Listening for primordial gravitational waves

Transcription

1 Listening for primordil grvittionl wves V(φ) Vlerie Domcke PC Pris Rencontres de Moriond bsed on rxiv: with Pierre Binétruy Muro Pieroni neutrinos grvittionl wves photons

2 Primordil vcuum fluctutions R (stndrd infltion) V(φ) f t N s = V 4 V vcuum fluctutions of inflton field nd metric during infltion φ modes leve horizon during infltion k < H outside horizon modes re frozen 4 t = V 3 fter infltion modes re-enter nd re red-shifted 0 scle fctor infltion = H ' 1 3 V 0 V rdition domintion Hubble rdius perturbtion mode (comoving scle) N = H dt mtter domintion 1:1 correltion f k N k V(φ k )!φ k wvelength GW spectrum sensitive to primordil spectrum (sclr potentil) nd post-infltionry expnsion Listening for primordil grvittionl wves Vlerie Domcke - PC

3 Direct detection vs CMB polristion CMB tensor nisotropies on lst scttering surfce GW trvels freely until tody direct polriztion of CMB photons through Thomson scttering distortion of spce s GW psses detector - Lensing: T -> E - dust contmintes primordil signl - B - modes most sensitive - ground-bsed interferometers - spce-bsed interferometers - pulsr timing rrys with r! 0.1 plnned direkt GW detectors cnnot see primordil vcuum fluctutions Listening for primordil grvittionl wves Vlerie Domcke - PC

4 Direct detection vs CMB polristion k[mpc -1 ] ΩGW h msec pulsr infltion r = 0.1 elis ET LIGO BBO/DECIGO f[hz] Listening for primordil grvittionl wves Vlerie Domcke - PC

5 ere H = ( )/ ( ) nd where prime denotes di erentition with respect to where dots re used to denote derivtives with respect to cosm forml time. f most relevnt formule.. pseudosclr infltion mogeneous field equtions 1 conforml time. The Friedmnn eqution reds: Genertion of guge field 3H = 1 1 ~ ~ V he B i. e rolling inflton induces genertion of qunt of guge ssuming field. In order to study is slowly vrying function in time we cn solve th s process we promote clssicl field ( x) to n opertor The( Fourier x). We decompose ~ must stisfy: modes of pseudo-sclr inflton coupled to U (1) guge field (following [? 3]) into nnihiltion nd cretion opertors! generic coupling for pseudosclr inflton: d ±Turner ( k) Widrow k Z 88 3 k ± ± ( k) X Grretson Field Croll 9 d k d H 1 ( µ ( x) = 1 k) (k) ei k x h.c. µ3/ e (k) µ (5) nber Sorbo 06./ 10/ 1 L = =±@µ ( Fµ F V( ) Fµ F. Brnby Nmb Peloso 11 (1) 4 4 Here subscript ± refers tobrnby twopjer helicity modes Peloso 1 of.. ~e± exp(i~k~x)). The corresponding helicity vectors ~e± (~k) st ere helicity vectors e± (k) re defined in such wy tht k e± =±0k e± = i k e±. (t x) 00re The resulting bckground equtions for (t) nd be generlized to N U (1) s by replcing Fkµ 0 /f[]. cross-product Eq. (4)resulting (rising in turnbckground from ntisymm µ (k! resulting bckground equtions of motion: en mode functions must stisfy equtions ±F ) in ± ± = 0. in Eq. (6). This d leds to tchyonic instbility in m Since we nd re looking we ssume ( ) ) nd /dt = ± 1/(H r (t) (tfor x)inflting re ~~ = constnt. Hence eqution for ± reds n exponentil growth of one of (3) two helicity modes of v 3H = he 1/4 1 k k/( d d± ( k) ~ ~ p ' e d = 3H = he Bi. () ( = 00 = (6) ~ rk ~ ± k ~k) ± k H r (4) d d d where we hve defined p p ere we hve defined d d ~ for. /( H) e dots re used totchyonic denote with to cosmic time tby wheres ~ derivtives ~ controlled / = denotes instbility respect guge field r r = 0 (3) H 0 d 0 ( ) > 0 < 0. The s conforml time. Thed Friedmnn eqution reds: W.l.o.g. let us ssume tht > 0 V (7) f H exponentil growth of guge field modes towrds of infltion modifies end slow-roll eqution of motion nd Friedmnn e 1 respect 1to~ cosmic noting derivtive3hwith conforml ~ i. time t nd denoting 4 > = V h E B (5) d we will be interested in cse O(1). Depending on sign of ~ ~ one of 4 H 1 ~ ~ bckrection on inflton eom new friction term: he Bi ' N e he B i ' N Friedmnn reds equtions solutions or of eq. (6) will develop n instbility. We ssume tht > 0 nd ~innlyticlly. ) < 0 so > 0. Typiclly e ect Friedmnn eqution is smll. Howe ming is tht slowly vrying function in time we cn solve eqution for dditionl source for sclr nd tensor fluctutions 1frequency 1!~ 1 isfor~ inflton this introduces n dditionl friction term w The solution tht reduces to positive for k ~ must 3H = V he B i. (4) Fourier modes of stisfy: /H increses towrds end of infltio significntly s ffected power spectrum of sclr nd tensor perturbtions 1!0 (± k )] ± ( k) = p [i F0 (± k ) G (8) tht for given sclr potent N dditionl e-folds implying d ( k kk) 5 Listening for primordil±grvittionl wves Vlerie Domcke - PC ~ nlyticlly. k ± k) =eqution 04 More. precisely ± ( nd relevnt for smll(6) [6]: wly vrying function in for The lst time we cn solve

