Higgs inflation in SUSY SU(5) GUT

Higgs inflation in SUSY SU(5) GUT Jinsu Kim in collaboration with Shinsuke Kawai (SKKU) Sungkyunkwan University Nov. 14, 015 @ APCTP, Seoul, Korea

:Y [LSPI YRM I WI [EW MR E LSX ERH HIRWI WXEXI XLIR RIE P] & FMPPMSR ]IE W EKS I TERWMSR WXE XIH >LEX EPP WXEXIH [MXL XLI -MK -ERK >LI -MK -ERK >LIS ]

[Cervantes-Cota Dehnen 1995] [Bezrukov Shaposhnikov 008] Higgs inflaton S = Z d 4 x p g apple 1 (M P + )R 1 gµ @ µ @ V ( ) 4RJPEXSR EW E ORS[R TE XMGPI 4R KSSH EK II IRX [MXL PERGO V ( )= 4 4 ' 0.13 SXIRXMEP YRWXEFPI EKEMRWX EHMEXM I GS IGXMSRW SR MRM EP GSYTPMRK :RI GER KS XS XLI 0MRWXIMR J E I ME I]P X ERWJS EXMSR( S = Z d 4 x p g g µ! g E µ = g µ =1+ apple M P R 1 gµ @ µ @ U( ). ( 0MRWXIMR J E I TSXIRXMEP U( )= V 4 d d = 1 M P " +6 M P # 1/

[Cervantes-Cota Dehnen 1995] [Bezrukov Shaposhnikov 008] Higgs inflaton S = Z d 4 x p g apple 1 (M P + )R 1 gµ @ µ @ V ( ) 4RJPEXSR EW E ORS[R TE XMGPI 4R KSSH EK II IRX [MXL PERGO V ( )= 4 4 ' 0.13 SXIRXMEP YRWXEFPI EKEMRWX EHMEXM I GS IGXMSRW SR MRM EP GSYTPMRK

[Cervantes-Cota Dehnen 1995] [Bezrukov Shaposhnikov 008] Higgs inflaton S = Z d 4 x p g apple 1 (M P + )R 1 gµ @ µ @ V ( ) 4RJPEXSR EW E ORS[R TE XMGPI 4R KSSH EK II IRX [MXL PERGO V ( )= 4 4 ' 0.13 SXIRXMEP YRWXEFPI EKEMRWX EHMEXM I GS IGXMSRW SR MRM EP GSYTPMRK >LI =XERHE H SHIP 3MKKW MW EX 0 WGEPI! 1S MRJPEXMSRE ] TL]WMGW UYERXY GS IGXMSR M!I! 0 MW RIIHIH!

[Cook et al. 014] Higgs inflaton [Hamada et al. 014] S = Z d 4 x p g apple 1 (M P + )R 1 gµ @ µ @ V ( ) [Allison 014] [Simone et al. 009] 4R XLI 0MRWXIMR J E I U = (µ) 4 4 (1 + /M P ) " s!# = min + (4 ) 4 ln 1 c /MP 1+ /MP + Assumption: SM is valid up to the ~Planck scale (i.e., no new physics)

Higgs inflaton [Hamada et al. 014] E KI XIRWS XS WGEPE EXMS MW TSWWMFPI! = EPP RSR MRM EP GSYTPMRK MW TSWWMFPI! -YX!! [from Hamada et al. 014] Assumption: SM is valid up to the ~Planck scale (i.e., no new physics)

[Cervantes-Cota Dehnen 1995][Bezrukov Shaposhnikov 008] Higgs inflaton S = Z d 4 x p g apple 1 (M P + )R 1 gµ @ µ @ V ( ) 4RJPEXSR EW E ORS[R TE XMGPI 4R KSSH EK II IRX [MXL PERGO SXIRXMEP YRWXEFPI EKEMRWX EHMEXM I GS IGXMSRW SR MRM EP GSYTPMRK >LI =XERHE H SHIP MW RSX XLI IRH SJ XLI WXS ]! SWWMFPI I XIRWMSRW( =YTI W] IX ] ERH ERH?RMJMIH >LIS ] 1S -E ]SKIRIWMW IYX MRS SWGMPPEXMSRW WII C E[EM 5 D

Outline =?=B =??> SHIP =IXYT =YTI TSXIRXMEP ELPI TSXIRXMEP =MRKPI 1MIPH M MX YPXMJMIPH 0JJIGXW = 3MKKW MRJPEXMSR PM MX E E IXI WTEGI.SW SPSKMGEP SFWI EFPIW =Y E ]

