HIGGS INFLATION & VACUUM STABILITY

Transcription

1 HIGGS INFLATION & VACUUM STABILITY Javier Rubio based on Phys. Rev. D 92, F. Bezrukov, J.R., M.Shaposhnikov

2 Outline Could the Higgs field itself be responsible for inflation? 1. Reminder of inflation/ HI at tree level What happens if our vacuum becomes unstable below the scale of inflation? 2. Potential problems with vacuum inst. Which is the relation between the SM parameters and the inflationary observables? Which are the requirements for this scenario to be self-consistent? 3. Self-consistent approach to HI 4. HI in the metastability scenario 5. Conclusions

3 IT IS A FACT OF LIFE THAT... The universe is almost flat, homogeneous and isotropic, but contains small density perturbations with almost flat spectrum T T 10 5 D T(x) T T(y) T Explaining this within the usual Big Bang theory requires enormous fine-tuning of initial conditions at the Planck scale. E / Z d 3 k k 3 eik(x y) k n s 1

4 Inflation & Scalar fields A period of accelerated expansion sourced by: a negative pressure ä a = (1 + 3w) > 0 6 w< 1 3 and a nearly constant energy density ä a =(H2 + Ḣ) > 0 H = r 3 const. Homogeneous scalar field in slow-roll +3H + V ( )=0 w = p = V ( ) V ( )

5 The quantum origin of structure Inflaton fluctuations = H 2 Curvature perturbations ds 2 = dt 2 a(t) 2 e 2 (t,x) dx 2 k P S(k) = 2 2 H Ḣ 2 Density perturbations CMB perturbations T

6 U need a scalar? There u are! m H = ± 0.21(stat) ± 0.11 (syst) GeV low or high, depending on your taste...but certainly particular...

7 Higgs mass predictions arxiv: ) Homer Simpson s prediction 775 GeV (1998)

8 Can we Higgsflate the Universe? h Chaotic inflation? New inflation? Linde 82 Too steep to inflate New inflation? Chaotic inflation? Linde 83 Too large primordial perturbations P R 10 3 v EW h

9 The SM in the presence of Gravity L = f(h)r 1 g 2 gµ w 2 G µ µ h h U(h) L = f(h)r 1 g 2 ( h)2 U(h) +ar 2 + br µ R µ + cr µ R µ + d R U(h) = h 2 v 2 2 f(h) =MP 2 + h h 2 4 Restricted dimension apple 4 No new degrees of freedom Scale invariance at h M P / p h

10 Higgs inflation at tree level L p = M P 2 + hh 2 R 1 g 2 2 (@h)2 4 (h2 vew) 2 2 Moving to the Einstein frame g µ = 2 (h)g µ 2 =1+ h h 2 M 2 P L g = M 2 P 2 R 1 2 gµ µ U( ) All the non-linearities moved to the scalar sector U( )= 4 ( 2 v 2 EW) 2 U( )= M 4 P 4 2 h 1 e p 2/3 M P (1 + hv 2 EW M 2 P 2 ) for for h<m P / h h>m P / h F. L. Bezrukov and M. Shaposhnikov Phys. Lett. B659 (2008)

11 A sufficiently flat potential Scale invariance JF --> shift symmetry EF U T T 10 5 U U( ) ' M 4 P 4 2 h 1 e p 2/3 M P /M P 2 h Only / 2 h is important

12 The primordial spectra Scalar pert. Tensor pert. P S (k) =A s k k ns s ln(k/k )+ 1 6 s (ln(k/k )) P T (k) =A t k k nt t ln(k/k )+... s d2 n s d ln k 2 n s ' 1 2 N ' 0.97 r ' 12 N 2 ' HI

