Oscillating scalar fields and the Hubble tension: a solution with novel features

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1 Oscllatg scalar felds ad the Hule teso: a soluto wth ovel features rtcal/sold) ad log zc (horzotal/dashed) as a fucto of the axo mass, e cotours for = ad the lack for = 3. Sce H0 = 0h km/s/mpc = tetal that helps to resolve the Hule teso rages etwee 8 ev. 0. 9H (zc ), ). fede (7) ermes zc. al at zc, the eld at zc s =, =, = 3, = 3, = 3.1 = 0.1 = 3.1 = (8) at fede (zc ) y, the rate state oce w ( t dscussed DE (zc ), the of the ackpeed of the oscllato re we plot ad, z , sumtted PRD Fgure. The evoluto of the fracto of the total eergy desty the EDE as a fucto of redshft for zc = 4 ad fede (zc ) = 0.1. Note that as the tal feld dsplacemet ecomes larger the asymmetry of fede (z) ad oscllato frequecy of the ackgroud feld creases. Trsta L. Smth (Swarthmore College) B. Wth Vva Poul (Uv. Motpeller) Mustafa Am (Rce U) Lear Perturatos

2 Hard to modfy late-tme expaso Poul Kox ad Mllea Modfcatos of early-tme expaso also hard, ut doale Poul, Smth, Karwal, Kamokowsk Kresch Escudero ad Wtte L Smth, Poul, Am Fgure y Vve Bov Verde, Treu, ad Ress

