Probing the Early Universe with Baryogenesis & Inflation Wilfried Buchmüller DESY, Hamburg ICTP Summer School,Trieste, June 015
Outline BARYOGENESIS 1. Electroweak baryogenesis. Leptogenesis 3. Other models INFLATION 1. The basic picture. Recent developments
I. The basic picture Key references A. Starobinsky ; A. Linde K. Freese, J. A. Friemann and A. V. Olinto, Phys. Rev. Lett. 65 (1990) 333 G. R. Dvali, Q. Shafi and R. K. Schaefer, Phys. Rev. Lett. 73 (1994) 1886 Reviews D. Baumann, arxiv:0907.544v (01) V. Mukhanov, Physical Foundations of Cosmology (005) D. S. Gorbunov and V. A. Rubakov, Theory of the Early Universe, Vol II (01)
Slowly rolling scalar fields Scalar field in curved space-time: Z S M = d 4 x p gl, L = 1 g µ @ µ @ V ( ), with stress energy tensor, i.e. energy density and pressure: T µ = p g S M g µ = @ µ @ + g µ L, = 1 + 1 (@ i ) + V ( ), p = 1 + 1 (@ i ) V ( ) field equations: Friedman equations and equation for : +3H + @ V =0
Slowly rolling homogeneous field ( V, H, @ V ) satisfies slow roll conditions: = M P = M P V 0 V V 00 V 1, 1 Equations of motion for scalar field and scale factor: Simplest example: chaotic inflation 3H = V 0, H + k a = 1 3M P V V ( )= p
Important parameters for models of inflaton: Exponential expansion, number of e-folds until end of inflation (time t e,field value e ): a e = ae N, N = Z te Field at N e-folds before end of inflation: t dth = 1 M P Z (N) = p pnm P, e d V V 0 = 1 p i.e. field super-planckian for N = 50...60; slow roll parameters: M P Spectral indices: = p 4N, = p 1 N tensor-to-scalar ratio: n s 1= 6 = p + N, n t = = p N V 0 = 16 r =8M P V
The microwave background sky as seen by Planck 013: fluctuations one million times smaller than average; best evidence for hot early universe
DM h =0.1199 ± 0.007 Planck power spectrum 015; implications: flat universe, abundance of matter & dark matter,... ; primordial density perturbations from QUANTUM FLUCTUATIONS [Chibisov, Mukhanov 81,...]
Correlation Functions of Photon Flux T (ˆn) T 0 = P lm a lmy lm (ˆn) C TT l / P m ha lm a lmi / R k dk s(k) Tl (k) primordial density fluctuations (inflation): s(k) transfer functions (observable at time of photon decoupling): Tl(k) parametrization of primordial scalar and tensor perturbations: ns 1 k s(k) =A s k, t (k) =A t k k nt, r = A t A s inflationary models: testable predictions for A s, n s, r
How well do inflation models describe the Planck data?
II. Recent developments Example of small field inflation: hybrid inflation, connection with leptogenesis and dark matter Impact of BICEP data Example of large field inflation: chaotic inflation in supergravity, connection with supersymmetry breaking and moduli stabilization The Starobinsky model...
SFI: supersymmetric hybrid inflation Leptogenesis & gravitinos: for thermal leptogenesis and typical superparticle masses, thermal production yields observed amount of dark matter: 3/ h = C T R 100 GeV m g, C 0.5 10 10 GeV m 3/ 1TeV 3/ h 0.1 is natural value; but why is reheating temperature close to minimal LG temperature? Simple observation: heavy neutrino decay width (for typical LG parameters) N 1 = m 1 8 M1 v F [WB, Domcke, Kamada, Schmitz 13, 14] 10 3 GeV, em 1 0.01 ev, M 1 10 10 GeV yields reheating temperature (for gas of decaying heavy neutrinos) T R 0. q 0 N 1 M P 10 10 GeV wanted for gravitino DM. Intriguing hint or misleading coincidence?
Spontaneous B-L breaking & false vacuum decay Supersymmetric SM with right-handed neutrinos: W M = h u ij10 i 10 j H u + h d ij5 i 10 j H d + h ij5 i n c jh u + h n i n c in c is 1 in SU(5) notation: hs 1, i = v B L / p 10 (q, u c,e c ), 5 (d c,l), n c ( c ) 1 W B L = v B L S 1 S yields heavy neutrino masses. ; B-L breaking: Lagrangian is determined by low energy physics: quark, lepton, neutrino masses etc, but it contains all ingredients wanted in cosmology: inflation, leptogenesis, dark matter,..., all related! Technically: Abelian Higgs model in unitary gauge; inflation ends with phase transition ( tachyonic preheating, spinodal decomposition )
3 0.5 0 / V M P 4 / Φ M P 1 0 1 0 1 S / v B-L H M P time-dependent masses of B-L Higgs, inflaton, heavy neutrinos... (bosons and fermions): m = 1 (3v (t) v B L), m = v (t), M i =(h n i ) v (t)...
