1. Quantum Gravity and the Cosmological Constant Enikő Regős Enikő Regős

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

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

4. Background space Background : maximally symmetric spaces : Background : maximally symmetric spaces : de Sitter de Sitter Spherical harmonics to solve spectrum ( λ_l ) Spherical harmonics to solve spectrum ( λ_l ) for potential : for potential : γ 1 ( R ) = γ 1 ( R ) = ∑ D / 2 ln [ κ² R / Λ4 ( a λ_l + d - c λ / R )] ∑ D / 2 ln [ κ² R / Λ4 ( a λ_l + d - c λ / R )] D_l : degeneracy, sum over multipoles l and spins D_l : degeneracy, sum over multipoles l and spins g = + h g = + h

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

6. Effective potential as function of curvature

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

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

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

10. Stability and matter fields λ_bare -> 2D phase diagram λ_bare -> 2D phase diagram stability stability include matter fields : include matter fields : 1. scalar 2. strong interaction : influence of confinement in gauge and influence of confinement in gauge and gravitational sectors on each other gravitational sectors on each other gravitational waves gravitational waves

11. Happy Birthday, Bernard !

12. Thank you for your attention