Inflation, Gravity Waves, and Dark Matter. Qaisar Shafi

Transcription

1 Inflation, Gravity Waves, and Dark Matter Qaisar Shafi Bartol Research Institute Department of Physics and Astronomy University of Delaware Feb 2015 University of Virginia Charlottesville, VA

2 Units ћ = c = k B = 1 M P = 1.2 x GeV (m P = 2.4 x GeV) l P = 1.6 x cm, t P = 5.4 x sec G = Newton s constant = M P -2 GeV -1 = cm = sec 1 MeV = K

3 ΛCDM Model (current paradigm) Λ stands for Dark Energy with Einstein s cosmological constant being the leading candidate ( P Λ = w Λ ρ Λ, with w Λ = -1 ) ρ Total = Λ ρ + ρ CDM + ρ M ρ c ρ Λ mp Fine tuning? CDM denotes cold dark matter (particle have tiny velocities) Where does ΛCDM come from? Image courtesy of NASA / WMAP Science Team

4 Four Fundamental Forces Force Strength Strong ~1 Electromagnetic ~10-2 Weak ~10-5 Gravity ~10-38 Standard Model of HE Physics General Relativity

5 STANDARD MODEL OF HE PHYSICS Provides excellent description of strong, weak and electromagnetic interactions. Based on local gauge symmetry SU (3) c SU (2) L U (1) Y QCD - strong interactions involving colored quarks & gluons Only color neutral states exist in nature Electromagnetic and weak interactions mediated by W ±, Z 0 bosons and γ, which have been found

6 proton neutron Color neutral atoms Two Key features: Color confinement; Asymptotic freedom;

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8 Higgs Boson Spin zero particle from spontaneous breaking of electroweak symmetry: SU(2) L U(1) Y φ U(1) EM φ 10 2 GeV(t sec) m h 125GeV (Huge discovery announced by ATLAS and CMS on July 4, 2012) Compare: Superconductor (Cooper pairs φ )

9 IS THERE NEW PHYSICS BEYOND THE STANDARD MODEL? Most Likely Yes! 1) Neutrino Oscillations (solar & atmospheric): These require non-zero (albeit tiny ) neutrino masses ~ ev. In the SM, neutrinos have zero mass. 2) Dark Matter (non-baryonic) SM has no plausible DM candidate

10 Oscillation Data sin 2 (2θ 12 ) = ± m 2 21 = (7.53 ± 0.18) 10 5 ev 2 sin 2 (2θ 23 ) = (normal mass hierarchy) sin 2 (2θ 23 ) = (inverted mass hierarchy) m 2 32 = (2.44 ± 0.06) 10 3 ev 2 (normal mass hierarchy) m 2 32 = (2.52 ± 0.07) 10 3 ev 2 (inverted mass hierarchy) sin 2 (2θ 13 ) = (9.3 ± 0.8) 10 2 Tiny masses (compared to quarks and charged leptons) Mixing angles large (compared to quark sector)

11 Dark Matter in The Universe Zwicky ( 1930) Galaxies in the Coma cluster seem to be moving too rapidly to be halo together by the gravitational attraction of the visible matter. Rotation curves of velocity versus radial distance for stars and gax provide indirect evidence for the existence of missing non-luminous mass. δρ/ρ 10 5 = structure formation (galaxies, clusters) hard without non-baryonic dark matter.

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13 Hot Big Bang Cosmology Comes from combining Standard Model (SM) of high energy physics with Einstein general relativity, and the assumption that on sufficiently large scales, the universe is isotropic and homogeneous. same in all directions position independent Three remarkable predictions (Consequences): 1. Expanding Universe 2. Cosmic Microwave Background Radiation (CMB) 3. Nucleosynthesis

14 Edwin Hubble H 0 = 67.8±0.9 (km/s)/mpc t 0 = 1/H 0 = ±0.038Gyr (Planck, arxiv: ) In natural units, H ev!

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16 A homogeneous and isotropic universe is described by the Robertson-Walker metric dr ds = dt + a ( t) + r ( dθ + sin θ dφ ), 2 1 k r where r, φ and θ are comoving polar coordinates, which remain fixed for objects that follow the general cosmological expansion. k is the scalar curvature of 3-space, with k = 0, +1, -1 describing a flat, closed and open universe respectively.