1 φ(t) (Tanh) <φ (t)> 1/ /v (Lattice) n B (x100) (Tanh) n B (x100) (Lattice) 10 1 0.1 Bosons: Lattice Tanh Fermions: Lattice Tanh <φ (t)> 1/ /v, nb(t) 0.1 0.01 Occupation number: n k 0.01 0.001 0.0001 1e-05 0.001 1e-06 5 10 15 0 5 30 time: mt 1e-07 0.1 1 k/m Rapid transition from false to true vacuum by fluctuations of waterfall B-L Higgs field; production of low momentum Higgs bosons (contain most energy), also other bosons and fermions coupled to B-L Higgs field [Garcia-Bellido, Morales 0], production of cosmic strings: initial conditions for reheating
Schematic view Gauge Higgs + Inflaton Right-handed Neutrinos Radiation + B-L asymmetry Gravitinos tachyonic preheating fast process slow process Comoving number density abs NHaL 10 50 10-1 10 0 10 1 10 10 3 10 45 10 40 10 35 10 30 N 1 th S Inverse temperature M 1 ê T N 1 nt i f a RH a RH a RH R B - L 10 5 10 0 10 1 10 10 3 10 4 10 5 10 6 10 7 10 8 Scale factor a Transition from end of inflation to hot early universe (typical parameters), calculated by means of Boltzmann equations: E @ @t Hp @ f X (t, p) = X X C X (Xi 0 j 0.. $ ij..) @p i 0 j 0.. ij.. yields correct baryon asymmetry and dark matter abundance G é
10 1 10-1 Inverse temperature M 1 ê T 10 0 10 1 10 10 3 10 11 THaL @GeVD 10 10 10 9 10 8 10 7 i f a RH a RH a RH 10 0 10 1 10 10 3 10 4 10 5 10 6 10 7 10 8 Scale factor a Time evolution of temperature: intermediate plateau ( maximal temperature ), determined by neutrino properties! Yields correct gravitino abundance when combined with standard formula
M1 @GeVD such that WGé h = 0.11 7 1010 mgé @GeVD 100 hb < hobs B 5 1010 50 3 1010 10 10 0 500 10 5 obs hnt B > hb M1 @GeVD mlsp @GeVD 1 1011 mgé = 1 TeV 1011 3000 vb-l = 5.0 1015 GeV 00 7 1010 Wwé > Wobs DM é w 100 mgé @TeVD 500 000 1500 1000 é G Whé > Wobs DM é h 500 10-5 10-4 10-3 10- é @evd m 1 10-1 10-5 100 10-4 10-3 é m1 @evd 10-10-1 100 Predictions for LHC (parameter scans): successful leptogenesis and gravitino DM (left) or neutralino DM (right, upper bounds) [non-thermally produced in decays of thermally produced gravitinos] constrains neutrino and superparticle masses
Spectral index & supersymmetry breaking Inflationary potential can be strongly affected by supersymmetry breaking (supergravity correction): V ( )=V 0 + V CW ( )+V SUGRA ( )+V 3/ ( ), V 0 = V CW ( )= V SUGRA ( )= v 4, 4 4 v 4 3 ln v/ p +..., v 4 8M 4 P 4 +..., V 3/ ( )= v m 3/ ( + )+... linear term turns hybrid inflation into two-field model in complex plane; strong effect on inflatonary observables, now dependent on trajectory, i.e. initial conditions! Inflation consistent with Planck data now possible (otherswise very difficult)
.0 1.5 m 3ê = 50 TeV Hs *, t * L Æ V,j < 0 V,j > 0 Æ Æ t @vd 1.0 VHs, tl Hs f, t f L 0.5 0.0 N = 50 Æ N = 0 H-v, 0L Hv, 0L -3 - -1 0 1 s @vd Two-field dynamics of complex inflaton in field space; all trajectories provide enough e-folds of expansion but only one yields the correct spectral index n s ' 0.96
100 TeV 1 PeV 10 PeV 10-10 TeV m 3ê 10-3 1 TeV 100 GeV Fine-tuned phase q f close to 0 l 10 GeV q f p ê 3 q f = 0 Cosmic string bound 10-4 1 GeV 100 MeV 10-5 m 3ê < 10 MeV 10 MeV A s > A s obs 10 14 10 15 10 16 v @GeVD Parameter scan: relations between scale of B-L breaking, gravitino mass and scalar spectral index (no problem!) cosmic string bound automatically fulfilled! Predicted tensor-to-scalar ratio: r. 10 6!! (typical for SF models)
March 014: BICEP Results BICEP: E signal Simulation: E from lensed ΛCDM+noise 50 1.7µK 1.7µK 1.8 55 60 0 µk 65 1.8 BICEP: B signal Simulation: B from lensed ΛCDM+noise Declination [deg.] 50 55 60 65 0.3µK 0.3µK 0.3 0 µk 0.3 50 0 Right ascension [deg.] 50 50 0 50 Have primordial gravitational waves been discovered in the CMB? r ' 0.? BICEP/Keck/Planck analysis: mostly dust!
