time
expansion… also
hard, but doable
Poulin, Smith, Karwal,
Kamionkowski 1811.04083
Kreisch++ 1902.00534
Escudero and Witte 1909.04044
Lin++ 1905.12618
Smith, Poulin, Amin 1908.06995

Figure by Vivien Bonvin

Verde, Treu, and Riess 1907.10625

CMB as a standard rulerrs (!M , !b )✓CMB =D(zdec ; !M , h)<latexit sha1_base64="1Yw6FhGXoH7GgW3uniksFwY0m1Y=">AAACNnicbVDLattAFB3l6TgvN112M8QEHAhGcgoNhEBIuujG4ELtBCwjRuMre/CMJGauAq7QV2WT78gumy5aSrb5hIxtUZrHgYHDOedy554wlcKg6z44S8srq2vrlY3q5tb2zm7tw17PJJnm0OWJTPR1yAxIEUMXBUq4TjUwFUq4CieXM//qBrQRSfwDpykMFBvFIhKcoZWCWtvHMSALcl8retm+KCg9o36kGc91YBp+omDEgvZRScLDIv/a+LmID4EXp/RfZHxYBLW623TnoG+JV5I6KdEJavf+MOGZghi5ZMb0PTfFQc40Ci6hqPqZgZTxCRtB39KYKTCDfH52QQ+sMqRRou2Lkc7V/ydypoyZqtAmFcOxee3NxPe8fobRySAXcZohxHyxKMokxYTOOqRDoYGjnFrCuBb2r5SPme0MbdNVW4L3+uS3pNdqesfN1vfP9fOLso4K+UT2SYN45As5J99Ih3QJJ7fkgfwmf5w755fz13lcRJeccuYjeQHn6RlPvKsR</latexit>✓CMB = 0.596506 ± 0.00018<latexit sha1_base64="sLm9SxnhXKId7IQOZ1ZGJxgbQlo=">AAACF3icbZDLSgMxFIYz9VbrrerSTbAIrspMtbUuhNJu3AgV7AU6tWTStA1NZobkjFCGvoUbX8WNC0Xc6s63Mb0stPWHwMd/zuHk/F4ouAbb/rYSK6tr6xvJzdTW9s7uXnr/oK6DSFFWo4EIVNMjmgnusxpwEKwZKkakJ1jDG1Ym9cYDU5oH/h2MQtaWpO/zHqcEjNVJZ10YMCCd2FUSV27KY4yvsJ3NXxbyduHepVxR7IbSWLZtO8VOOjMlI7wMzhwyaK5qJ/3ldgMaSeYDFUTrlmOH0I6JAk4FG6fcSLOQ0CHps5ZBn0im2/H0rjE+MU4X9wJlng946v6eiInUeiQ90ykJDPRibWL+V2tF0Cu2Y+6HETCfzhb1IoEhwJOQcJcrRkGMDBCquPkrpgOiCAUTZcqE4CyevAz1XNY5y+ZuzzOl8jyOJDpCx+gUOegCldA1qqIaougRPaNX9GY9WS/Wu/Uxa01Y85lD9EfW5w+48JvW</latexit>• Bumps and wiggles give us !M , !b<latexit