Phase transition in the fine structure constant Danny Marfatia - - PowerPoint PPT Presentation

Phase transition in the fine structure constant

Danny Marfatia University of Kansas

with Anchordoqui, Barger and Goldberg (0711.4055)

Mass-varying neutrinos

ρDE ∼ 3M 2

PlH2 0 ∼ (2.4 × 10−3 eV)4

Coupling neutrinos to a light scalar may explain Fardon, Nelson, Weiner

ΩDE ∼ ΩM δm2 ∼ (10 × 10−3eV)2

Veff(mν) = mνnν + V (mν)

Text Minimize wrt mν

Nelson

Status (from low to high redshifts)

Measurements of transition frequencies in atomic clocks give the limit Abundance ratio of Sm-149 to Sm-147 at the Oklo natural reactor shows no variation in the last 1.7 Gyr: Meteoritic data (z < 0.5) constrain the beta-decay rate

• f Re-187 back to the time of solar system formation

(4.6 Gyr): Comparison of transition lines in QSO spectra (0.5 < z < 4) indicate ∆α/α = (−0.57 ± 0.10) × 10−5

|∆α/α| < 5 × 10−15

|∆α/α| < 10−7

∆α/α = (8 ± 8) × 10−7

Measurements of the CMB (z = 1100) accurately determine the temperature at decoupling which depends on the binding energy of hydrogen. Current constraint is Primordial abundances from BBN (z = 10 billion) depend critically on the neutron-proton mass difference which depends on alpha. Current limit:

|∆α/α| < 0.02 |∆α/α| < 0.02

V NR

eff

= mν(A) nν + V [M(A)] = m2

D

M(A) nν + V [M(A)] V REL

eff

= mν(A)2 nν Eν + V [M(A)] = m4

D

EνM(A)2 nν + V [M(A)]

Phase transition in alpha

dV NR

eff

dA =

• −m2

D nν

M 2 + V ′(M) dM dA = 0 dV REL

eff

dA =

• − 2m4

D nν

Eν M 3 + V ′(M) dM dA = 0 V′(M) ≡ ∂V (M)/∂M

Stationary points given by

M Mo j V ′(M) V ′(Mo) = nν ni

ν,c

j = 2, 3 if i = NR, REL nNR

ν,c ≡ M 2

• m2

D

V ′(Mo) , nREL

ν,c

≡ M 3

• 2 m4

D

V ′(Mo) M(A) ≃ Mo[1 + A2/f 2] in the vicinity of the min

Assumption I: M has a unique stationary point

Additional stationary points will exist if

nν > nν,c nν < nν,c

Assumption II: is an increasing fn of M

M 2V ′(M)

M Mo k = nν ni

ν,c

k = 1, 2 for i = NR, REL nNR

ν,c =

Λ4 mν,0 , nREL

ν,c

= Eν Λ4 2 m2

ν,0

≃ Tν Λ4 m2

ν,0

V [M(A)] = Λ4 ln(|M(A)/Mo|) mν,0 ≡ m2

D/Mo

Example

For nonrelativistic neutrinos with subcritical neutrino density, the only stationary point is A = 0 with M = Mo

= ⇒ mν = mν,0

No stability issues because neutrino mass is independent of neutrino density

For nonrelativistic neutrinos with supercritical neutrino density,

mν = Λ4/nν

1.8 Λ mν,0 1/3 < ∼ Tν Λ < ∼ 1.1 2.9

• Λ4

−3

mν,0/0.05 eV 1/3 < ∼ 1 + z < ∼ 6.5 Λ−3 Λ−3 ≡ Λ/(10−3 eV)

Window of instability

Acceleron mediates an attractive force between neutrinos which can form nuggets that behave like CDM

Afshordi, Zaldarriaga, Kohri

The instability is avoidable ...

β ≡

• d ln mν

dA

• =
• d ln M

dA

• <
• ΩCDM − Ων

2 Ων 1 MPl ≃ 10 MPl M = Mo eA2/f 2 = ⇒ β = 2|A| f 2 < 10 MPl

|A| f

<

• ln 12 (mν,0/0.05 eV)

Λ−3

< 1.7 for Λ−3 ≃ 0.6(mν,0/0.05 eV)1/4 = ⇒ f/MPl > 0.34 ... if growth-slowing effects (dragging) provided by CDM dominate over the acceleron-neutrino coupling Tν < 1.1Λ = ⇒

Bjaelde et al.

If

Lem = −1 4 ZF (A/MPl) FµνF µν = −1 4 (1 + κ A/MPl + . . .) FµνF µν κ ≡ ∂AZF |0

• ∆α

α

• = κ A

MPl = κ A f · f MPl

Discontinuity in alpha

Λ−3 ≃ 0.61(mν,0/0.05 eV)1/4 ρA ρDE ∼ 4 × 10−3 mν,0 0.05 eV

Accommodating null low redshift data

Requiring that the acceleron not vary from its ground state till z = 0.5, so that alpha does not vary, gives The energy density of the acceleron does not saturate the present dark energy Neutrinos are nonrelativistic with supercritical density for 0.5 < z < 4

M(A) Mo = 1 + z 1 + zc 3 = ⇒ |A| f =

• 3 ln

1 + z 1 + zc

• |A|/f ≃ 1.4

f/MPl ≥ 0.34

• ∆α

α

• >

∼ 0.5 κ

κ ∼ 10−5

Reproducing the signal in quasar spectra

For z = 2 , zc = 0.5 With

Need to explain the data

M Mo =

• 3ζ(3)

2π2 T 2

ν m2 ν,0

Λ4

• ∆α

α

• ≃ 3 κ f

MPl ,

• ∆α

α

• ≃ 5 κ f

MPl κ < 0.02 recombination κ < 0.01 BBN

Consistent with CMB and BBN data?

nν > nREL

ν,c

as soon as neutrinos become relativistic = ⇒ |A|/f ≃

• ln (10 z)

CMB BBN