3 <latext sha1_ase64="1yw6fhgxoh7ggw3uksfwy0m1y=">aaacncvdlattafb3l6tgvn11m8qehahgcgonhebiuujg4eltbcwjrumre/cmjgauaq7qvwt78gumy5asr5hixtuzrhgyhdoedy554wlckg6z44s8srqvrly3q5tzm7tw17pjjm0owjtpr1yaxieumxbuq4tjuwfuq4cexm//qbrqrsfwdpykmfbvfihkcozwcwtvhmsalcl8retm+kcg9o36kgc91ybp+omdegvzrscldiv/a+lmid4exp/rfzhxyblw63tog+jv5i6kdejavf+mogzgh5zm0ptffqc40c6hqpqzgztxcrtb39kyktcdfh5qq+smqrroulkc7v/ydypoyzqtamfcoxee3nxpe8forysaxczohxhyxkmokxytooqrdoygjfrcubr5spme0mdnvw4l3+us3pndqesfn1vfp9folso4k+utsyn45as5j99ih3qjj7fkgfwmf5w755fz13lcrjeccuyjeqh6rlpvksr</latext> CMB as a stadard ruler CMB = r s(! M,! ) D(z dec ;! M,h) CMB = ± <latext sha1_ase64="slm9sxhxkid7iqoz1zgjxgqlo=">aaacf3czdlsgmxfiyz9vrrerstairspmtuuhnju3agv7au6twtsta1nzokjfcgvoux8wnc0xc6s63m0stpwhwmd/zuhk/f4oua/rysk6tr6xvjzdtw9s7uxr/ok6dsffwo4eivnmjmgusxpwekwzkkakj1jdg1ym9cydu5oh/hmqtawpo/zhqcejnvjzymccdfusv7ky4yvsj3nxxyduhepvxr7iswlzto8voojmli7wmzhwyak5qj/3ldgmaseydfutrlmoh0i6jak4fg6fcsloq0chps5zb0m/h0rje+mu4x9wjlg946v6eiueq90ykjdprwl+vtf0cuy+6hetcfzh1ioehwjoqcjcrrkgmdbcqupkrpgocautzcqe4cyevaz1xny5y+zuzzol8jyojdpcx+guoegclda1qqiaougrpanx9gy9ws/wu/uxa01y85ld9efw5w+48jvw</latext> Bumps ad wggles gve us! M,! <latext sha1_ase64="7udgpcxw8qghq3v3hafisnto6zc=">aaab+czdlsgmxfiyz9vrapln8eujayuwvdft4esryc7tdkekzwguq5jrythhcencec+tvfxrsdh+epj4zzmckz9kgnxg876dwsrqvpgco0tzu+ew91tapgqtjpzmqk6engfukkahhpfoogjesptahq9rcfnjusztkja0udqmgjkrbw65z7kzidc9mcotctefvvjrgmfg4vkksrul+9vsqpj8jghrtu+l5ggwpqzejk1iv1srbeiqgpgtrie50km1o8bj6/rhljv9wscz+3sq1zrmy9sj0dmqbdru/o/wjc18wwquzgkhgg8xxsdbojpzapluegzaglc9laih0ghgxajrucv/jlzwjvqv5ztxz3xqlf5xeuwse4afabxegdm5aazqbbo/ggycn+fjexhey95a8hjzw7ahzmfp9rvk7w=</latext>! M = ± <latext sha1_ase64="f6wtoqdoueh/omejcigehafos=">aaacbxczdlsgmxfiyz9vrdsllojfcfumue3qtgng6gcvubgdjppg1nzoyki5tsjrtfxy0lrdz6du58gzptllt1h8dhf87h5pxbwpsjvntfvzw19y3pulred3t17/6ct4lqsixju3wipyftgwzprtipfggwb0du7d1qqfkf3epxqt+bbxejgsdawx+7saad7n/cs+huul3mqdcrbh0hid8uz5ajlgpkoqxynx37y+3hjbu00orjpxrisq3wvizwum05kakjpm8iddezyuovnzldm4alx+jcmpxmrhjp398qec6xgijcdauuhwqxl5+1xqrdc/cotvnclzrwhkoy5hfgsm0mj5mmdmehm/grjeetmtamuzejaycvq7taqvk9a5elzlcrtbetgbzwcbc9aan6ajwocar/amxsg9ws9wo/wx7y1youzh+cprm8fepyvfa==</latext>! =0.037 ± <latext sha1_ase64="5rrvupyimd+jkrocm6fjuch74i0=">aaacb3czdlssnafiy9vrlepskmeucpjqtsnuhtjsok9qbpczdpph84kywylncdg1/fjqtf3pok7wj0wvrdwmd/zuhm+yoeuaks69sorayurw+unytzu7e++qufgqcckjwmw16ajge0im1ffso9rbdea0a6wfgmr3cfja0ju7vjceer8oihhqjps3fphzjtoid+avtgqw49q0e14zpzlx/hmduzacbsaqqgums3v9xbjfnoiouzkrjvw4ymquxyxmk4qsylwga1jxoeojfenrtjck+1m4bhlpslfjy5vycyxkwc8eb3cqrgcrgwm//v+qkkl7mrkmqsit8kuqrxdpbq4oijgxsyaebzu/xxeriikx1drydgl568dbztdrzt15txldxfegr+aeaeneat3iiwaammhsezeavvxppxyrwh/pwklhmhii/mj5/ac3lac=</latext> h = ± <latext sha1_ase64="prdbvembplrptneqpppxyku=">aaab+3cvdltgixfo3gc/e14tjnizfxnzkbbdcmrdcumzfhahpskr1oaduttmmke37fjqunceupupnvldalbu9yc0/oute9puhmqnku+3lnja3tfyu4w9/ypdi/u4fzrijfp4yhfshsgrrgvpkwpzqqs4j4wegmnzo/c4jkypg4kfpy+jznbi0pbhpiw3s4hheq9ep1su1fsxdx7sduys6qvadejlpaqynafv38y4yqtotfdsvu8n9z+qsmmjfzoz8oem8qspsm1qgtpsflm6fwxojdgeysvncw4x6eynfxkkpd8wkr3qsvr5+j/xs3r45aduxikma8fchmgdqtqcahlqrrnjueyunrrcpkurym7gkjgrv9cvrpf1viptvq+wgjdzhhlwcs7abfbahttahwcfsdgctydv/bmzawx6936wi7mrgzbpyb9fkdwqkrra==</latext>

