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Quantum Gravity and the Cosmological Constant

Quantum Gravity and the Cosmological Constant . Enikő Regős. Explain Λ from quantum fluctuations in gravity Radiative corrections induce Λ. Quantum gravity and accelerator physics Extra dimensional models (strings) Particle astrophysics : dark matter search, mass of particles

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Quantum Gravity and the Cosmological Constant

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  1. Quantum Gravity and the Cosmological Constant Enikő Regős

  2. Explain Λ from quantum fluctuations in gravity Radiative corrections induce Λ Quantum gravity and accelerator physics Extra dimensional models (strings) Particle astrophysics : dark matter search, mass of particles Quantum black holes Astrophysical observations and quantum physics

  3. Effective potential for the curvature • Effective action: S [ g ] = - κ² ∫ dx √g ( R – 2 λ ) • One-loop approximation : Γ [g] = S [g] + Tr ln ∂² S [g] / ∂g ∂g / 2 • Gauge fixing and regularization • Sharp cutoff : - D² < Λ² • Spin projection : metric tensor fluctuation : TT, LT, LL, Tr

  4. Background space • Background : maximally symmetric spaces : de Sitter • Spherical harmonics to solve spectrum( λ_l ) for potential : • γ1 ( R ) = ∑ D / 2 ln [ κ² R / Λ4 ( a λ_l + d - c λ / R )] D_l : degeneracy, sum over multipoles l and spins g = < g > + h

  5. Casimir effect • In a box : • Γ [0] = (L Λ)^4 ( ln μ² / Λ² – ½ ) / 32 Π² • Fit numerical results for gravity : • γ ( R ) = - v κ² / R + c1 Λ^4 ( 1 / R² – • 1 / R² (Λ) ) ln ( c2 κ² / Λ² ) v = 3200 Π² / 3 R ( Λ) = c3 Λ² • Metric tensor controls geometry

  6. Effective potential as function of curvature

  7. Energetically preferred curvature • Minimize effective potential • Quantum phase transition at : • κ² = Λ² / c2 : critical coupling • Low cutoff phase, below : • R_min = 2 c1 ( Λ^4 / v κ² ) ln ( c2 κ² / Λ² ) • High cutoff phase : • R_min = 0 : flat • 2 phases : flat and strongly curved space-time • Condensation of metric tensor

  8. Running Newton constant • κ² ( R ) = κ² - ( R / v ) γ1 ( R ) • G ( R ) = 1 / ( 16 Πκ² ( R ) ) • Infrared Landau pole in low-cutoff phase : R_L = R_min /2 : • Confinement of gravitons ( experiments ) • G ( R ) increasing in high-cutoff phase • Savvidy vacuum

  9. Induced cosmological constant • Γ [g] = κ²_eff ∫ dx √g (x) F ( R (x) ) • F ( R ) = R – 2 λ – g R² • κ_eff = κ • λ = c1 ( Λ^4 / 2 v κ² ) ln ( c2 κ² / Λ² ) • Λ > 0 : curved phase • Λ < 0 : flat phase • Or running G

  10. Stability and matter fields • λ_bare -> 2D phase diagram • stability • include matter fields : • scalar • strong interaction : influence of confinement in gauge and gravitational sectors on each other • gravitational waves

  11. Happy Birthday, Bernard !

  12. Thank you for your attention

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