17 Geometry of the Universe Friedmann Equation ρ Ω = ρ c k + ( ah ) 1 2, where 3H 2 ρc = 8π G = critical density Closed ( Ω > 1 or k = 1) Open( Ω < 1 or k = -1) Flat( Ω = 1 or k = 0) Image courtesy of NASA:

18 Solving Friedmann Equations: For flat universe Matter ρ m NM = V ρ H 2 3 m a a& a 2 ρ a( t) t 2/3 Radiation ρ γ Nhc = V λ 4 ρ a γ a( t) t 1/ 2 Vacuum ( ρ Λ = const. ) 0 ρλ a a( t) e H t

19 Flatness Problem Cosmological Problems Present energy density of the universe is determined to be equal to its critical value corresponding to a flat universe. This means that in the early universe k 1 = ( ah ) Ω 2 Ω BBN t (for a radiation dominated universe) 55 ( Ω 1 10 ) GUT How does this come about?

20 Horizon Problem Image courtesy of W. Kinney Why the CMB is so uniform on large scales?

21 Origin of primordial density fluctuation which lead to Large Scale Structure and also explain δt/t ~ 10-5 observed by COBE/WMAP and other experiments? Origin of baryon asymmetry (n b /n γ ~ )?

22 Inflationary Cosmology [Guth, Linde, Albrecht & Steinhardt, Starobinsky, Mukhanov, Hawking,... ] Successful Primordial Inflation should: Explain flatness, isotropy; Provide origin of δt T ; Offer testable predictions for n s, r, dn s /d ln k; Recover Hot Big Bang Cosmology; Explain the observed baryon asymmetry; Offer plausible CDM candidate; Physics Beyond the SM?

23 Inflation can be defined as: Cosmic Inflation d 1 < 0, dt ah a& & > 0, a decreasing comoving horizon an accelerated expansion P < ρ / 3, a negative pressure repulsive gravity Consider a scalar field φ drives inflation ρφ 1 = & φ 2 +V ( φ ) V, 2 a( t) Slow rolling scalar field acts as an inflaton Ht e inflation

24 Cosmic Inflation Tiny patch ~10-28 cm > 1 cm after 60 e-foldings (time constant ~10-38 sec) Inflation over radiation dominated universe (hot big bang) Quantum fluctuations of inflation field give rise to nearly scale invariant, adiabatic, Gaussian density perturbations Seed for forming large scale structure

25 Log(LENGTH) H -1 N HOR = ln(r RH /R 1 ) N GAL = ln(r RH /R g ) H -1 ~ t ~ R 1/n λ HOR λ GAL (No Inflation) Inflation Standard Cosmology R 1 R g R RH R EQ R Today Log(R) Image courtesy of Kolb & Turner

26 k Solution to the Flatness Problem 1 = Ω 2 ( ah ) 2N Ω f 1 = Ωi 1 e 0, where N = H Δt 50 Solution to the Horizon Problem Image courtesy of W. Kinney

27 Slow-roll Inflation Inflation is driven by some potential V (φ): Slow-roll parameters: ɛ = m2 p 2 ( V V ) 2, ( ) η = m 2 V p V. The spectral index n s and the tensor to scalar ratio r are given by n s 1 d ln 2 R d ln k, r 2 h, 2 R where 2 h and 2 R are the spectra of primordial gravity waves and curvature perturbation respectively. Assuming slow-roll approximation (i.e. (ɛ, η ) 1), the spectral index n s and the tensor to scalar ratio r are given by n s 1 6ɛ + 2η, r 16ɛ.

28 Slow-roll Inflation The tensor to scalar ratio r can be related to the energy scale of inflation via V (φ 0 ) 1/4 = r 1/4 GeV. The amplitude of the curvature perturbation is given by ( 2 R = 1 V/m 4 ) p 24π 2 ɛ = (WMAP7 normalization). φ=φ 0 The spectrum of the tensor perturbation is given by ( ) 2 h = 2 V 3 π 2 m 4 P φ=φ 0. The number of e-folds after the comoving scale l 0 = 2 π/k 0 has crossed the horizon is given by N 0 = 1 φ0 ( V ) m 2 p φ e V dφ. Inflation ends when max[ɛ(φ e ), η(φ e ) ] = 1.