4 <latext sha1_ase64="fza5e9jflbv4r/dmazw3abkvy=">aaacmxcvdlssnafj3uv6vqks3g0vw05duyt0um66rgaf0iywmuyaozmhmxohhpysg/9e3hshft/wkhw09mjfdofdy5x4zlriw5hpha3td947p4pdo+kr8etytucix6ekirxzgieeydulxusiioyebq4jfwfykpv9z8ifjcioyjfabxsdkkvssxw6ppi5woijkwj6wepzeqkxmrpxmbtgwdl1rrxr6snl5xudd0yxvdn+aam8rckgpyomox30zuhjoahbizjmtqngjppyhlhjsqnekbjhcrqtoaihcow0vfgxsgu9ksxsjhx/06kkbbgjqm0dsf+telv7drpp3vkpdenekhavfkjgzkcexzqpzxgyaakimyp+veplkpsbvysyvgrp+8sxo13zra4/1sut+gucrxiblca1m0aat0ayd0auyvib38ae+tvdtp1p34vwgracoqcr0h5+adwgp/o=</latext> <latext sha1_ase64="1yw6fhgxoh7ggw3uksfwy0m1y=">aaacncvdlattafb3l6tgvn11m8qehahgcgonhebiuujg4eltbcwjrumre/cmjgauaq7qvwt78gumy5asr5hixtuzrhgyhdoedy554wlckg6z44s8srqvrly3q5tzm7tw17pjjm0owjtpr1yaxieumxbuq4tjuwfuq4cexm//qbrqrsfwdpykmfbvfihkcozwcwtvhmsalcl8retm+kcg9o36kgc91ybp+omdegvzrscldiv/a+lmid4exp/rfzhxyblw63tog+jv5i6kdejavf+mogzgh5zm0ptffqc40c6hqpqzgztxcrtb39kyktcdfh5qq+smqrroulkc7v/ydypoyzqtamfcoxee3nxpe8forysaxczohxhyxkmokxytooqrdoygjfrcubr5spme0mdnvw4l3+us3pndqesfn1vfp9folso4k+utsyn45as5j99ih3qjj7fkgfwmf5w755fz13lcrjeccuyjeqh6rlpvksr</latext> CMB as a stadard ruler CMB = r s(! M,! ) D(z dec ;! M,h) <latext sha1_ase64="w9b4ialkyi9yofuvofts9ltmq=">aaab+xcvbns8naen34wetx1koxxsj4kkkv9fjaxehgvajotndtmu3u3c7qrqqv+jfw+kepwfeppfug1z0nyha4/3zpzf6aca3cctjct7z7e0v94/odw6tk9oozrjfgvtmohe9ukmeaxawmhwxqpyksggxdcxpudydmaz7etzbnms/jmoyrpwsmfnbymgjmg9jxhzotel7iptdra68qtsauvaaxlzdiaczzdfqqrfuuk4kfewwccjyre5lmkafjmmr9qmmfzxeuzfgmuay4szsogvfb/t+reajvoemubez61zul/39dki7p+dxmggl6xjrlakmcz7hgadcmqpaghptmr0rrsysmombhf15xxsqvxd6rt8azsxrxlna5ukbxyew3qi7uuqu1euut9ixe0zuvwy/wu/wxnwpkz9afw5w8myjnf</latext> CMB r s = z * / h, r <latext sha1_ase64="sezows9mrqgjyw0ohh0lvcwzf8=">aaab9xcvbnswmxejtx7v+vt16crbg5tdkux6mvjbfsbs3znnugzpoqzjwy9h948aciv/+ln/+nashx0w8hhvhpl5oelmwn//9irqvrg/nwtzu5ecf+gywsca0tyavuhdhqzgstwy5slncrxygxhn1o/+u1yvlc7g3rgpbisywdzjdxlpisdc+q7plesesx/rqmgkyuoimtv7xq9oxjimpsirjy9qbrw3xdoywumk0ekmvzm8ichru4pqazq6eobo9fektsth0uz9pzhjhxhlrognuhwfsm49eo7hrvtdlqwwcjjffcucut+eaa+05rypyee83crygmsceuqaklorg8evl0qug/ny5e6vl3o4sjderzdkqrwcvw4hrrugycgz3fn+/je/hevy95a87lzg7hd7zph+aki=</latext> s dz c s (z) H(z) h h = r s r s = =0.1 Aylor Also eed to keep θ EQ ad θ damp early uchaged