6 pseudosclr infltion f Listening for primordil grvittionl wves Vlerie Domcke - PC

7 bckground dynmics useful clssifiction of infltion models: ε V = β Mukhnov 13 N O(1/ N p1 ) p evolution of infltion field evolution of / p = /( p H) 3 prmeters: αβ p (C) (B) mx / (N N ) p/ 1 6= 0 =0 N CMB 0 N N N CMB N N N N CMB dditionl friction CMB observbles evluted t lter point on n s ' 1 O(1) N N O r = 16 N N <N CMB ' 60 rpid increse of for lrge vlues of p enters eom exponentilly n s reduced r incresed lrge effects t end of infltion in prticulr for lrge p (smll r!) Listening for primordil grvittionl wves Vlerie Domcke - PC

8 ns 1=. (49)! p r= ~ Bi/ ~ s H h E N s (k) = s (k)vc s (k)guge = 3 H The constrints on se prmeters from Plnck mission [15] red (t 68% CL for d ln k s = d ln k (13) perturbtion power spectr ns nd s 95% with CL for r): ~ Bi ~ he 1. (14) 3H ns = ± s = ± r < (50) t lrge scles guge contributions re smll nd! pproches scle-invrint! spectrum α field infltion. t negligible guge H fluctutions during EB contribution In slow-roll pproximtion nd for vcuum t smll CMB 1 H stndrd spectrum of scles guge 7 H 4 πξ Δ s (k) = Δ s (k)vc Δ s (k)guge = Ω = ( e ) 3bH φ! Figure 5: Power spectrum GW 6! π φ scles quntities bove re given by: of sclr perturbtions for ll models with sme prmeters nd color code of 1 π M P M Pξ contributions dominte nd spectrum is given by:!! Fig. 4. The upper horizontl line estimtes PBH bound lower one indictes COBE normliztion. α EB 1 1 V( ) b = 1 πξ (k) ' (15) N! = n ' 1 6 (51) s s V V ( )r.' 16 V 3ΛH φ4 ( ) N s N V tht fields s sclr by modifying where V is Note defined in Eq. guge (1) nd V ect is defined V =spectrum V /V. in It twofold is usefulwy: to express bckground slow-roll eqution of motion nd byp = modifying eqution of motion for 1 (Qudrtic) V s: p =of (Strobinsky) 1 drefined ln V clcultion fluctutions directly. more solution to -14 Eq. (11) cn be found 10 V p = 3 (Hilltop) dn [8] with which estimte bove grees up to n order one fctor. p = 4 (Hilltop) yielding [1]: 10-7 ΩGW h V = Δs 10-5 in p N (5) The tensor fluctutions re governed by6 ns = 1. linerized Einstein (53) β eqution [17]: εv! 10-4 p d ln dhij nsb 0.96 suggests N For p > term proportionl tod hij is negligible indicting tht h = T. p <.4 for N* < d d 10 0 d ij 10 5 MP f[hz] ij b Smll non gussinities: s discussed in [7 11] to respect constrints on smll gure 5: Power spectrum of sclr perturbtions for ll models with sme prmeters nd color code of (16) f[hz] Figure 6: Grvittionl wve spectrum for ll models with sme prmeters nd color code of Fig. 4. We re lso showing sensitivity curves for (from left to