sha1_base64="7UDGPcXW8QgHq3V3HaFIsNTO6Zc=">AAAB+nicbZDLSgMxFIYz9VbrbapLN8EiuJAyUwVdFt24ESrYC7TDkEkzbWguQ5JRythHceNCEbc+iTvfxrSdhbb+EPj4zzmckz9KGNXG876dwsrq2vpGcbO0tb2zu+eW91tapgqTJpZMqk6ENGFUkKahhpFOogjiESPtaHQ9rbcfiNJUinszTkjA0UDQmGJkrBW65Z7kZIDC29McotCteFVvJrgMfg4VkKsRul+9vsQpJ8JghrTu+l5iggwpQzEjk1Iv1SRBeIQGpGtRIE50kM1On8Bj6/RhLJV9wsCZ+3siQ1zrMY9sJ0dmqBdrU/O/Wjc18WWQUZGkhgg8XxSnDBoJpznAPlUEGza2gLCi9laIh0ghbGxaJRuCv/jlZWjVqv5ZtXZ3Xqlf5XEUwSE4AifABxegDm5AAzQBBo/gGbyCN+fJeXHenY95a8HJZw7AHzmfP9rVk7w=</latexit><latexit sha1_base64="F6WtoqDOuEh/o2MeJcIGE2HAfOs=">AAACBXicbZDLSgMxFIYz9VbrbdSlLoJFcFUmbUE3QtGNG6GCvUBnGDJppg1NZoYkI5TSjRtfxY0LRdz6Du58GzPtLLT1h8DHf87h5PxBwpnSjvNtFVZW19Y3ipulre2d3T17/6Ct4lQS2iIxj2U3wIpyFtGWZprTbiIpFgGnnWB0ndU7D1QqFkf3epxQT+BBxEJGsDaWbx+7saAD7N/CS+hUUL3mQDcRBh0HId8uZ5AJLgPKoQxyNX37y+3HJBU00oRjpXrISbQ3wVIzwum05KaKJpiM8ID2DEZYUOVNZldM4alx+jCMpXmRhjP398QEC6XGIjCdAuuhWqxl5n+1XqrDC2/CoiTVNCLzRWHKoY5hFgnsM0mJ5mMDmEhm/grJEEtMtAmuZEJAiycvQ7taQbVK9a5eblzlcRTBETgBZwCBc9AAN6AJWoCAR/AMXsGb9WS9WO/Wx7y1YOUzh+CPrM8fEpyVFA==</latexit>!M = 0.1430 ± 0.0011<latexit sha1_base64="5rRVuPyIMD+JkROCm6FjuCh74I0=">AAACB3icbZDLSsNAFIYn9VbrLepSkMEiuCpJqtSNUHTjsoK9QBPCZDpph84kYWYilNCdG1/FjQtF3PoK7nwbJ20W2vrDwMd/zuHM+YOEUaks69sorayurW+UNytb2zu7e+b+QUfGqcCkjWMWi16AJGE0Im1FFSO9RBDEA0a6wfgmr3cfiJA0ju7VJCEeR8OIhhQjpS3fPHZjTobID+AVtGqW49Qb0E14zpZlX/hmdUZacBnsAqqgUMs3v9xBjFNOIoUZkrJvW4nyMiQUxYxMK24qSYLwGA1JX2OEOJFeNrtjCk+1M4BhLPSLFJy5vycyxKWc8EB3cqRGcrGWm//V+qkKL72MRkmqSITni8KUQRXDPBQ4oIJgxSYaEBZU/xXiERIIKx1dRYdgL568DB2nZtdrzt15tXldxFEGR+AEnAEbNEAT3IIWaAMMHsEzeAVvxpPxYrwbH/PWklHMHII/Mj5/AC3nlac=</latexit>!b = 0.02237 ± 0.00015

