review and work in progress (bbn) thomas dent … · thomas dent institut für theoretische physik...

Introduction Astrophysical spectra Oklo Atomic clocks Theoretical questions Cosmology

Varying “Constants” in Cosmology and Astrophysics and. . .Review and work in progress (BBN)

Thomas Dent

Institut für Theoretische PhysikUniversity of Heidelberg

Bielefeld Kosmologietag, May 2005

Introduction

Astrophysical measurements from spectral linesAlphamu ≡ mp/me

Other quantities

Atomic clocks

Theoretical questionsRelations between alpha, mu, . . .Spacetime dependence and WEP violation

CosmologyCMBBBN

Main references:

1. J.-P. Uzan, Rev.Mod.Phys. 75 (2003) 403 [hep-ph/0205340], also astro-ph/0409424

2. Springer Lecture Notes 648 (2004) “Astrophysics, Clocks and Fundamental Constants”,ed. Karshenboim and Peik (see astro-ph/0310318)

3. K.A. Bronnikov and S.A. Kononogov, gr-qc/0604002

4. C.M. Müller, G. Schäfer and C. Wetterich, “Nucleosynthesis and the variation of fundamentalcouplings”, astro-ph/0405373

Introduction

Other quantities

Atomic clocks

CosmologyCMBBBN

Main references:

Introduction

Other quantities

Atomic clocks

CosmologyCMBBBN

Main references:

Introduction

Other quantities

Atomic clocks

CosmologyCMBBBN

Main references:

Introduction

Other quantities

Atomic clocks

CosmologyCMBBBN

Main references:

Introduction

Other quantities

Atomic clocks

CosmologyCMBBBN

Main references:

Introduction

Other quantities

Atomic clocks

CosmologyCMBBBN

Main references:

MotivationNew physics can arise from examining basic assumptions of existing theory . . .

• Space and time a fixed background (Newton)⇒ dynamical spacetime (Einstein)

• Vacuum is inert and empty space ⇒ Vacuum fluctuates (QFT) and has quantumnumbers (Higgs mechanism) and dynamical condensates (QCD)

• Vacuum gravitates (Λ)?• . . . evolves over time – “cosmon”, quintessence?

Measuring different fundamental constants at different points in spacetime breaksEinstein equivalence principle (Local Position Invariance)

Doing physics with “varying constants”:

1. Look for signals and set limits

2. Look for related effects (WEP violation)

3. A nonzero signal can rule out unified theories, test models of quintessence. . .

Prelude: atomic and molecular transitionsRelative measurements of different transitions provide direct and accuratemeasurements of dimensionless constants

Transition Energy scaling

Gross structure Ry

Atomic Fine structure α2 Ry

Hyperfine structure α2(µ/µB) Ry

Electronic structure Ry

Molecular Vibrational structure (me/mp)1/2 Ry

Rotational structure (me/mp) Ry

Relativistic corrections Function of α2

(from Karshenboim & Peik 2004)

? α2Ry and smaller scales accessible to optical/IR spectroscopy

? Vibro/rotational structure may be accessible depending on redshift

Alpha: measurement methods

absorption system, z = z_abs

ωz = ω0 + qh` αz

´2 − 1i

“Many-multiplet” method: different species with different q coefficients enhancesensitivity (Murphy et al., astro-ph/0209488)

Most recent result, 143 systems (astro-ph/0310318)

∆αα

= (−0.57± 0.11) · 10−5, 0.2 < zabs < 4.2

More spectra still being analyzed. . .

ωz = ω0 + qh` αz

´2 − 1i

∆αα

= (−0.57± 0.11) · 10−5, 0.2 < zabs < 4.2

ωz = ω0 + qh` αz

´2 − 1i

∆αα

= (−0.57± 0.11) · 10−5, 0.2 < zabs < 4.2

Other results on alpha

α= (0.15± 0.43) · 10−5, 1.6 ≤ z ≤ 2.9 Chand et al. 2004

α= (0.4± 1.5) · 10−6, zabs = 1.84, 1.15 Levshakov et al. 2004

Levshakov et al. astro-ph/0511765) claim errors below 10−6 for single absorptionsystems – but throw away 2 measurements out of 36 (> 3σ difference)

Absorption systems are complicated, fitting & analysis methods still under debate.