29 Scalar and Tensor Perturbations During inflation, the universe contains a uniform scalar (inflaton) field and a uniform background metric. There are quantum mechanical fluctuations about this zero-order scheme. According to inflationary cosmology, this generates δρ/ρ as well as gravity waves (from tensor fluctuations in the gravitational metric).

30 (1) V = m 2 φ 2 = δρ ρ m M P = m GeV (2) V = λφ 4 = δρ ρ λ = λ (tiny quartic coupling) Can Standard Model Higgs field drive inflation?

31 Angular scale Dl[µK 2 ] Planck (2013), arxiv: Multipole moment, l

32 CMB to Parameters Peak Locations First Peak Height Second Peak Height Overall Tilt Distance to LSS Matter/Radiation Density Ratio Baryon/Radiation Density Ratio Amplitude Ratio Of Large/Small Scale 3-D Geometry Dark Energy Age of the Universe Hubble Parameter Dark Matter Density Baryon Density Primordial Power Spectrum Optical Depth Image courtesy of E. Komatsu

33 Gravity Waves from Inflation Inflation also generates tensor fluctuations in the gravitation metric which correspond to gravity waves. They induce fluctuations in the CMB and provide a unique signature of inflation. Their discovery would have far reaching implications for inflationary cosmology. The PLANCK satellite now in orbit has an excellent chance to detect gravity waves if inflation is driven by a grand unified theory with a characteristic energy scale ~ GeV. (note LHC cm energy ~ 10 4 GeV!)

34 CMB Polarization CMB radiation is expected to be polarized from Compton scattering during (matter-radiation) decoupling. To produce polarized radiation the incoming radiation must have a non-zero quadrupole. One expects the polarization signal to be small.

35 Polarization is generated by both scalar and tensor perturbations. E modes (varies in strength in the same direction as its orientation) B modes (varies in strength in a direction different from that in which it is pointing)

36 BICEP 2 Result BICEP 2 a few months ago surprised many people with their results that r 0.2 (0.16). Some tension with the Planck upper bound r < Somewhat earlier WMAP 9 stated that r < 0.13.

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39 WMAP nine year data

40 Radiatively Corrected φ 2 Potential: n s vs. r for radiatively corrected φ 2 potential. The dashed portions are for κ < 0. The one loop radiative correction is larger than the tree level potential in the portions displayed in gray. N is taken as 50 (left curves) and 60 (right curves).

41 Standard Model Higgs Inflation? Update of RGE analysis 3- loop level) BuOazzo et al., JHEP 12 (2013) 089

42 Tree Level Gauge Singlet Higgs Inflation Consider the following Higgs Potential: V (φ) = V 0 [1 ( φ M ) 2 ] 2 (tree level) Here φ is a gauge singlet field. V Φ Belowvev BV inflation Above vev AV inflation WMAP/Planck data favors BV inflation M Φ

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44 Supersymmetry

45 A. Arbey, M. Battaglia, A. Djouadi, F. Mahmoudi and J. Quevillon, Phys. Lett. B 708, 162 (2012)

46 Supersymmetric Higgs (Hybrid) Inflation

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48 More complete analysis:

49 Dark Matter Candidates Candidates includes: WIMP(weakly interaction massive ( GeV) particle) Axions very light (~10-5 ev), very weakly interaction particle Wimpzilla very massive (10 12 GeV), perhaps not entirely stable, particle Gravitino kev mass partner of graviton; behaves as warm dark matter?

50 WIMP Candidates ( GeV in mass) Neutralino (neutral, spin ½, stable, light supersymmetric particle) Lightest neutral Kaluza Klein particle (E.g. KK excitation of some suitable known particle) Dark (mirror/hidden universe) baryons

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53 Indirect Search

54 The predictions of r (primordial gravity waves) for various inflation models: 1.Gauge Singlet Higgs Inflation: r 0.02 for n s SM Higgs Inflation: r ~ 0.003, n s ~ Non-Minimal ϕ 4 Inflation: r for n s Dark Matter Inflation: r MSSM Inflation: r ~ with 0.93 n s 1 6.Susy Higgs (Hybrid) Inflation: r 10-4 (minimal), r 0.03 (non-minimal) Planck (2015) says that r < 0.09

55 Summary Many Challenges: Dark Matter Supersymmetry Gravity Waves Neutrino Physics Proton Decay Dark Energy