h = 0.6736 ± 0.054<latexit sha1_base64="PRdBnbVemBPLRPTNEnqppnPXykU=">AAAB+3icbVDLTgIxFO3gC/E14tJNIzFxNZkBBDcmRDcuMZFHAhPSKR1oaDuTtmMkE37FjQuNceuPuPNvLDALBU9yc0/OuTe9PUHMqNKu+23lNja3tnfyu4W9/YPDI/u42FZRIjFp4YhFshsgRRgVpKWpZqQbS4J4wEgnmNzO/c4jkYpG4kFPY+JzNBI0pBhpIw3s4hheQ9ep1Su1fsxdx72sDuyS6QvAdeJlpAQyNAf2V38Y4YQToTFDSvU8N9Z+iqSmmJFZoZ8oEiM8QSPSM1QgTpSfLm6fwXOjDGEYSVNCw4X6eyNFXKkpD8wkR3qsVr25+J/XS3R45adUxIkmAi8fChMGdQTnQcAhlQRrNjUEYUnNrRCPkURYm7gKJgRv9cvrpF12vIpTvq+WGjdZHHlwCs7ABfBAHTTAHWiCFsDgCTyDV/BmzawX6936WI7mrGznBPyB9fkDwQKRrA==</latexit>

CMB as a standard rulerrs (!M , !b )✓CMB =D(zdec ; !M , h)<latexit sha1_base64="1Yw6FhGXoH7GgW3uniksFwY0m1Y=">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</latexit>✓CMB / h, rs<latexit sha1_base64="w9iB4IaLk2yI9yoFuvOfTs9LTmQ=">AAAB+XicbVBNS8NAEN34WetX1KOXxSJ4KkkV9Fjaixehgv2AJoTNdtMu3U3C7qRQQv+JFw+KePWfePPfuG1z0NYHA4/3ZpiZF6aCa3Ccb2tjc2t7Z7e0V94/ODw6tk9OOzrJFGVtmohE9UKimeAxawMHwXqpYkSGgnXDcXPudydMaZ7ETzBNmS/JMOYRpwSMFNi2ByMGJMg9JXHzoTEL7IpTdRbA68QtSAUVaAX2lzdIaCZZDFQQrfuuk4KfEwWcCjYre5lmKaFjMmR9Q2MimfbzxeUzfGmUAY4SZSoGvFB/T+REaj2VoemUBEZ61ZuL/3n9DKI7P+dxmgGL6XJRlAkMCZ7HgAdcMQpiagihiptbMR0RRSiYsMomBHf15XXSqVXd62rt8aZSbxRxlNA5ukBXyEW3qI7uUQu1EUUT9Ixe0ZuVWy/Wu/WxbN2wipkz9AfW5w8MYJNF</latexit><latexit sha1_base64="sEZiows9MrqGjyW0ohH0lvcWZf8=">AAAB9XicbVBNSwMxEJ2tX7V+VT16CRbBg5TdKuix6MVjBfsBbS3ZNNuGZpOQZJWy9H948aCIV/+LN/+NabsHbX0w8Hhvhpl5oeLMWN//9nIrq2vrG/nNwtb2zu5ecf+gYWSiCa0TyaVuhdhQzgStW2Y5bSlNcRxy2gxHN1O/+Ui1YVLc27Gi3RgPBIsYwdZJDx2lpbISDc+Q7pleseSX/RnQMgkyUoIMtV7xq9OXJImpsIRjY9qBr2w3xdoywumk0EkMVZiM8IC2HRU4pqabzq6eoBOn9FEktSth0Uz9PZHi2JhxHLrOGNuhWfSm4n9eO7HRVTdlQiWWCjJfFCUcuT+nEaA+05RYPnYEE83crYgMscbEuqAKLoRg8eVl0qiUg/Ny5e6iVL3O4sjDERzDKQRwCVW4hRrUgYCGZ3iFN+/Je/HevY95a87LZg7hD7zPH+2akiI=</latexit>

z*cs(z)rs =dz∫∞ H(z)<latexit sha1_base64="FZA5ie92JflBv4r/dmAZw3aBkVY=">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</latexit>

h=hrs
0.74 0.67== 0.1rs
0.67 Aylor++ 1811.00537

Also need to keep θEQ and θdamp nearly unchanged

Scalar field and Early Dark Energy
Minimally coupled, initially slowly-rolling field, that eventually dilutes faster than matter
But see Capparelli++
1909.04621¨ + 3H ˙ + dVn ( ) = 0d• We study an oscillating (toy) potentialV(ϕ) ∝ (1 − cos ϕ/f )n8V( )<latexit sha1_base64="ZXlVxgmmFT5lqMGNJnKg9gekf1U=">AAAB7nicbVBNSwMxEJ34WetX1aOXYBHqpexWQY9FLx4r2A9ol5JNs21oNhuSrFCW/ggvHhTx6u/x5r8xbfegrQ8GHu/NMDMvVIIb63nfaG19Y3Nru7BT3N3bPzgsHR23TJJqypo0EYnuhMQwwSVrWm4F6yjNSBwK1g7HdzO//cS04Yl8tBPFgpgMJY84JdZJ7Valp0b8ol8qe1VvDrxK/JyUIUejX/rqDRKaxkxaKogxXd9TNsiItpwKNi32UsMUoWMyZF1HJYmZCbL5uVN87pQBjhLtSlo8V39PZCQ2ZhKHrjMmdmSWvZn4n9dNbXQTZFyq1DJJF4uiVGCb4NnveMA1o1ZMHCFUc3crpiOiCbUuoaILwV9+eZW0alX/slp7uCrXb/M4CnAKZ1ABH66hDvfQgCZQGMMzvMIbUugFvaOPResaymdO4A/Q5w+FLo8I</latexit>