5 <latext sha1_ase64="nqe/sr5idizsjxx5ewgdcdyje=">aaab7xcvbnswmxej3ur1q/qh69bivgqe6qomef48v7ae0s8mmtymyxjvhl/4mxd4p49f9489+ytvq1gcdj/dmmjkxjoi63fqlcyura+udwsw3v7o6v9w+arqwasgzvqulsawtxlkg5vawdqizupbwuhoduq3pgxmkho05yejob5bgxdqpug/czqlste1zsblxm/jxxiue+vv7p9rdoysusfmaje4knmqitp4jnst3usitqermwjqosxmweezact5xsh9hsrusfs/u3xmzy0zx6hrjikdmkvvkv7dvixqczl0lqmatzrveqsfv4+jruc8ofwnhcnxc3yrpkghcrquo5elwf19ejs3zq9rp+/rnru8jkcathcao+xeen7qaodadwcm/wcm9iorf0jj7mrqwuzxzch6dph0p4juw=</latext> Mmally coupled, tally slowly-rollg feld, that evetually dlutes faster tha matter But see Capparell Scalar feld ad Early Dark Eergy We study a oscllatg (toy) potetal V(ϕ) (1 cos ϕ/f ) +3H + dv ( ) d =0 V ( ) <latext sha1_ase64="zxlvxgmmft5lqmgnjkg9gekf1u=">aaab7cvbnswmxej34wetx1aoxybhqpexwqy9flx4ra9ol5jns1onhusrfcw/ggvhhtx6u/x5r8xfegrq8ghu/nmdmvvii63fag19y3nru7bt3n3pzgshr3tjjqypo0eyuhmqwwsvrwm4f6yjnsbwk1g7hdzo//cs04yl8tbpfgpgmjy84jdzj7valp08ol8qe1vvdrxk/jyuiuejx/rqdrkaxkxakogxxd9tnsitpwkn3usmuowmyzf1hjymzcl5uvn87pqbjhltslo8v39pzcqzhkhrjmmdmswvz49dnxqtzfyq1djjf4uvgc4nvema1o1zmhcfuc3crpocuuoailwv9+ezw0alx/slp7ucrx/m4cakz1abh66hdvfqgczqgmmzvmiuugfvaopresaymdo4a/q5w+flo8i</latext> /f mostly cotrols the e.o.s. oce the feld s oscllatg: w = ( 1)/( + 1)! = 1: matter,! = : radato, etc. EDE/ tot f EDE (z c ) Fgure y Tav Karwal z c w Perturatos are essetal! plot y T. Karwal Dyamcs s specfed y z c, f EDE (z c ),, ϕ Whe EDE happes how large how fast t dlutes dyamcs of perturatos

