Antonino Marcian Fudan University Matter-Bounce !Spin !Cosmology - PowerPoint PPT Presentation

Antonino Marcianò Fudan University Matter-Bounce !Spin !Cosmology & ! consistency !with !cosmological !data ! based !on S. Alexander, C. Bambi, A. Marciano & L. Modesto arXiv:1402.5880 S. Alexander, Y. Cai & A. Marciano arXiv:1406.1456 FFP14 Marseille, July the 17th 1/18 mercoledì 16 luglio 14

Standard Big-Bang Cosmology i) Universe’s expansion and Hubble’s law ii) Black-body spectrum CMB radiation iii) BBN and primordial elements G µ ν = 8 π G c 4 T µ ν Einstein equations FFP14 Marseille, July the 17th 2/18 mercoledì 16 luglio 14

Problems of SBB Cosmology i) Horizon problem ii) Flatness problem iii) Size/entropy problem Inflation FFP14 Marseille, July the 17th 3/18 mercoledì 16 luglio 14

Inflation i) Horizon problem % ' % φ ' const ! a ( t ) = e Ht ii) Flatness problem % K / % rad ∼ a ( t ) 2 % K / % φ = 1 /a ( t ) 2 iii) Size/entropy problem Universe empty , then δφ a 2 a 2 ≡ H 2 = 8 ⇡ G ˙ ds 2 = dt 2 − a 2 ( t )[ dx 2 + dy 2 + dz 2 ] % = % φ + % rad + % matt . + % K 3 c 4 % with a bonus! Causal mechanism for generating primordial cosmological (Chibisov & Mukhanov 1981) perturbations originate as quantum vacuum fluctuations! FFP14 Marseille, July the 17th 4/18 mercoledì 16 luglio 14

Cosmological perturbations/structure formations Cosmological fluctuations links early Universe theories to observations Fluctuations of matter − → large − scale structure G µ ν = 8 π G c 4 T µ ν Fluctuations of metric − → CMB anisotropies Matter and metric fluctuations coupled though the Einstein equations! Fluctuations are small today, and were small in the early Universe: linear perturbations FFP14 Marseille, July the 17th 5/18 mercoledì 16 luglio 14

Structure formation at work: heuristics ds 2 = dt 2 − a 2 ( t )[ dx 2 + dy 2 + dz 2 ] d 2 � ~ dt + k 2 dt 2 + 3 H d � ~ k ( t ) e ı ~ k · ~ x , k k � ( t, ~ x ) = � ~ k = 0 a 2 � ~ a k ⌧ 1 harmonic oscillator behavior H a k � 1 overdamped oscillator H FFP14 Marseille, July the 17th 6/18 mercoledì 16 luglio 14

Structure formation and flat power-spectrum ds 2 = a 2 ( ⌘ )[(1 + 2 ' ( ⌘ , ~ x )) d ⌘ 2 − (1 − 2 ( ⌘ , ~ x 2 ] x )) d ~ � ( ⌘ , ~ x ) = � 0 ( ⌘ ) + �� ( ⌘ , ~ x ) 16 π GR + 1 1 Z d 4 x √− g [ − S = 2 ∂ µ φ∂ µ φ − V ( φ )] S (2) = 1 d 4 x [ v 0 2 − v ,i v ,i + z 00 Z z v 2 ] 2 v = a ( η )[ δφ + φ 0 0 H ϕ ] z = a φ 0 0 / H Scale Invariance! P R ( k, t ) ' H 2 Curvature fluctuations variable v = z R FFP14 Marseille, July the 17th 7/18 mercoledì 16 luglio 14

Inflation and Matter-Bounce Cosmology Deficiencies of Inflation Cosmological singularity: not a theory of very early Universe High level of arbitrariness in the mechanism involving scalar field Trans − Planckian problem for cosmological perturbations Criteria to bear in mind Horizon � Hubble radius Fluctuations mode have λ � H − 1 for a long period (squeezing) Mechanism accounting for scale − invariant primordial spectrum FFP14 Marseille, July the 17th 8/18 mercoledì 16 luglio 14

