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 0 ∼ (2 . 4 × 10 − 3 eV) 4 ρ DE ∼ 3 M 2 Pl H 2 δ m 2 ∼ (10 × 10 − 3 eV) 2 Coupling neutrinos to a light scalar may explain Fardon, Nelson, Weiner Ω DE ∼ Ω M

Minimize wrt m ν V e ff ( m ν ) = m ν n ν + V ( m ν ) Text Nelson

Status (from low to high redshifts) Measurements of transition frequencies in atomic clocks give the limit | ∆ α / α | < 5 × 10 − 15 Abundance ratio of Sm-149 to Sm-147 at the Oklo natural reactor shows no variation in the last 1.7 Gyr: | ∆ α / α | < 10 − 7 Meteoritic data (z < 0.5) constrain the beta-decay rate of Re-187 back to the time of solar system formation (4.6 Gyr): ∆ α / α = (8 ± 8) × 10 − 7 Comparison of transition lines in QSO spectra (0.5 < z < 4) indicate ∆ α / α = ( − 0 . 57 ± 0 . 10) × 10 − 5

Measurements of the CMB (z = 1100) accurately determine the temperature at decoupling which depends on the binding energy of hydrogen. Current constraint is | ∆ α / α | < 0 . 02 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

Phase transition in alpha V NR = m ν ( A ) n ν + V [ M ( A )] e ff m 2 D = M ( A ) n ν + V [ M ( A )] n ν V REL m ν ( A ) 2 = � E ν � + V [ M ( A )] e ff m 4 D = � E ν � M ( A ) 2 n ν + V [ M ( A )]

Stationary points given by � dM dV NR − m 2 � D n ν e ff + V ′ ( M ) = = 0 M 2 d A d A � dM dV REL − 2 m 4 � D n ν e ff � E ν � M 3 + V ′ ( M ) = = 0 d A d A V ′ ( M ) ≡ ∂ V ( M ) / ∂ M

Assumption I: M has a unique stationary point M ( A ) ≃ M o [1 + A 2 /f 2 ] in the vicinity of the min Additional stationary points will exist if � M � j V ′ ( M ) V ′ ( M o ) = n ν j = 2 , 3 if i = NR , REL n i M o ν , c ν , c ≡ M 2 M 3 n NR o n REL o V ′ ( M o ) , V ′ ( M o ) ≡ ν , c m 2 2 m 4 D D

Assumption II: is an increasing fn of M M 2 V ′ ( M ) n ν > n ν ,c n ν < n ν ,c

Example V [ M ( A )] = Λ 4 ln( | M ( A ) /M o | ) � M � k = n ν k = 1 , 2 for i = NR , REL n i M o ν , c Λ 4 = � E ν � Λ 4 ≃ T ν Λ 4 n NR n REL , ν , c = ν , c 2 m 2 m 2 m ν , 0 ν , 0 ν , 0 m ν , 0 ≡ m 2 D /M o

For nonrelativistic neutrinos with subcritical neutrino density, the only stationary point is A = 0 with M = M o ⇒ m ν = m ν , 0 = No stability issues because neutrino mass is independent of neutrino density For nonrelativistic neutrinos with supercritical neutrino density, m ν = Λ 4 /n ν

Window of instability Acceleron mediates an attractive force between neutrinos which can form nuggets that behave like CDM Afshordi, Zaldarriaga, Kohri � Λ � 1 / 3 T ν < < 1 . 8 ∼ 1 . 1 ∼ Λ m ν , 0 � 1 / 3 Λ 4 � − 3 < ∼ 1 + z < 2 . 9 ∼ 6 . 5 Λ − 3 m ν , 0 / 0 . 05 eV Λ − 3 ≡ Λ / (10 − 3 eV) The instability is avoidable ...

... if growth-slowing effects (dragging) provided by CDM dominate over the acceleron-neutrino coupling Bjaelde et al. � � � � � d ln m ν d ln M Ω CDM − Ω ν 1 ≃ 10 � � � � β ≡ � < � = � � � � d A d A 2 Ω ν M Pl M Pl � � ⇒ β = 2 |A| < 10 M = M o e A 2 /f 2 If = f 2 M Pl � ln 12 ( m ν , 0 / 0 . 05 eV) |A| T ν < 1 . 1 Λ = < 1 . 7 < ⇒ f Λ − 3 for Λ − 3 ≃ 0 . 6( m ν , 0 / 0 . 05 eV) 1 / 4 ⇒ f/M Pl > 0 . 34 =

Discontinuity in alpha L em = − 1 4 Z F ( A /M Pl ) F µ ν F µ ν = − 1 4 (1 + κ A /M Pl + . . . ) F µ ν F µ ν κ ≡ ∂ A Z F | 0 � � ∆ α � = κ A = κ A f � � f · � � M Pl M Pl α �

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 Λ − 3 ≃ 0 . 61( m ν , 0 / 0 . 05 eV) 1 / 4 ρ A m ν , 0 ∼ 4 × 10 − 3 0 . 05 eV ρ DE The energy density of the acceleron does not saturate the present dark energy Neutrinos are nonrelativistic with supercritical density for 0.5 < z < 4

Reproducing the signal in quasar spectra � 1 + z � 1 + z � � 3 � M ( A ) ⇒ |A| = = = 3 ln 1 + z c M o f 1 + z c For z = 2 , z c = 0 . 5 |A| /f ≃ 1 . 4 With f/M Pl ≥ 0 . 34 � � ∆ α � � � > ∼ 0 . 5 κ � � α � to explain the data Need κ ∼ 10 − 5

Consistent with CMB and BBN data? n ν > n REL as soon as neutrinos become relativistic ν , c � ν m 2 T 2 3 ζ (3) M � ν , 0 = ⇒ |A| /f ≃ ln (10 z ) = 2 π 2 Λ 4 M o CMB BBN � � � � ∆ α � ≃ 3 κ f ∆ α � ≃ 5 κ f � � � � , � � � � M Pl M Pl α α � � 0 . 02 recombination < κ 0 . 01 BBN < κ