6 Log(zc).1 9As Early dark eergy ad the Hule teso 7 Poul, Smth, Karwal, 1.00 s = δp / δρ ) PRL 1 (019) Kamokowsk 0.98Studed cycle-averaged (ceff Solved exact (lear) equatos Smth, Poul, ad Am EDE4 ΛCDM Log(zc) reo As H As s4 Log(zc) fede(zc) 0.16 V(ϕ) = m f (1 cos ϕ/f ) reo Ft Plack CMB, JLA, BAO, SH0ES r dstrutos 6of the cosmologcal parameters recostructed from a ru to all dat e (lue) 4 5 EDE M. top ± m = 3.4 ev show: th CDM ad (red) cosmology. From to ottom we f = pl 3.0 Log(zc) As s reo ad f (z ) vs a suset of parameters, the 1D posteror dstruto of the E EDE c.7 /f = -3of-H -1 the 1 gray 3 ato ads. 0. <latext sha1_ase64="nqe/sr5idizsjxx5ewgdcdyje=">aaab7xcvbnswmxej3ur1q/qh69bivgqe6qomef48v7ae0s8mmtymyxjvhl/4mxd4p49f9489+ytvq1gcdj/dmmjkxjoi63fqlcyura+udwsw3v7o6v9w+arqwasgzvqulsawtxlkg5vawdqizupbwuhoduq3pgxmkho05yejob5bgxdqpug/czqlste1zsblxm/jxxiue+vv7p9rdoysusfmaje4knmqitp4jnst3usitqermwjqosxmweezact5xsh9hsrusfs/u3xmzy0zx6hrjikdmkvvkv7dvixqczl0lqmatzrveqsfv4+jruc8ofwnhcnxc3yrpkghcrquo5elwf19ejs3zq9rp+/rnru8jkcathcao+xeen7qaodadwcm/wcm9iorf0jj7mrqwuzxzch6dph0p4juw=</latext> <latext sha1_ase64="9id89gw5p3lbj3fhk3spq0a83o=">aaab7cvbns8naen34wetx1aoxxsj4kkkv9ciuvxs0c9oq9lsj+3szsstoqs+o8efdeq7/hm//gzudtj4yelw3w8y8ijhcoot+ovrg5t4wd4u7e/sfh6e4zejucjywma6ezaduhookajuqdwij7wb8p/pt6cnfudjw4ersqeqro0ert15jbmj6pjceegq8tlszkqpdlx71bznmifhljjol6oj+xjqklmfa7kugeshahdsxwlwpjz/nwppfkgiaxtqwqztxfexmljjlegemgi7msjct//o6kyy3fzukiovlguppjtge/04hqwffolgfcc3sr5somgueungg4c/vepa1yp3wak+xpvrd3kcbxjkzsgf8cg1qzehudnwsmypjnx8uykzovz7wswtecfoae/ihz+qp3fy9t</latext> 0.8 Θ cotrols effectve soud-speed; order to ft CMB, ceff 9As Log(zc) As Dark 0.07 See0.98 also 1.00 Acoustc The EDE cosmology fts the CMB power spectrum just as well as ΛCDM s L reo Eergy,.5

7 Detectg the EDE wth CMB data oly Future CMB expermet lke CMB-S4 wll e ale to detect the EDE wthout SH0ES data. Plack CMB-S4 Fducal model: f(z c ) = 0.1 z c = 3.5 h = 0.7 fede(zc) Log (z c ) H 0 Wthout cludg the EDE: oe mght strogly as H 0 ad ω values. CDM CDM Plack CMB-S4 EDE EDE Plack CMB-S H !

8 Novel predcto: No-lear structures from the EDE The lear Kle-Gordo equato exhts parametrc resoace: modes passg through the resoace ad expereces growth, potetally ecomg olear. Floquet aalyss: EDE models wth.1 ecome o lear, ut oly has whe o-lear. f EDE (z l ) 1 % e.g. Am =, Θ = 3 Am, Lozaov, ad Smth, prep GWs ad o-lear structures may have oservale cosequeces the small-scale CMB

9 Coclusos A EDE ca resolve the Hule teso Plaed CMB mssos (.e., CMB-S4) wll see the EDE f t s there! CMB kows aout the evoluto of EDE perturatos; data prefers potetal s flatter Θ 1.5 where Uque predctos: f V(ϕ) = λϕ 4 aroud mmum, parametrc resoace leads to late-tme ( z 0 ) o-lear scalar feld dyamcs (cludg GWs) Isocurvature perturatos Statstcally sgfcat mpact o other tesos (S8, Ales) May ft to a larger class of scalar felds; the axverse. ϕ EDE fortfed!