Fermionic Matter-Bounce Are Einstein equations rusting? Fermioinc matter may violate the null energy conditions! Armendariz-Picon, Alexander, Biswas, Brandenberger, Magueijo, Kibble, Poplawski... 4 H 2 =  3 % tot = 0 3 H − H 2 = ¨ a 2 a a = −  ˙ 6 ( % tot + 3 p tot ) > 0 1 At the bounce 0 � 4 � 2 0 2 4 t BCS condensation or torsion may provide four fermion contribution to the energy density % tot ' m + ⇠ FFP14 Marseille, July the 17th 9/18 mercoledì 16 luglio 14

Fermi-Bounce Spin Cosmology: one field S. Alexander, C. Bambi, A. Marciano & L. Modesto, arXiv:1402.5880 S Holst = 1 Z d 4 x | e | e µ J P IJ KL KL = � [ I K � J ] P IJ L − ✏ IJ ( ω ) I e ν KL F KL / (2 � ) µ ν 2 κ M Z n 1 1 � ı h ⇣ ⌘ i o ψγ I e µ d 4 x | e | S Dirac = αγ 5 ı r µ ψ � m ψψ + h . c . I 2 M Theory with torsion! [Alexander, Biswas, Magueijo, Kibble, Poplawski...] FFP14 Marseille, July the 17th 10/18 mercoledì 16 luglio 14

One fermion species: integrating out torsion S. Alexander, C. Bambi, A. Marciano & L. Modesto, arXiv:1402.5880 Theory with torsion I C µJK =  � e µ J L = ψγ L γ 5 ψ � � ✏ IJKL J L − 2 ✓ ⌘ I [ J J K ] � � 2 + 1 4 S GR = 1 Z d 4 x | e | e µ J R IJ I e ν µ ν 2 κ M Z ⇣ ⌘ S Dirac = 1 ψγ I e µ I ı e d 4 x | e | r µ ψ � m ψψ + h . c . 2 M Z d 4 x | e | J L J M η LM S Int = − ξκ M FFP14 Marseille, July the 17th 11/18 mercoledì 16 luglio 14

Parameter space of the theory S. Alexander, C. Bambi, A. Marciano & L. Modesto, arXiv:1402.5880 γ 2 ✓ ◆ ξ = 3 1 + 2 αγ − 1 γ 2 + 1 α 2 16 FFP14 Marseille, July the 17th 12/18 mercoledì 16 luglio 14

Bounce & scale-invariant power-spectrum S. Alexander, C. Bambi, A. Marciano & L. Modesto, arXiv:1402.5880 Fermionic bounce a 6 + κ | ˜ H 2 = ξ κ 2 n 2 E | 2 6 a ( t ) 4 + m κ n 0 0 } 3 3 a 3 ◆ 1 ✓ 3 m κ n 0 ( t − t 0 ) 2 − ξ κ n 0 3 a = ! 4 a 3 + κ | ˜ m a ( t ) 4 +4 ξκ 2 n 2 E | 2 H − H 2 = ¨ a = − 1 a m κ n 0 ˙ 0 a 6 6 Adiabatic scalar perturbations f ( t ) ' (1 � ξκψψ /m ) δρ ζ = ζ = f ( t )( δψψ + ψδψ ) ρ + p ψψ P ( k ) ' mH 2 Scale-invariance E P ( k ) ' m k 3 | Γ ( | ν | ) | 2 | k η | − | ν | − 1 32 n 0 16 n 0 | ξ | = 3 η E = 2 / ( a E H E ) = 2 /H E ν 2 = 1 − 8 ξ 8 FFP14 Marseille, July the 17th 13/18 mercoledì 16 luglio 14

