Inflation with Superstrings? Grant Mathews Univ. Notre Dame - - PowerPoint PPT Presentation

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Grant Mathews – Univ. Notre Dame

Inflation with Superstrings?

Gravitation and Cosmology 2018 Yukawa Institute for Theoretical Physics

• Feb. 28, 2018

arXiv:1701.00577

It is natural that the universe is born

• ut of a landscape of superstrings

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Is there new trans-Plankian physics imprinted on the Cosmic Microwave Background?

New physics always shows up as small deviations

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WMAP 9yr

Some possible explanations for dip at l = 20

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• Cosmic Variance: Planck XX arXiv:1502.02114
• Modified inflation effective potential

– Harza, et al. arXiv:1405.2012, – Kitazawa and Sagnotti 1411.6396v2, – Yang and Ma arXiv:1501.00282

• ….
• ….
• Planck-mass particles coupled to inflation

– GJM, M. R. Gangopadhyay, K. Ichiki, and T. Kajino, Phys.

• Rev. D92, 123519 (2015). arXiv: 1504.06913

How does this work?

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• The total Lagrangian density is given as :

Ltot = 1 2∂µφ∂µφ − V (φ) + i ¯ ψγµψ − m ¯ ψψ + Nλφ ¯ ψψ

• Then the fermion has the effective mass :

M(φ) = m − Nλφ

• This vanishes for a critical value of the inflaton field,

φ∗ = m/Nλ

Ltot = 1 2@µ@µ − V () + i ¯ / @µ − m ¯ + N ¯

Classical and Quantum Gravity 31 053001 (2014). [35] D. J. H. Chung, E. W. Kolb, A. Riotto, and I. I. Tkachev,

• Phys. Rev. D 62, 043508 (2000).

[36] G. J. Mathews, D. Chung, K. Ichiki, T. Kajino, and M. Orito, Phys. Rev. D70, 083505 (2004).

Mathews et al. PRD (2015)

When φ = φ*, resonant particle production occurs

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h ¯ i = n⇤Θ(t t⇤) exp [3H⇤(t t⇤)]

n⇤ = 2 π2 Z 1 dkp k2

p |βk|2 = Nλ3/2

2π3 | ˙ φ⇤|3/2

|βk|2 = exp ✓ −πk2 a2

⇤Nλ| ˙

φ⇤| ◆ .

How does this affect inflation?

• Causes a jump in the evolution of the scalar

field

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˙ (t > t⇤) = ˙ ⇤ exp [3H(t t⇤)] V 0()⇤ 3H⇤ ⇥ 1 exp [3H(t t⇤)] ⇤ + Nn⇤(t t⇤) exp [3H⇤(t t⇤)]

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• In this case using the above equation for the fluctuation as it

exists the horizon the perturbation in the primordial power spectrum is : δH = [δH(a)]Nλ=0 1 + Θ(a − a∗)(Nλn∗/| ˙ φ∗|H∗)(a∗/a)3 ln (a/a∗) (6)

Causes Dip

Alters the primordial power spectrum δH(a) = H2 5π ˙ φ

Cl = π dk k

∞

∫

jl

2 2k

H0 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ δ H

2 (k)

2 new parameters in fit to CMB

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H(k) = [H(a)]Nλ=0 1 + Θ(k k⇤)A(k⇤/k)3 ln (k/k⇤)

⇤

g k⇤/k = a⇤/a,

k⇤ = `⇤ rlss

A = | ˙ φ∗|−1Nλn∗H−1

∗

multipole Amplitude

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l = 20 l = 2 1/k

500 1000 1500 2000 2500 3000 5 10 15 20 25 30 35 40 45 50 PLANCK best fit power law

MCMC fit to CMB Power Spectrum

Mathews et al. PRD (2015)

k* A

Amplitude, A, relates to the inflaton coupling λ and number N of degenerate Fermions

A = | ˙ φ∗|−1Nλn∗H−1

∗

A ∼ 1.3Nλ5/2

λ ≈ (1.0 ± 0.5) N 2/5

⇤

≈ Nλ5/2 2 √ 5π7/2 1 p δH(k⇤)|λ=0

COBE Normalization

k∗ relates to the fermion mass m for a given inflation model:

V (φ) = Λφm4

pl

✓ φ mpl ◆α

be deduced from e m ≈ φ⇤/λ3/2.

