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

Matter-Bounce !Spin !Cosmology & ! consistency !with !cosmological !data !

• S. Alexander, C. Bambi, A. Marciano & L. Modesto

arXiv:1402.5880

• S. Alexander,
• Y. Cai & A. Marciano

arXiv:1406.1456 based !on 1/18

Antonino Marcianò

Fudan University

FFP14 Marseille, July the 17th

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 Gµν = 8πG c4 Tµν

Einstein equations 2/18 FFP14 Marseille, July the 17th

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Problems of SBB Cosmology

i) Horizon problem ii) Flatness problem iii) Size/entropy problem Inflation

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Inflation

i) Horizon problem ii) Flatness problem iii) Size/entropy problem

˙ a2 a2 ≡ H2 = 8⇡G 3c4 %

% = %φ + %rad + %matt. + %K

ds2 = dt2 − a2(t)[dx2 + dy2 + dz2]

%K/%rad ∼ a(t)2

% ' %φ ' const ! a(t) = eHt

Universe empty, then δφ

with a bonus!

Causal mechanism for generating primordial cosmological (Chibisov & Mukhanov 1981) perturbations originate as quantum vacuum fluctuations!

%K/%φ = 1/a(t)2

4/18 FFP14 Marseille, July the 17th

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Cosmological perturbations/structure formations

Cosmological fluctuations links early Universe theories to observations

Fluctuations of metric − → CMB anisotropies Fluctuations of matter − → large−scale structure Gµν = 8πG c4 Tµν

Matter and metric fluctuations coupled though the Einstein equations! Fluctuations are small today, and were small in the early Universe: linear perturbations 5/18 FFP14 Marseille, July the 17th

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Structure formation at work: heuristics

a k ⌧ 1 H

a k 1 H

harmonic oscillator behavior

• verdamped oscillator

ds2 = dt2 − a2(t)[dx2 + dy2 + dz2]

(t, ~ x) = ~

k(t) eı~ k·~ x,

d2~

k

dt2 + 3H d~

k

dt + k2 a2 ~

k = 0

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Structure formation and flat power-spectrum

ds2 = a2(⌘)[(1 + 2'(⌘, ~ x))d⌘2 − (1 − 2 (⌘, ~ x))d~ x2]

(⌘, ~ x) = 0(⌘) + (⌘, ~ x) S = Z d4x√−g[− 1 16πGR + 1 2∂µφ∂µφ − V (φ)]

Scale Invariance! Curvature fluctuations variable

v = zR

PR(k, t) ' H2

v = a(η)[δφ + φ0 H ϕ]

S(2) = 1 2 Z d4x[v02 − v,i v,i + z00 z v2]

z = aφ0

0/H

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Inflation and Matter-Bounce Cosmology

Criteria to bear in mind

Horizon Hubble radius Fluctuations mode have λ H−1for a long period (squeezing) Mechanism accounting for scale−invariant primordial spectrum

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

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Fermionic Matter-Bounce

4 2 2 4 1 2 3 4

a t

At the bounce Fermioinc matter may violate the null energy conditions!

Armendariz-Picon, Alexander, Biswas, Brandenberger, Magueijo, Kibble, Poplawski...

BCS condensation or torsion may provide four fermion contribution to the energy density

%tot ' m + ⇠

H2 =  3 %tot = 0

˙ H − H2 = ¨ a a = − 6 (%tot + 3ptot) > 0

Are Einstein equations rusting?

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Fermi-Bounce Spin Cosmology: one field

• S. Alexander, C. Bambi, A. Marciano & L. Modesto, arXiv:1402.5880

SHolst = 1 2κ Z

M

d4x |e| eµ

I eν JP IJ KLF KL µν

(ω)

SDirac = Z

M

d4x |e| n1 2 h ψγIeµ

I

⇣ 1 ı αγ5 ⌘ ırµψ mψψ i + h.c.

• P IJ

KL = [I KJ] L − ✏IJ KL/(2)

10/18

Theory with torsion!

[Alexander, Biswas, Magueijo, Kibble, Poplawski...]

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One fermion species: integrating out torsion

• S. Alexander, C. Bambi, A. Marciano & L. Modesto, arXiv:1402.5880

Theory with torsion

eµ

I CµJK = 

4

• 2 + 1
• ✏IJKL JL − 2✓ ⌘I[J JK]
• JL = ψγLγ5ψ

SGR = 1 2κ Z

M

d4x|e|eµ

I eν JRIJ µν

SDirac = 1 2 Z

M

d4x|e| ⇣ ψγIeµ

I ıe

rµψ mψψ ⌘ + h.c. SInt =−ξκ Z

M

d4x|e| JL JM ηLM

11/18 FFP14 Marseille, July the 17th

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Parameter space of the theory

• S. Alexander, C. Bambi, A. Marciano & L. Modesto, arXiv:1402.5880

ξ = 3 16 γ2 γ2 + 1 ✓ 1 + 2 αγ − 1 α2 ◆

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H2 = ξ κ2 3 n2 a6 + κ | ˜ E|2 6 a(t)4 + m κ 3 n0 a3 ˙ H − H2 = ¨ a a = −1 6 mκ n0 a3 + κ | ˜ E|2 a(t)4 +4 ξκ2 n2 a6 !