Emission lines also proposed:

α= (0.7± 1.4) · 10−4, 0.16 < z < 0.80 O III doublet, Bahcall et al. 2003

“Many-multiplet” emission line method may extend sensitivity to 10−5···−6

(astro-ph/0504027)

α= (0.15± 0.43) · 10−5, 1.6 ≤ z ≤ 2.9 Chand et al. 2004

(astro-ph/0504027)

α= (0.15± 0.43) · 10−5, 1.6 ≤ z ≤ 2.9 Chand et al. 2004

(astro-ph/0504027)

A new mu?

µ ≡ mp

Method uses vibro-rotational transitions of molecular hydrogen H2 (Lyman/Wernerbands) with different dependences on the reduced mass (Varshalovich 1993, 1995)

2002 :δµ

µ= (5.0± 1.8) · 10−5, zabs = 3.02 Ivanchik et al.

2005 :δµ

µ= (3.05± 0.75) · 10−5 (A), (1.65± 0.74) · 10−5 (B) Ivanchik et al.

where (A) and (B) are two different sets of laboratory wavelengths. Difficult to measurewavelengths in the extreme UV. . .

With new lab measurements:

µ= (2.4± 0.6) · 10−5, zabs = 3.02, 2.59 Reinhold et al., PRL 2006

A new mu?

µ ≡ mp

2002 :δµ

2005 :δµ

A new mu?

µ ≡ mp

2002 :δµ

2005 :δµ

Other dimensionless constants? y ≡ α2gp

(µp = gpe/4mp)Probe by comparing 21cm H I line and molecular rotation

y= (−0.20± 0.44) · 10−5 (z = 0.247), (−0.16± 0.54) · 10−5 (z = 0.685)

Murphy et al. 2001

? x ≡ α2gpµ−1

Compare UV heavy element transitions with H I line

x= (1.17± 1.01) · 10−5, 0.24 ≤ zabs ≤ 2.04

Tzanavaris et al. 2005

If slow cosmological evolution of α and µ is assumed, this is consistent withnegative ∆ ln α and positive ∆ ln µ. . .

Other dimensionless constants? y ≡ α2gp

(µp = gpe/4mp)Probe by comparing 21cm H I line and molecular rotation

y= (−0.20± 0.44) · 10−5 (z = 0.247), (−0.16± 0.54) · 10−5 (z = 0.685)

Murphy et al. 2001

? x ≡ α2gpµ−1

Compare UV heavy element transitions with H I line

x= (1.17± 1.01) · 10−5, 0.24 ≤ zabs ≤ 2.04

Tzanavaris et al. 2005

If slow cosmological evolution of α and µ is assumed, this is consistent withnegative ∆ ln α and positive ∆ ln µ. . .

Oklo natural nuclear reactor2 billion years ago (z = 0.1–0.15) naturally enriched uranium in a rock formation with awater moderator. . .Resulting isotopic ratios in rock samples differ radically from any other terrestrialmaterial

ExampleSamarium: consider ratio 149Sm/147Sm, normally 0.9measured to be about 0.02 in OkloResonant neutron capture

149Sm + n → 150Sm + γ

Today Er,0 = 97.3 meV with a width of ' 60 meV

Resonance energy arises from 〈Hc + Hn〉 where Hc ∝ α

dα〈Hc〉 ' 1 MeV

Need to know neutron fluence and spectrum: estimate from other isotopes e.g.

143Nd(n, γ)144Nd

cross-section has no sharp resonances and depends weakly on α

149Sm + n → 150Sm + γ

dα〈Hc〉 ' 1 MeV

143Nd(n, γ)144Nd

149Sm + n → 150Sm + γ

dα〈Hc〉 ' 1 MeV

143Nd(n, γ)144Nd

Oklo bound

-200 -100 0 100 200

TC =450 K TC =1000 K

D Er , meV

Most recent bound

−5.6× 10−8 < ∆α/α < 6× 10−8, α̇/α ≤ 3.5× 10−17 y−1

Petrov et al. hep-ph/0506186, see also Damour & Dyson 1996

Atomic clocksAbsolute frequency standard (definition of the second) is 133Cs ground state hyperfinetransitionMeasure some other transition in the lab over years ⇒bound on fundamental “constant” variations (up to variation of µCs)