[Georgi Glashow 1974] [Dimopoulos Georgi 1981] [Sakai 1981] SU(5) GUT SU(3) c SU() L U(1) Y EYKI JMIPH = 3MKKW JMIPH 4 =(8, 1, 0) +(1, 3, 0) +(1, 1, 0) +(3,, 5/6) {z } {z } {z } {z } gluon A a µ B µ Xµ,Y µ 5 =(3, 1, 1/3) {z } T +(1,, 1/) {z } D +( 3,, 5/6) {z } = HSYFPIX 3MKKW X µ,y µ.spsy IH X MTPIX 3MKKW h T i =0?> 3MKKW JMIPH 1I MSR JMIPHW 4 : 10 : ij 5 : i in 4 H in 5 H u D H in 5 H d

=YTI TSXIRXMEP W = H(µ + )H + m Tr( )+ 3 Tr( 3 ) r = 15 S diag 3 1, 1, 1,, 3 {z } SU(5)!SU(3) SU() U(1) H = Hc H u H = Hc H d WMRKPIX GLM EP WYTI JMIPH W S =0) m p hsi =0 30 W = µ + r! 15 S H c H c + µ r! 3 10 S H u H d + 1 ms 3 p 30 S3 8 < : H u = H c = H c =0 0 H 0 H d = d 0 µ p 3/10 hsi =0 µ + p /15 hsi M GUT = 10 16 GeV H 0 u 9 = ; W = =) µ hsi MGUT ev hsi r 3 10 (S ev)h0 uh 0 d + 1 ms m 3ev S3

ELPI TSXIRXMEP GSRHMXMSRW JS XLI MRJPEXSR TSXIRXMEP( M WYJJMGMIRXP] JPEX MM RS XEGL]SRMG MRWXEFMPMX] MMM XLI = EGYY [Arai Kawai Okada 011] TSWWMFMPMXMIW JS XLI ELPI TSXIRXMEP( =1 M GYFMG SHIP 1 3 Tr + H + H + M MMM MM HH + H H + e! 3 Tr +Tr + 3 Tr =1 MM WI XMG SHIP 1 3 Tr + H + H + M MMM MM HH + H H + 3 Tr + e! 3 Tr 3

JPEX HM IGXMSR IWGEPMRK H 0 u = H 0 d = 1 p ' S = 1 p s ' = 1 p h EK ERKMER HIRWMX] =1 L J = p g J apple 1 R J 1 6 s + 1 6!s3 + 1 s4 + 4 apple =1!s s! = e! p 15 v = p ev ( V J = 3 (s 40 n s+! apple v) h + 1 apple apple ) h 3 s(s v) 1 h 6 h 3 s(s v) s + vh 3 vs 3 h (s v)o 80 h i 4+ (3 / 1)h + +! 6apple s4 1 gµ J @ µh@ h =1 1 applegµ J @ µs@ s V J 1 6 s + 1 s4 +! 6 s6 + apple =1 s 9!s 4! = e! 4 v = p ev ( V J = 3 (s 40 n ( +6!s ) apple v) h + 1 apple 4 apple ) h 3 s(s v) 1 h 6 h 3 s(s v) s 3 + vh 3 vs 3 h (s v)o 80 h i 4+ (3 / 1)h + +8!s!s 4 3apple s 4 GYFMG SHIP WI XMG SHIP

Higgs in 4R XLI PM MX SJ X M MEP W JMIPH H]RE MGW( s = v =0 L J = p g J apple 1 R J 1 gµ J @ µh@ h 3 160 h 4 =1+ h 4 1 6 = =0.5! = 100 = 10000 = 4646 n s =0.968 r =0.0096

Higgs in 4R XLI PM MX SJ X M MEP W JMIPH H]RE MGW( s = v =0 L J = p g J apple 1 R J 1 gµ J @ µh@ h 3 160 h 4 =1+ h 4 1 6 = =0.5! = 100 = 10000 = 4646 n s =0.968 r =0.0096 4R KSSH EK II IRX [MXL PERGO FYX TLIRS IRSPSKMGEPP] RSX EPPS[IH RS = EGYY YPXMJMIPH EREP]WMW

Multifield analysis in [Sasaki et al. 1996][Nakamura et al. 1996][Gordon et al. 001][Peterson et al. 011] [Kaiser et al. 013][Schutz et al. 014][etc.].SW SPSKMGEP SFWI EFPIW( S[I WTIGX Y =TIGX EP MRHI P R (k) =P R (k ) 1+T RS(t,t) = >IRWS XS WGEPE EXMS n s 1+ d ln P R d ln k r P T P R = 16 1+T RS H 1 1+T RS (t,t) Z t T RS (t,t)= dt 0 (t 0 )H(t 0 )T SS (t,t) t applez t T SS (t,t)=exp dt 0 (t 0 )H(t 0 ) t > ERWJI JYRGXMSR

Multifield analysis in,pks MXL ( =SP I XLI FEGOK SYRH IUYEXMSR SJ SXMSR JS [E H MR XM I 1MRH XLI IRH SJ MRJPEXMSR end Ḣ H =1 =SP I XLI FEGOK SYRH IUYEXMSR SJ SXMSR FEGO[E H MR XM I 1MRH XLI LS M SR G SWWMRK N e = 60.S TYXI XLI GSW SPSKMGEP SFWI EFPIW

Multifield analysis in LI I XS PSSO I LE I TE E IXI W(,,,!, L]WMGW SJ ERH?RMJMGEXMSR(, O(1) ) = =0.5 SR MRM EP GSYTPMRK PERGO RS EPMWEXMSR( A s =.07 10 9 ) Fix I E I PIJX [MXL X[S TE E IXI W(,!

