Download presentation

Presentation is loading. Please wait.

Published byTrystan Bish Modified over 2 years ago

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

Similar presentations

OK

University of Arizona D IMITRIOS P SALTIS Tests of General Relativity with the SKA.

University of Arizona D IMITRIOS P SALTIS Tests of General Relativity with the SKA.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on energy giving food for kids Ppt on linear equations in two variables 6th Ppt on tata company profile Ppt on precautions of tsunami japan Ppt on environmental pollution in hindi Conjunctions for kids ppt on batteries Ppt on transportation in animals for class 10 Ppt on piezoelectric power generation Download ppt on recession in india Ppt on personality development of students