right): milli-second pulsr timing elis dvnced g. 4. The uppermplitude horizontl estimtes@ PBH bound lower one indictes COBE normliztion. primordil non line gussinities we need CM N NCMB fixes one increse t smll scles to universl vlue B prmeter =NCM5B..5. This implies: LIGO. Current bounds re denoted by solid lines expected sensitivities of upcoming experiments by dshed lines. See min text for detils. lrge power on smll scles -> PBHs low scle models feture stronger increse gure 4: Evolution of prmeter governing strength of guge interctions for models with CM B =..5. (54) nerly on smll scles Onset on coupling α 18 erent vlues of p suniversl defined in Eq.mplitude (0). The H prmeters for Strobinsky model re sof in increse Fig. 3 depends N =NCM B rmeters for or models re listed in pp.. More detils on derivtion of this constrint re given in Sec. 5. we find both universl nd infltion model specific fetures e in tension with estimted PBH bound of [11] when we restrict to cse N = 1. s 14 is discrepncy is however only by O(1) fctor it cn both be ddressed by tking into Listening for primordil grvittionl wves Vlerie Domcke - PC count oreticl uncertinties in PBH bound (see lso Sec. 5) or by considering

9 prmeters of GW spectrum mx (f GW ) p 1 < p (f GW ) GW f1: guge contribution tkes over in f: guge friction supersedes Hubble friction log GW (f 1 GW1 ) CMB Ω GW Ω GW r Δ s mx ε 1 : fixed by : determined by f CMB (f 1 GW1 ) f mx described by (implicit) nlyticl equtions log f ε V! β N p L α 4Λ φf!f p : slope of increse nd vcuum mplitude β : vcuum mplitude α / Λ: shifts spectrum horizontlly multi-frequency direct GW tests (eg SK elis LIGO/VIRGO) plus CMB polristion cn constrin ll 3 prmeters Listening for primordil grvittionl wves Vlerie Domcke - PC

10 In cse of positive detection upcoming elis mission would potentilly llow to pseudosclr Strobinsky infltion di erentite between se two cses s well s constrin vlue of /. fixed by Δ V (φ ) = V0 (1 e prmeters: s ) γ φ p= β = 1 / (γ ) α /Λ observbles: slow-roll observbles ns r non-gussinity prmeter ξcmb direct GW sensitivity LIGO/VIRGO O1 (current) O:15/16 O5:0- see Buchmuller VD Kmd Schmitz 13 for sugr reliztion () LIGO plot. (b) elis plot. remrkble complementrity between different mesurements nd multi-messenger nlysismodel of microphysics infltion! Figure 7: Plot ofmulti-frequency ( / ) prmeter spce for Strobinsky with contour of lines for ns (solid blue) r = { } (dotted) nd CMB = { } (dshed). The ornge shded regions denote projected sensitivity for dvnced LIGO in10 O nd O5 run (left pnel) nd for elis in Listening for primordil grvittionl wves Vlerie Domcke - PC