13 On the edge of stability SM remains perturbative all the way up till the inflat./planck scale µ d (µ) d log(µ) = +# #y 4 t Non trivial interplay between Higgs self-coupling and top quark Yukawa coupling (no gravity) y t =0.9176, m t =170.0 y t =0.9235, m t =171.0 y t =0.9294, m t =172.0 y t =0.9359, m t =173.1 y t =0.9413, m t =174.0 y t =0.9472, m t = e+10 1e+15 1e+20 µ(gev) µ, GeV Is there a reason for that? M. Lindner, M. Sher, and H. W. Zaglauer, Phys.Lett., B228, 139 (1989), C. Froggatt and H. B. Nielsen, Phys.Lett., B368,96 (1996), M. Shaposhnikov and C. Wetterich, Phys.Lett., B683, 196 (2010), M. Veltman, Acta Phys.Polon., B12, 437 (1981), B683, 196 (2010), M. Holthausen, K.S.Lim, M.Lindner and references therein... Gravitational corrections? Lalak,Lewicki, Olszewki arxiv , Branchina, Massina Phys.Rev.Lett. 111 (2013) etc...

14 Top quark & vac. instability y crit t = s Mh Stable M t =172.38±0.66 GeV Metastable M h, GeV CMS Tevatron y t (µ=173.2 GeV) See F. Bezrukov, M. Shaposhnikov J.Exp.Theor.Phys. 120 (2015) and references therein

15 Top quark & vac. instability y crit t = s Mh Stable Metastable LHC/Tevatron See F. Bezrukov, M. Shaposhnikov J.Exp.Theor.Phys. 120 (2015) and references therein

16 Top quark & vac. instability y crit t = s Mh Stable M t =172.38±0.66 GeV Metastable M h, GeV CMS y t (µ=173.2 GeV) See F. Bezrukov, M. Shaposhnikov J.Exp.Theor.Phys. 120 (2015) and references therein

17 Imagine that the top and Higgs masses are measured with a precision enough to conclude that our vacuum is not completely stable... Should new physics appear at the scale? µ 0 Is Higgs inflation Before the LHC Higgs discovery, it it was very tempting to identify the inflaton as the Higgs boson of the SM [...]. However, the recent LHC and Tevatron measurements [...] indicate that the Higgs potential. turns negative at a scale below the typical cosmic inflation scale. [...] new physics is indispensable to reach a stable electroweak vacuum after inflation by Anonymous Informer I If m h and m t are close to the measured central value, Higgs inflation is not possible and V eff becomes negative much before M P by Anonymous Informer II How did we end in the right EW minimum?

18 HI is non-renormalizable U( ) ' M 4 P 4 2 h 1 e Non-polynomial p 2/3 M P 2 Quantum corrections should be introduced by interpreting the theory as an EFT in which a particular set of higher dim. operators are included but... Which set of operators?

19 The naive approach In the absence of new physics the cutoff scale might be as large as the Planck scale, where gravitational interactions become important for sure Consider all kind of Planck scale suppressed operators... V '...added in the Einstein frame M 4 P 4 2 h V n = c n n M n 4 P...added in the Jordan frame V ' 4 h 4 V n = c n h n M n 4 P During inflation V V c n 2 h M P M P n During inflation V V c n Infamous cosmological hierarchy problem? h M P h M P / h n 4 c n But is this self-consistent? n 4 2

20 The self-consistent approach A self-consistent approach is to define the cutoff from the theory itself by considering all possible reactions between the SM constituents and add all kind of operators suppressed by these cutoffs Compute the quadratic lagrangian 2. Get rid of the mixings in the quadratic action 3. Read out the cutoff from higher order operators

21 Strong Coupling p h h M P P M P h S h h 2 M P G Weak Coupling M P p h M P h h A consistent EFT : Cutoffs are parametrically larger than all the energy scales involved in the history of the Universe

22 The minimal approach Select a particular set of UV completions within the previous set. Add only the higher dimensional operators generated by radiative corrections ( i.e. those needed to make theory finite at every order in PT). Fixed by the divergencies Arbitrary An L ct = + B n O n (Partially) controllable link between the low and high energy parameters of the model F. Bezrukov, A. Magnin, M. Shaposhnikov, and S. Sibiryakov JHEP 1101 (2011) 016, See also C.P. Burguess, S.P. Patil, M.Trott JHEP 1406 (2014) 010