64𝒛𝒄

2-2-1123/f<latexit sha1_base64="NqE/sbR5IdnIzSjXx5eWgdcdYJE=">AAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqe6qoMeiF48V7Ae0S8mm2TY2myxJVihL/4MXD4p49f9489+YtnvQ1gcDj/dmmJkXJoIb63nfqLCyura+UdwsbW3v7O6V9w+aRqWasgZVQul2SAwTXLKG5VawdqIZiUPBWuHoduq3npg2XMkHO05YEJOB5BGnxDqp2U2G/CzqlSte1ZsBLxM/JxXIUe+Vv7p9RdOYSUsFMabje4kNMqItp4JNSt3UsITQERmwjqOSxMwE2ezaCT5xSh9HSruSFs/U3xMZiY0Zx6HrjIkdmkVvKv7ndVIbXQcZl0lqmaTzRVEqsFV4+jruc82oFWNHCNXc3YrpkGhCrQuo5ELwF19eJs3zqn9RPb+/rNRu8jiKcATHcAo+XEEN7qAODaDwCM/wCm9IoRf0jj7mrQWUzxzCH6DPH0P4juw=</latexit>⇢EDE /⇢tot-3• n mostly controls the e.o.s. once the fieldn−1n+1fEDE(zc)
Figure by Tanvi Karwal<latexit sha1_base64="dcZbALJ0x9BuRSqZDhy1TZuuZnE=">AAACBnicbVBLSwMxGMz6rPW16lGEYBE81d0q6LGoBY8V7AO6y5JNs21oslmSrFCWnrz4V7x4UMSrv8Gb/8a0XVBbBwKTme8jmQkTRpV2nC9rYXFpeWW1sFZc39jc2rZ3dptKpBKTBhZMyHaIFGE0Jg1NNSPtRBLEQ0Za4eBq7LfuiVRUxHd6mBCfo15MI4qRNlJgH3iyL4LMkxzWrmujk5+rFnoU2CWn7EwA54mbkxLIUQ/sT68rcMpJrDFDSnVcJ9F+hqSmmJFR0UsVSRAeoB7pGBojTpSfTWKM4JFRujAS0pxYw4n6eyNDXKkhD80kR7qvZr2x+J/XSXV04Wc0TlJNYjx9KEqZiQjHncAulQRrNjQEYUnNXyHuI4mwNs0VTQnubOR50qyU3dNy5fasVL3M6yiAfXAIjoELzkEV3IA6aAAMHsATeAGv1qP1bL1Z79PRBSvf2QN/YH18A/7gmNM=</latexit>

is oscillating: wn = (n − 1)/(n + 1)
!n = 1: matter, n! = 2: radiation, etc.

wn ≡• Perturbations are essential!

plot by T. Karwal• Dynamics is specified by zc, fEDE(zc), n, ϕi
When EDE happens… how large… how fast it dilutes… dynamics of perturbations

10Log10(zc)2.1n

10 2 bcdm

10 9As

Early dark energy and the Hubble tension

7Poulin, Smith, Karwal,

1.00

ns

2= ⟨δP⟩/⟨δρ⟩) in PRL 122 (2019) Kamionkowski•0.98Studied ‘cycle-averaged’ (ceﬀ• Solved exact (linear) equations in 1908.06995 Smith, Poulin, and Amin
0.96

3.4 3.6 3.8

35EDE4nΛCDM

Log10(zc)

reio

0.12

0.114 0.126 0.138
cdm

2.22 2.27 2.32210

2.1b2.2910 As

2.3 0.96

0.080.04

cdm

0.138

68

71

H074

0.114 0.126 0.138

2.22 2.27 2.32 2.1 2.2 2.3 0.96 0.98 1.00
90.05
0.10 0.15
3 ns45
10 2 b3.3 3.6 10 3.9As
cdm

Log10(zc)fEDE(zc)

