1. Dark Energy and Quantum Gravity Dark Energy and Quantum Gravity 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 Quantum black holes: energy spectrum, dependence with parameters of space- times, e.g. strings Quantum black holes: energy spectrum, dependence with parameters of space- times, e.g. strings Entropy Entropy

3. Quantum gravity and accelerator physics Obtain limits from collider experiments Obtain limits from collider experiments Graviton interference effects at Large Hadron Collider, CERN Graviton interference effects at Large Hadron Collider, CERN Decay modes of particles with mass in TeV range Decay modes of particles with mass in TeV range Hadron/lepton scatterings and Hadron/lepton scatterings and decays in extra-dimensional models decays in extra-dimensional models Super symmetry, string theory Super symmetry, string theory Limits from cosmology and astrophysics: cosmic rays and supernovae Limits from cosmology and astrophysics: cosmic rays and supernovae Particle astrophysics Particle astrophysics  Dark matter  mass of particles, Ex: Axions Ex: Axions Evidence from Evidence from observations for extra D observations for extra D  Alternative to missing mass problem : scale dependent G mass problem : scale dependent G

4. Cosmic rays and supernovae ; Cosmic rays : Nature’s free collider SN cores emit large fluxes of KK gravitons producing a cosmic background -> radiative decays : diffuse γ – ray background SN cores emit large fluxes of KK gravitons producing a cosmic background -> radiative decays : diffuse γ – ray background Cooling limit from SN 1987A neutrino burst -> bound on radius of extra dimensions Cooling limit from SN 1987A neutrino burst -> bound on radius of extra dimensions Cosmic neutrinos produce black holes, energy loss from graviton mediated interactions cannot explain cosmic ray events above a limit Cosmic neutrinos produce black holes, energy loss from graviton mediated interactions cannot explain cosmic ray events above a limit BH’s in observable collisions of elementary particles if ED BH’s in observable collisions of elementary particles if ED CR signals from mini BH’s in ED, evaporation of mini BHs CR signals from mini BH’s in ED, evaporation of mini BHs

5. Galaxy simulations and axion mass Collisional Cold Dark Matter interaction cross sections Collisional Cold Dark Matter interaction cross sections Halo structure, cusps Halo structure, cusps Number and size of extra dimensions Number and size of extra dimensions

6. 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

7. 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

8. 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

9. Effective potential as function of curvature

10. 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

11. 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

12. 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

13. 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

14. Thank you for your attention !