11 Conclusion nd Outlook GW stronomy hs begun - nd we re only t very beginning! If inflton is pseudosclr GW signl of cosmic infltion cn be enhnced by mny orders of mgnitude in prticulr in rnge of elis nd LIGO/VIRGO. The spectrum is n sensitive to shpe of inflton potentil. Universlity clsses of infltion describe rnge of predictions bsed on only three prmeters. The complementrity of CMB nd direct GW mesurements provides powerful probe of physics of cosmic infltion. For future:.. prticle physics: identifiction of possible guge groups.. cosmology: reheting bryogenesis eg Kusenko Schmitz Yngid 14; nber Sbncilr 15; dshed Sfkinkis 15 Listening for primordil grvittionl wves Vlerie Domcke - PC

12 bckup slides Listening for primordil grvittionl wves 1 Vlerie Domcke - PC

13 Some useful properties of GWs perturbtions of bckground metric: ds = ( )( µ h µ (x ))dx µ dx! governed by linerized Einstein eqution! h 00 ij(k ) k 00 h ij (k ) = 16 G {z ij (k } ) {z } {z } source term from T µ H ( h ij = h ij TT - guge) {z } k H : h ij cos(! )/ k H : h ij const. useful plne wve expnsion: Z h Z ij (x ) = X P = Z 1 1 dk Z d ˆk hp (k) T k ( ) {z } ( i )/( ) e P ij ˆk e ik ( ˆkx ) trnsfer function expnsion coe cients polriztion tensor P = observtionl quntity in direct detection GW = GW (k ) GW ( ) = 1 ln k 3 G Dḣij (x ) ḣij (x )E Listening for primordil grvittionl wves Vlerie Domcke - PC

14 Primordil vcuum fluctutions (stndrd infltion) BICEP 14 hypoticl primordil contribution with r ~ 0.17 CMB r = t / s Lensing - pek t t_cmb - GW t_cmb - current bound r ~ 0.1 ΩGW h GW (k) = eq msec pulsr infltion r = 0.1 t 1 direct k 0 H 0 k[mpc -1 ] time elis T k ' RH t 1 r LIGO for k eq k k RH k RH / T RH - scle invrint spectrum - sensitivity to entire cosmologicl history - not detectble in ner future ET BBO/DECIGO f[hz] Rubkov 8 Turner White Lidsey 93 Seto Yokoym 03 Smith Kmionkowski 05 here: T RH = GeV Listening for primordil grvittionl wves Vlerie Domcke - PC

15 Or stochstic bckgrounds Preheting & cosmic strings t GUT scle new physics t TeV nd beyond? W GW h infltion H1L HL H9L H cosmic strings r ~ D H8L H7L H6L H5L H3L H4L NG cosmic strings preheting ΩGW f (Hz) plot from Bhupl Dev Mzumdr 16 GUT-scle phse trnsition fter hybrid infltion Buchmuller Domcke Kmd Schmitz 1 unresolved BH mergers first order phse trnsitions LIGO/VIRGO collbortion 16 Cprini et l 15 Listening for primordil grvittionl wves Vlerie Domcke - PC

16 furr observtionl signtures brief overview: CMB: sclr nd tensor fluctutions in prticulr non-gussinities blue GW signl (enhnced on smll scles) mximlly chirl. suppressed t CMB scles but interesting for LIS LIGO/VIRGO PBH formtion due to enhnced ' sclr power on smll scles indirekt GW bound from primordil mgnetic fields N e in BBN nd CMB Brnby Nmb Peloso 11 Brnby Peloso 11 Brnby Pjer Peloso 1 Meerburg Pjer 1 nber Sorbo 1 Linde Mooij Pjer 1 llen 96 Pgno Slvti Melchiorre 15 Durrer Hollenstein Jin 11 Cprini Sorbo 14 Fujit et l 15 very interesting setup for multi-messenger nlysis min focus here on CMB nd direct GW observtions cn inflton guge field coupling enble us to probe microphysics of infltion? Listening for primordil grvittionl wves Vlerie Domcke - PC