0.126

V(ϕ) = m 2f 2(1 − cos ϕ/f )nn

0.04 0.08 0.12

0.5
reio

1.52.5i• Fit Planck CMB, JLA, BAO, SH0ES810 2 b0.114
r distributions6of the cosmological parameters reconstructed from a run to all dat+2.3−270.03 0.07 0.11
7e 2.32
3.4 3.6 3.8 (blue)
45 EDE
0.114 0.126
0.138
2.22
2.27
2.32
2.1 M
2.2 top
2.3
0.96
0.98 ×1.00
4 3±m
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10eV show: th⇤CDM
and(red)cosmology.
Fromtobottom
wef
=
0.18
0.06
29
pl−3.0•
Log10(zc)
10
10 As
nsn
cdm
breio
2andf(z)vsasubsetofparameters,
the1D
posterior
distributionof the E
EDE c
2.27/f = ⇥-3of-2H-1 in the12 gray3inationbands.
02.22<latexit sha1_base64="NqE/sbR5IdnIzSjXx5eWgdcdYJE=">AAAB7XicbVBNSwMxEJ3Ur1q/qh69BIvgqe6qoMeiF48V7Ae0S8mm2TY2myxJVihL/4MXD4p49f9489+YtnvQ1gcDj/dmmJkXJoIb63nfqLCyura+UdwsbW3v7O6V9w+aRqWasgZVQul2SAwTXLKG5VawdqIZiUPBWuHoduq3npg2XMkHO05YEJOB5BGnxDqp2U2G/CzqlSte1ZsBLxM/JxXIUe+Vv7p9RdOYSUsFMabje4kNMqItp4JNSt3UsITQERmwjqOSxMwE2ezaCT5xSh9HSruSFs/U3xMZiY0Zx6HrjIkdmkVvKv7ndVIbXQcZl0lqmaTzRVEqsFV4+jruc82oFWNHCNXc3YrpkGhCrQuo5ELwF19eJs3zqn9RPb+/rNRu8jiKcATHcAo+XEEN7qAODaDwCM/wCm9IoRf0jj7mrQWUzxzCH6DPH0P4juw=</latexit><latexit sha1_base64="9ID89gw5p3lBj3fhk32SpQ0a83o=">AAAB7nicbVBNS8NAEN34WetX1aOXxSJ4KkkV9CIUvXis0C9oQ9lsJ+3SzSbsToQS+iO8eFDEq7/Hm//GbZuDtj4YeLw3w8y8IJHCoOt+O2vrG5tb24Wd4u7e/sFh6ei4ZeJUc2jyWMa6EzADUihookAJnUQDiwIJ7WB8P/PbT6CNiFUDJwn4ERsqEQrO0Ert215jBMj6pbJbceegq8TLSZnkqPdLX71BzNMIFHLJjOl6boJ+xjQKLmFa7KUGEsbHbAhdSxWLwPjZ/NwpPbfKgIaxtqWQztXfExmLjJlEge2MGI7MsjcT//O6KYY3fiZUkiIovlgUppJiTGe/04HQwFFOLGFcC3sr5SOmGUebUNGG4C2/vEpa1Yp3Wak+XpVrd3kcBXJKzsgF8cg1qZEHUidNwsmYPJNX8uYkzovz7nwsWtecfOaE/IHz+QP3FY9T</latexit>2≃ 0.8• Θi controls eﬀective sound-speed; in order to fit CMB, ceﬀ

10 9As

2.3
3.4 3.6 3.8Log10(zc)345

0.114 0.126 0.138

n2.22 2.27 2.32

10 2 bcdm

2.1

2.2

10 9As

2.3 0.96
0.03 Dark
0.07
See0.98
also 1.00‘Acoustic

2.2•2.1 The EDE cosmology fits the CMB power spectrum just as well as ΛCDM
0.05 0.10 0.15

3.3

3.6

3.9

345

0.5

1.5

0.11

ns Lin++ 1905.12618
reio
Energy’,2.5

Detecting the EDE with CMB data only
• Future CMB experiment like CMB-S4 will be able to detect the EDE without SH0ES data.
Fiducial model:f(zc) = 0.12
zc = 103.5
h = 0.72

fEDE (zc )PlanckCMB-S4

0.20
0.15
0.10
0.05
3.2

3.5

3.8Log10 (zc )68 70 72 74
H0• Without including the EDE: one might strongly bias H0 and ωcdm values.
⇤CDM Planck⇤CDM CMB-S4

66

6870

H07274

EDE Planck
EDE CMB-S4

0.116 0.124 0.132 0.140!cdm

Novel prediction: Non-linear structures from the EDE• The linear Klein-Gordon equation exhibits parametric resonance: modes passing

through the resonance band experiences growth, potentially becoming nonlinear.
e.g. Amin++ 1410.3808• Floquet analysis: EDE models with n ≲ 2.1 become non linear, but only n ≃ 2 hasfEDE(znl) ≳ 1 % when non-linear.
n = 2, Θi = 3

Amin, Lozanov, and Smith, in prep.
1.4 × 10-12
1.2 × 10-12
1. × 10-12
8. × 10-13
6. × 10-13
4. × 10-13
2. × 10-130

1. × 10-16

2. × 10-16

5. × 10-16

1. × 10-15• GWs and non-linear structures may have observable consequences in the small-scale
CMBConclusions• An EDE can resolve the Hubble tension• Planned CMB missions (i.e., CMB-S4) will see the EDE if it is there!
• CMB knows about the evolution of EDE perturbations; data prefers Θi ≳ 1.5 where
potential is flatter• Unique predictions: if V(ϕ) = λϕ 4 around minimum, parametric resonance leads tolate-time (z ≃ 10 − 100) non-linear scalar field dynamics (including GWs)

• Isocurvature perturbations• Statistically insignificant impact on other ‘tensions’ (S8, Alens)• May fit into a larger class of scalar fields; the axiverse….

ϕ EDE fortified !