23 Top quark in Higgs background L F = y f p h! LA = y f 2 L t ( + )= y t p 2 F ( + ) t t = y t p 2 F ( ) t t + y t p 2 df ( ) d t t +... t At low energies At high energies F = F 0 (0) = 1 F h p 2 y f p F ( ) 2 F = M P p 1 e apple 1/2 h y t F 0 F 0 (1) =0 t Consider the propagation of the top quark Add counterterms to cancel divergencies at small

24 One-loop effective potential At low energies At high energies F = F 0 (0) = 1 F = const. F 0 ( 0 )=0 Add counterterms to cancel divergencies new tree level

25 Eff. behaviour of coupling constants yt m h = GeV m t = GeV Neglecting the running of 1 and yt1 1 between µ M P / h and M P / p h y t (µ)! y t (µ)+ y t F k m Dashed dy t = Dotted dy t = (µ)! (µ) l " F F 00 F The shape of the asymptotics is maintained m h = GeV m t = GeV dl = dl = 0 dl = # k m Dashed dy t = Dotted dy t =

26 Restoring Higgs inflation (M P / ) y t y t (M P / ) (M P / ) y t y t (M P / ) Higgs inflation requires absolute stability of the SM vacuum Higgs inflation can be possible even in the case of a metastable vacuum Non-critical Critical Not to scale!! 10 3 l 0-5 h -10 m h = GeV m t = GeV k m But how to avoid finishing in the wrong vacuum???

27 The Universe collapses 8 6 a j kf kf

28 Sketch of effective potential (not to scale!)

29 Sketch of effective potential (not to scale!) Inflation takes place with the standard initial conditions

30 Sketch of effective potential (not to scale!) Higgs oscillates and particle creation takes place. J. Garcia-Bellido, D.G. Figueroa, J.R., Phys.Rev. D79 (2009) F. Bezrukov, D. Gorbunov and M. Shaposhnikov JCAP 0906 (2009) 029 J. Repond, J. R, M. Shaposhnkov, in preparation

31 Combined Preheating n k ((j + 1) + )=n k (1 + ) e F (j) e 2 P j i=1 µ k(i+1)

32 Sketch of effective potential (not to scale!) V T = 1 X 6 2 P Z 1 0 k 4 dk 1 k (m) e k(m)t 1 I f t h e r e h e a t i n g temperature is large enough the wrong minimum disappears. arxiv: F. Bezrukov, J.R., M.Shaposhnikov

33 Sketch of effective potential (not to scale!) The field settles down at the true EW minimum and stays there till the present time.

34 Symmetry restoration r r c r F r B r W r Z Higgs Fermions Bosons W bosons Z bosons j T R ' GeV 10 7 U U T = 8 x GeV T = 7 x GeV T = 6 x GeV T = 5 x GeV T = kf T + ' GeV T R >T + Higgs inflation can be possible even if our vacuum is not completely stable

35 What about lifetime? 4 2 SM + x-coupling SM 10 7 U U kf Z. Lalak,M. Lewicki, P. Olszewki JHEP 1405 (2014) 119, V. Branchina, E. Messina Phys.Rev.Lett. 111 (2013) etc... For SM computation see : J. R. Espinosa and M. Quiros, Phys. Lett. B 353 (1995) 257 J. R. Espinosa, G. F. Giudice and A. Riotto, JCAP 0805 (2008) 002

36 CONCLUSIONS The Higgs field can inflate the Universe HI provides universal predictions if the UV completion respects SI n s ' 1 2 N ' 0.97 r ' 12 N 2 ' The relation of these predictions to LE observables contains an irreducible theoretical uncertainty. UV completion? Higgs inflation can be possible even if our vacuum is metastable The HI scenario is just a particular realization of a general idea. Vacuum instability is not necessarily a problem if: The potential is modified below the scale of inflation The reheating process is efficient enough as to make the wrong minimum disappear temporally.