Fermi-Bounce Spin Cosmology: two fields Y. Cai & A. Marciano, arXiv:1406.1456 S. Alexander, Anisotropies and necessity of two fields ρ A ⇠ Tr( γ i γ j ) ψψ h δ ¯ ¯ m � 4 P ζ n 0 /M 2 ψδψ i M 2 p p New theory involving two fermionc species is needed ⇣ ⌘ L ψ = 1 I ı e ψγ I e µ + h . c . � ξκ J L ψ J K heavy background field r µ ψ � m ψ ψψ ψ η LK 2 ⇣ ⌘ L χ = 1 χγ I e µ I ı e + h . c . � ξκ J L χ J K light field for perturbations r µ χ � m χ χχ χ η LK 2 m ψ n ψ � m χ n χ m ψ > >m χ ! 1 ξκ ( n 2 ψ + n 2 3 χ ) x ) i = m 2 3 κ m ψ n ψ ζ ' m χ ( δχ χ + χ δχ ) �� h ���� i χ ( t − t 0 ) 2 − a = P S = h ⇣ ( t, ~ x ) ⇣ ( t, ~ 4 m 2 m ψ n ψ 4( ) 2 m ψ ψψ ψ FFP14 Marseille, July the 17th 14/18 mercoledì 16 luglio 14

Scale-invariant scalar perturbations Y. Cai & A. Marciano, arXiv:1406.1456 S. Alexander, Power-spectrum for the curvature perturbations P S = m 3 k 2 χ n χ 4(1+ γ −√ 1+4 γ ) n S � 1 ⌘ d ln P S d ln k ' � 2 γ = − 2 ξ n χ m χ 4 π 2 a 2 ( k η ) 3 −√ 1+4 γ 3( γ � 2) m 2 ψ n 2 n ψ m ψ ψ scale-invariance γ = 2 ( i . e . ξ = − n ψ m ψ /n χ m χ ) P S = m 3 4 π 2 a 2 η 2 = m 3 H 2 χ n χ χ n χ 1 E m 2 ψ n 2 m 2 ψ n 2 16 π 2 ψ ψ FFP14 Marseille, July the 17th 15/18 mercoledì 16 luglio 14

Primordial g-waves and see-saw mechanism Y. Cai & A. Marciano, arXiv:1406.1456 S. Alexander, Tensor perturbations Scalar perturbations m 2 H 2 P S = m 3 4 π 2 a 2 η 2 = m 3 P T = 1 = 1 H 2 χ n χ χ n χ 1 ψ E E a 2 ϑ 2 E M 2 ϑ 2 | ξ | M 2 m 2 ψ n 2 m 2 ψ n 2 16 π 2 p p ψ ψ m 2 n 2 r = 16 π 2 ψ ψ ϑ 2 m 3 n χ M 2 χ p ' 10 7 m 3 ψ . 10 − 11 | ξ | M 2 n ψ χ m 2 compatible with p | ξ | = ( n ψ m ψ ) / ( n χ m χ ) n χ n ψ m 2 n 2 m χ < 10 − 3 eV ψ ψ ∼ O (1) m ψ . 10 − 4 M p m 3 n χ M 2 χ p FFP14 Marseille, July the 17th 16/18 mercoledì 16 luglio 14

Conclusions i) Matter-Bounce realized with fermionic fields can account for CMBR physics ii) Inflation is not the only paradigm for early cosmology, and the eventual observation of primordial gravitational waves do not necessarily imply Inflation iii) Observations of primordial gravitational waves can be attained within a model that entails a cosmological see-saw mechanism FFP14 Marseille, July the 17th 17/18 mercoledì 16 luglio 14

Thank you! ... and thanks to: FFP14 Marseille, July the 17th 18/18 mercoledì 16 luglio 14

mercoledì 16 luglio 14

mercoledì 16 luglio 14

mercoledì 16 luglio 14

mercoledì 16 luglio 14

Standard Big-Bang Cosmology Universe’s expansion and Hubble’s law ds 2 = dt 2 − dl 2 v = H l H = ˙ a dl 2 = a ( t ) 2 [ dx 2 + dy 2 + dz 2 ] a mercoledì 16 luglio 14

Standard Big-Bang Cosmology Black-body spectrum CMB radiation λ max ∼ T − 1 T − 1 ∼ a ( t ) mercoledì 16 luglio 14

FFP14 Marseille, July the 17th mercoledì 16 luglio 14