Example

• Atomic hydrogen 1S-2S transition νH ∝ Ry• Mercury electric quadrupole transition νHg ∝ Ryα−3.2

• Cesium hyperfine transition νCs ∝ Ryα2 µCsµB

Eliminate µCs to obtain α̇/α = (−0.9± 2.9) · 10−15 y−1 Fischer et al. PRL 2004

Peik et al. (PRL 2004) use single Y b+ ion to obtain limit

α̇/α < 2.0× 10−15 y−1 (1σ)

Example

α̇/α < 2.0× 10−15 y−1 (1σ)

Example

α̇/α < 2.0× 10−15 y−1 (1σ)

Unification relations between alpha, mu, . . .Unified theories ought to predict low-energy parameters

α, sin2 θW , ΛQCD, ml, mq , GF . . .

⇒ functional relations between α, µ,. . .Calmet & Fritszch, Langacker et al., TD & Fairbairn 2001

Example (Simple GUT with varying coupling)Fundamental scale MU , GUT coupling αU

α' 0.5

M∝ e−2π/9α3(M)

“ mcmbmt

”2/27× · · ·

to lowest order:∆ ln

M' 17∆ ln αU

Define R ≡ ∆ ln µ/∆ ln α

⇒ R ' 34??

Unification relations between alpha, mu, . . .Unified theories ought to predict low-energy parameters

α, sin2 θW , ΛQCD, ml, mq , GF . . .

⇒ functional relations between α, µ,. . .Calmet & Fritszch, Langacker et al., TD & Fairbairn 2001

Example (Simple GUT with varying coupling)Fundamental scale MU , GUT coupling αU

α' 0.5

M∝ e−2π/9α3(M)

“ mcmbmt

”2/27× · · ·

to lowest order:∆ ln

M' 17∆ ln αU

Define R ≡ ∆ ln µ/∆ ln α

⇒ R ' 34??

Mass generation and thresholdsWhat about mass generation: how is the hierarchy explained?

〈φ〉MU

Both technicolor and hidden sector SUSY-breaking use dynamical scale

〈φ〉MU

= exp(2π/bhαh(MU ))× polynomial

if αh varies with αU then

∆ ln〈φ〉MU

' 34∆ ln αU ' 68∆ ln α

• Variation of me

• Threshold effects in running of α3 and αem

• Light quark mass contributions to mp not negligible• Superpartner thresholds m̃ important in SUSY-GUT TD, 2003

For SUSY-GUT with varying m̃: R = 4± 5

Dependence of nuclear magnetic moments µN on quark masses (Flambaum 2003, 2006):significant theoretical uncertainty remains, simple “valence model” invalid

〈φ〉MU

∆ ln〈φ〉MU

' 34∆ ln αU ' 68∆ ln α

• Variation of me

〈φ〉MU

∆ ln〈φ〉MU

' 34∆ ln αU ' 68∆ ln α

• Variation of me

Spacetime dependence of variationsExplicit violation of Poincaré invariance (LPI) difficult to understandReplace by “spontaneous” violation: cosmologically varying scalar “Cosmon” ϕ(x, t)Dimensionless “constants” are functions of ϕ

General theoretical framework: introduce actionZd4xL(gµν , ϕ, matter)

try to solve for ϕ(x, t)

Questions:

• Does variation of ϕ inside virialized systems track cosmological evolution?(Yes! Wetterich 2002, Shaw & Barrow 2005)

• Does the value of ϕ differ in different environments?(Yes – but not much!)

• Does ϕ(t) vary monotonically or oscillate? (Fujii 2003)

• What drives the variation? (potential V (ϕ), coupling to matter, . . . )

• What is the mass of the field?

• Does the field have other effects?

Questions:

WEPLight scalar coupled to electromagnetic energy mediates composition-dependent force

L = mN (ϕ)N̄N + · · · , mp,n = mN,QCD + Bp,n(α0 + λϕ)

For a given model, find ϕ force between Earth and 1 proton or neutron

Proton fraction fp is 0.456 for Cu, 0.385 for U ⇒ differential acceleration

η ≡ 2|a1 − a2||a1 + a2|

∝λ2

(∆fnBn + ∆fpBp)

Current limit η ≤ 10−13, Eöt-Wash expt.