Bounce & scale-invariant power-spectrum

• S. Alexander, C. Bambi, A. Marciano & L. Modesto, arXiv:1402.5880

}

a = ✓3mκn0 4 (t − t0)2 − ξ κn0 m ◆ 1

3

ζ = δρ ρ + p

ζ = f(t)(δψψ + ψδψ) f(t) ' (1 ξκψψ/m) ψψ

Fermionic bounce Adiabatic scalar perturbations Scale-invariance 13/18 P(k) ' m k3|Γ(|ν|)|2 16 n0 |kη|−|ν|−1 ν2 = 1 − 8ξ |ξ| = 3 8

P(k) ' mH2

E

32 n0

ηE = 2/(aEHE) = 2/HE

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Fermi-Bounce Spin Cosmology: two fields

• S. Alexander,
• Y. Cai & A. Marciano, arXiv:1406.1456

Anisotropies and necessity of two fields ρA ⇠ Tr(γiγj) M 2

p

¯ ψψhδ ¯ ψδψi

m 4Pζ n0/M 2

p

New theory involving two fermionc species is needed

Lψ = 1 2 ⇣ ψγIeµ

I ıe

rµψ mψψψ ⌘ + h.c. ξκ JL

ψ JK ψ ηLK

Lχ = 1 2 ⇣ χγIeµ

I ıe

rµχ mχχχ ⌘ + h.c. ξκ JL

χ JK χ ηLK

heavy background field light field for perturbations

mψnψ mχnχ mψ > >mχ

a= 3κmψnψ 4 (t − t0)2− ξκ (n2

ψ + n2 χ)

mψnψ ! 1

3

PS = h⇣(t, ~ x)⇣(t, ~ x)i = m2

χ

m2

ψ

hi 4( )2

ζ ' mχ (δχ χ + χ δχ) mψψψ

14/18 FFP14 Marseille, July the 17th

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Scale-invariant scalar perturbations

• S. Alexander,
• Y. Cai & A. Marciano, arXiv:1406.1456

PS = m3

χnχ

m2

ψn2 ψ

k2 4π2a2 (kη)

4(1+γ−√1+4γ) 3−√1+4γ

γ = −2ξnχmχ nψmψ nS 1 ⌘ d ln PS d ln k ' 2 3(γ 2)

Power-spectrum for the curvature perturbations

γ = 2 (i.e. ξ = −nψmψ/nχmχ)

scale-invariance

PS = m3

χnχ

m2

ψn2 ψ

1 4π2a2η2 = m3

χnχ

m2

ψn2 ψ

H2

E

16π2

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Primordial g-waves and see-saw mechanism

• S. Alexander,
• Y. Cai & A. Marciano, arXiv:1406.1456

Scalar perturbations Tensor perturbations

PS = m3

χnχ

m2

ψn2 ψ

1 4π2a2η2 = m3

χnχ

m2

ψn2 ψ

H2

E

16π2 PT = 1 ϑ2 H2

E

a2

EM 2 p

= 1 ϑ2 m2

ψ

|ξ|M 2

p

r = 16π2 ϑ2 m2

ψ

m3

χ

n2

ψ

nχM 2

p

m2

ψ . 10−11 |ξ| M 2 p

m2

ψ

m3

χ

n2

ψ

nχM 2

p

∼ O(1) nψ nχ ' 107 m3

χ

nψ

|ξ| = (nψmψ)/(nχmχ)

mψ . 10−4 Mp

mχ < 10−3eV compatible with 16/18 FFP14 Marseille, July the 17th

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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

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Thank you!

18/18

... and thanks to:

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Standard Big-Bang Cosmology

dl2 = a(t)2[dx2 + dy2 + dz2]

ds2 = dt2 − dl2

v = H l

H = ˙ a a

Universe’s expansion and Hubble’s law

mercoledì 16 luglio 14

Standard Big-Bang Cosmology

T −1 ∼ a(t)

λmax ∼ T −1

Black-body spectrum CMB radiation

mercoledì 16 luglio 14

FFP14 Marseille, July the 17th

mercoledì 16 luglio 14