HOT Quadrupole Anisotropy E < 0 E > 0 COLD e Thomson Scattering B < 0 B > 0 Linear Polarization [adapted from Baumann 1] Polarization: density quadrupole anisotropy generates via Thompson scattering of polarized photons; analysis of tensor spherical harmonics: two patterns of linear polarization, E-modes and B-modes (different under space relection); origin of B-modes: gravitational waves, dust...
0.05 BKxBK (BKxBK αbkxp)/(1 α) BB l(l+1)c l /π [µk ] 0.04 0.03 0.0 0.01 0 0.01 0 50 100 150 00 50 300 Multipole L/L peak 1 0.8 0.6 0.4 Fiducial analysis Cleaning analysis Joint BICEP/Keck/Planck analysis (015) upper: BICEP/Keck spectrum before and after subtraction of dust contribution lower: likelihood fit; primordial BB signal almost σ effect; favoured value of r about 0.05 More data this year, BB signal not yet excluded!! 0. 0 0 0.1 0. 0.3 r
LFI: chaotic inflation in supergravity Motivation: Planck/BICEP data, LFI in effective field theory (supergravity), recent work in string inflation(axion monodromy, aligned axions, inflation in F-theory models...). Minimal setup: inflaton, volume modulus (e.g. KKLT), supersymmetry breaking and uplift to Minkowski vacuum from AdS vacuum (eg. Polonyi field) [WB, Dudas, Heurtier, Westphal, Wieck, Winckler 15] V W = W 0 + Ae at + fx + 1 m, K = 3ln T + T + k X + 1 + 1-1 - 100 150 00 50 Σ super- & Kahler potential for modulus, Polonyi field and inflaton yield supergravity scalar potential
local minimum for modulus exits for sufficiently small inflaton field; integrating out the modulus yields effective inflaton potential: V (') 3 mm 3/' 1 1 8 m ' m 3/ V (φ) 1.5 10-8 1. 10-8 5. 10-9 1 m φ φ V (φ) Numerical preditions: m 3/ > q mm 3/ '? 5 10 5 10 14 GeV 5 10 15 0 5 30 φ n s =0.966, r =0.106
r 0.5 0. 0.15 0.1 0.05 Planck 014 (TT,TE,EE) + lowp Flattened chaotic inflation Natural inflation V / ' p, p apple N e = 60 N e = 50 flattening of chaotic potential due to moduli effects is generic phenomenon resulting effective inflation potentials probably still not good enough to fit the Planck data 0 4 0.96 0.98 1 n s
The Starobinsky model Consider modified gravitational action: S = M P Z d 4 x p gf(r), f(r) =R 1 6M R perform Weyl rescaling, g µ = S = M P Z d 4 x g µ,then p 3 g R + gµ @ µ @ + 3M (1 ) change to canonically normalized field, =exp(/ p 6)'/M P ), S = M P Z d 4 x perfect model of inflation: p 1 g R + gµ @ µ @ + V ('), V( )= 3 4 M M P 1 e p 6 ' M P n s ' 1 N ' 0.9636, r ' 1 N ' 0.004 Why???
Escher in the sky [Kallosh, Linde 15] r0.00 0.5 0.0 0.15 0.10 N=50 Convex Concave N=60 = 100 Planck TT+lowP Planck TT+lowP+BKP +lensing+ext class of potentials that interpolate between chaotic and Starobinsky: 1 p g L = 1 R 1 (1 @ 1 6 ) m 1 R 1 @' 3 m tanh ' p 6 0.05 0.00 = 5 = 10 0.95 0.96 0.97 0.98 0.99 1.00 preditions: n s ' 1 N, r ' 1 N n s
metric on hyperboloid with radius of Poincare s disk: ds = dx + dy, 1 x +y 3 R = p 3... this should inspire your future work about the early universe...