If ∆ϕ sources ∆α then λ > 10−7 ⇒

STEP will see a signal (η ≥ 10−18) (Dvali & Zaldarriaga 2001)

This is a very conservative estimate: in more general models ϕ couples to QCD also⇒ Earth’s φ field may be 2 orders of magnitude larger (Wetterich 2002)

. . . MICROSCOPE η ≥ 10−15?

η ≡ 2|a1 − a2||a1 + a2|

∝λ2

(∆fnBn + ∆fpBp)

η ≡ 2|a1 − a2||a1 + a2|

∝λ2

(∆fnBn + ∆fpBp)

Cosmology: CMBα affects CMB through Thomson scattering, recombination history

0.95 <αCMB

α0< 1.02 (1σ), z ∼ 103 (Martins et al. 2004)

Relatively weak bound, degenerate with variations in other cosmological parameters. . .

Cosmology: CMBα affects CMB through Thomson scattering, recombination history

0.95 <αCMB

α0< 1.02 (1σ), z ∼ 103 (Martins et al. 2004)

Relatively weak bound, degenerate with variations in other cosmological parameters. . .

Cosmology: BBN (z ∼ 1010)1. Simple treatment: All neutrons end up in 4He, use helium abundance Yp

Yp = 2(n/p)f e−tN /τ

1 + (n/p)f e−tN /τ

• (n/p)f = e−Q/Tf : freezeout of weak interactions, compare Γ(n ↔ p) with H• tN : “nucleosynthesis time”, compare T with deuterium binding energy Bd

• τ : neutron lifetime

Already depends on every fundamental force (weak, strong, electromagnetic,gravitational)

2. More sophisticated semi-analytic treatment (Müller, Schäfer, Wetterich 2004)

ci∆Xi

for 6 “fundamental parameters” Xi

parameter Xi MP α 〈φ〉 me mq ∆m

ci -0.81 1.9 3.4 0.39 -1.59 -5.36

mq ≡ (md + mu)/2, ∆m ≡ md −mu, ΛQCD is constant unit of energy

Cosmology: BBN (z ∼ 1010)1. Simple treatment: All neutrons end up in 4He, use helium abundance Yp

Yp = 2(n/p)f e−tN /τ

1 + (n/p)f e−tN /τ

• (n/p)f = e−Q/Tf : freezeout of weak interactions, compare Γ(n ↔ p) with H• tN : “nucleosynthesis time”, compare T with deuterium binding energy Bd

• τ : neutron lifetime

Already depends on every fundamental force (weak, strong, electromagnetic,gravitational)

2. More sophisticated semi-analytic treatment (Müller, Schäfer, Wetterich 2004)

ci∆Xi

for 6 “fundamental parameters” Xi

parameter Xi MP α 〈φ〉 me mq ∆m

ci -0.81 1.9 3.4 0.39 -1.59 -5.36

mq ≡ (md + mu)/2, ∆m ≡ md −mu, ΛQCD is constant unit of energy

BBN: current project3. Selected previous work:• Variation of other abundances (4He, 7Li, D) under α, with numerical code

Bergström et al. 1999, Nollett & Lopez 2002 ⇒ bounds at 2–3% level• Variation of all light elements (4He, 3Li, 7Li, 6Li, D) under α and 〈φ〉, semi-analytic

approach:Landau et al. 2004, Chamoun et al. 2005 ⇒ similar bounds

Ideally: run numerical code incorporating dependence on all fundamental parameters(with S. Stern, C. Wetterich)

Dependence of Bd and nuclear reaction rates on mq is a complex and (in general)unsolved problem!Nuclear theory could tell us something at low energies: chiral EFT, pionless EFTChen & Savage 1999, current work of Chen & collaborators on np → dγ

Warning: current astrophysical data appear in conflict – risk to misinterpretobservational problems as varying constants. . . (Steigman review 2005)

SummaryMany methods exist to investigate EEP and constancy of fundamental “constants”:

• Astrophysical spectra

• Nuclear reactions and decays

• Atomic clocks

• Cosmology

• WEP violation

Unlikely source of new physics, but huge implications of any positive result

BBN bounds are currently incomplete, require more theoretical work. . .and better observations!

• Atomic clocks

• Cosmology

• WEP violation

• Atomic clocks

• Cosmology

• WEP violation

review and work in progress (bbn) thomas dent … · thomas dent institut für theoretische physik...

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