Multifield analysis in LI I XS PSSO SXIRXMEP WLETIW =MRKYPE MX] [EPPW GYFMG WI XMG S XEGL]SRMG MRWXEFMPMX] = EGYY

Multifield analysis in LI I XS PSSO I E I PIJX [MXL X[S TE E IXI W(,! GYFMG SHIP =MRKYPE MX] [EPPW s = s ±! ± p +! s < 0 <v<s + : real when >! ) > 0 and! < 1 v v WI XMG SHIP s = s ± ± p +9! 9! : 4 complex when! < 9 : Re and Im when! > 0 :4Rewhen :4Imwhen 9 <! < 0 & > 0 9 <! < 0 & < 0 E E IXI IKMSRW [I E I MRXI IWXIH

Multifield analysis in LI I XS PSSO & X]TIW SJ X ENIGXS MIW RY I MGEP WSPYXMSRW IJI IRGI GEWIW?RTL]WMGEP?RTL]WMGEP?> = GYFMG cubic : (,!, ) = (10000, 116, 585) sextic : (,!, ) =( 3000, 10 7, 6450) WI XMG

Multifield analysis in LI I XS PSSO 1EXI SJ X ENIGXS MIW GYFMG WI XMG

Multifield analysis in.sw SPSKMGEP SFWI EFPIW 3. 10-9 {000, 10000}! {5 10 5, 1 10 7 }.YFMG GEWI Scalar Power Spectrum.6 10-9 =I XMG GEWI Scalar Power Spectrum 3. 10-9.5 10-9.8 10-9.4 10-9 Ps.6 10-9 Ps.3 10-9.4 10-9. 10-9. 10-9 000 4000 6000 8000 10 000 z.1 10-9 0 40 60 80 100 w Hin units of 10 5 L We have fixed!

Multifield analysis in.sw SPSKMGEP SFWI EFPIW.YFMG GEWI 0.9674 Scalar Spectral Index 0.00308 Tensor-to-Scalar Ratio 0.00307 0.9673 0.00306 0.00305 ns 0.967 r 0.00304 0.00303 0.9671 0.0030 0.00301 0.9670 000 4000 6000 8000 10 000 z 0.00300 000 4000 6000 8000 10 000 z n s =0.96705 0.9674 r =0.00301 0.00308 We have fixed!

Multifield analysis in.sw SPSKMGEP SFWI EFPIW =I XMG GEWI Scalar Spectral Index Tensor-to-Scalar Ratio 0.968 0.00310 0.9680 0.00305 0.9678 0.00300 ns 0.9676 r 0.0095 0.9674 0.0090 0.967 0.0085 0.9670 0 40 60 80 100 0.0080 0 40 60 80 100 w Hin units of 10 5 L w Hin units of 10 5 L n s =0.9670 0.9684 r =0.0080 0.00305 We have fixed!

Multifield analysis in.sw SPSKMGEP SFWI EFPIW.YFMG GEWI n s =0.96705 0.9674 r =0.00301 0.00308 =I XMG GEWI n s =0.9670 0.9684 r =0.0080 0.00305

Multifield analysis in.sw SPSKMGEP SFWI EFPIW.YFMG GEWI n s =0.96705 0.9674 r =0.00301 0.00308 =I XMG GEWI n s =0.9670 0.9684 r =0.0080 0.00305 YPXMJMIPH IJJIGXW E I RIKPMKMFPI! IE P] WX EMKLX EPSRK L E KI EWW WUYE IH EPSRK W 4WSGY EXY I SHI MW EFWIRX!

Summary YPXMJMIPH IJJIGXW SR =YTI W] IX MG 3MKKW MRJPEXMSR MR =??> SHIP E I WXYHMIH! I WLS[ LS[ XLI GS E MERX JS EPMW GER FI YXMPMWIH XS GS TYXI GSW SPSKMGEP SFWI EFPIW WYGL EW XLI TS[I WTIGX E XLI WTIGX EP MRHMGIW XLI XIRWS XS WGEPE EXMS! YPXMJMIPH IJJIGXW E I RIKPMKMFPI! Comment 4WSGY EXY I J EGXMSR MW RIKPMKMFPI! [Kawai & JK 015] I YWIH XLI FEGO[E H HIPXE JS EPMW XS GS TYXI RSR EYWWMERMX]! O f local NL 1

Thank you Jinsu Kim with Shinsuke Kawai Sungkyunkwan University @ The 51st Workshop on Gravitation and Numerical Relativity for APCTP Focus Research Program 14 Nov. 015