The fermi m = Nλφ⇤. For this pur

=>

m ⇠ (8 11) mpl 3/2

α = 2/3 => φ∗ = p 2αN∗mpl m = Nλ √ 2α p N − ln (k∗/kH)

Suppose this particle is a Superstring: How could you know?

• There should be similar resonant couplings

corresponding to different excitations of the same string.

• Could this be the l =2 suppression or more?

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Resonant Superstring Excitations during Inflation

• G. J. Mathews1,2, M. R.

Gangopadhyay1, K. Ichiki3, T. Kajino2,4,5

1Center for Astrophysics, Department of Physics,

arXiv:1701.00577

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10 20 30 40 50 60 70 l 500 1000 1500 2000 2500 l(l+1)Cl

TT/2

π 10 20 30 40 50 60 70 80 90 l

• 0.5

0.5 1 l(l+1)Cl

EE/2

π

TT EE

MCMC fit to multiple dips in the CMB power spectrum

Gangopadhyay, Mathews, Ichiki, Kajino arXiv:1701.00577

` ≈ 2, A = 1.7 ± 1.5, k⇤(n + 1) = 0.0004 ± 0.0003 h Mpc1 ` ≈ 20, A = 1.7 ± 1.5, k⇤(n) = 0.0015 ± 0.0005 h Mpc1

` ≈ 60, A = 1.7 ± 1.5, k∗(n − 1) = 0.005 ± 0.004 h Mpc−1

Do these states look like Excitation modes of a superstring?

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• 1. Momentum states in the compact dimension
• 2. Oscillations
• 3. Winding around the compact dimensions

A simple example: D=26 Bosonic closed string with 1 dimension compacted in a circle of radius R M 2 = n2 R2 + w2R2 α02 + 2 α0 (N + ˜ N + 2)

Momentum States Winding Potential Energy Oscillations

N = X (αµ

−nαnµ + α−nαn)

˜ N = X (−˜ αµ

−n˜

αnµ + ˜ α−n˜ αn) N − ˜ N + nw = 0

Special Cases:

• nly oscillations

Only momentum

• r winding states

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M2 ≈ ✓Nosc + ξ α0 ◆ , Case I. ξ ≡ α0 ✓ n R ◆2 .

M2 ≈ ✓n2 + ξ R2 ◆ , Case II. ξ = 2R2 α0 (N + ˜ N − 2)

Can fix the ratio of mass states

≈ M2(`⇤ = 2) M2(`⇤ = 20) ≡ R+1 ≈ N − ln (k⇤(n + 1)/kH) N − ln (k⇤(n)/kH)

M2(`⇤ = 20) M2(`⇤ = 60) ≡ R1 ≈ N − ln (k⇤(n)/kH) N − ln (k⇤(n − 1)/kH)

wer spectrum. That is, we infer from es: M2(`∗=2)

M2(`=20) ≡ R+1 = 1.024 ± 0.050.

M (

ain M2(`∗=20)

M2(`=60) ≡ R−1 = 1.024 ± 0.030.

• f how this might relate to string par

Case of simple oscillations

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R+1 = (Nosc + 1) Nosc Nosc = 1 R+1 − 1

=>

− ce Nosc = 42+∞

−28

ly, the uncertaint ≈ M2(`⇤ = 2) M2(`⇤ = 20) ≡ R+1 ≈ N − ln (k⇤(n + 1)/kH) N − ln (k⇤(n)/kH)

Physical properties of the Superstring

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⇡ (1.0 ± 0.5) N 2/5 .

m ⇠ (8 11) mpl 3/2

Coupling Constant is Small because N is large

− ce Nosc = 42+∞

−28

ly, the uncertaint

Very large Very uncertain

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Conclusions

• Marginal evidence of sequential dips in the CMB

power spectrum

• These could be caused by resonant coupling to

successive excitations of a superstring during inflation.

• The regular spacing and constant amplitude of the

dips is consistent with mass eigenstates corresponding to successive oscillations or momentum states of a single closed superstring.

• Uncertainties are too large to make definitive

conclusion