Quantum Gravity and the Quantum Gravity and the
Cosmological Constant Cosmological Constant
Enikő Regős Enikő Regős
Astrophysical observations and quantum physics Astrophysical observations and quantum physics
Explain Explain ΛΛ from from
quantum fluctuations quantum fluctuations
in gravity in gravity
Radiative corrections Radiative corrections induce
induce ΛΛ
Quantum gravity and Quantum gravity and accelerator physics
accelerator physics
Extra dimensional Extra dimensional models (strings) models (strings)
Particle astrophysics : Particle astrophysics : dark matter search, dark matter search,
mass of particles mass of particles
Quantum black holesQuantum black holes
Effective potential for the curvature Effective potential for the curvature
Effective actionEffective action: :
S [ g ] = - S [ g ] = - κκ² ∫ dx √g ( R – 2 ² ∫ dx √g ( R – 2 λλ ) )
One-loop approximation :One-loop approximation :
ΓΓ [g] = S [g] + Tr ln [g] = S [g] + Tr ln ∂∂² S [g] / ∂g ∂g / 2² S [g] / ∂g ∂g / 2
Gauge fixing and regularizationGauge fixing and regularization
Sharp cutoffSharp cutoff : - D² < : - D² < ΛΛ² ²
Spin projectionSpin projection : :
metric tensormetric tensor fluctuation fluctuation : TT, LT, LL, Tr : TT, LT, LL, Tr
Background space Background space
Background Background : maximally symmetric spaces :: maximally symmetric spaces : de Sitterde Sitter
Spherical harmonics to solve Spherical harmonics to solve spectrumspectrum ( ( λλ_l )_l ) for potential :for potential :
γγ1 ( R ) = 1 ( R ) = ∑
∑ D / 2 ln [ D / 2 ln [ κκ² R / ² R / Λ4 ( a Λ4 ( a λλ_l + d - c _l + d - c λλ / R )] / R )]
D_l : degeneracy, sum over multipoles l and D_l : degeneracy, sum over multipoles l and spins
spins
g = < g > + h g = < g > + h
Casimir effect Casimir effect
In a boxIn a box : :
ΓΓ [0] = (L [0] = (L ΛΛ)^4 ( ln )^4 ( ln μμ² / ² / ΛΛ² – ½ ) / 32 ² – ½ ) / 32 ΠΠ²²
Fit numerical results for gravityFit numerical results for gravity : :
γγ ( R ) = - v ( R ) = - v κκ² / R + c1 ² / R + c1 ΛΛ^4 ( 1 / R² –^4 ( 1 / R² –
1 / R² (1 / R² (ΛΛ) ) ln ( c2 ) ) ln ( c2 κκ² / ² / ΛΛ² )² )
v = 3200 v = 3200 ΠΠ² / 3² / 3
R ( R ( ΛΛ) = c3 ) = c3 ΛΛ²²
Metric tensor controls geometryMetric tensor controls geometry
Effective potential as function of curvature
Effective potential as function of curvature
Energetically preferred curvature Energetically preferred curvature
Minimize effective potentialMinimize effective potential
Quantum phase transitionQuantum phase transition at : at :
κκ² = ² = ΛΛ² / c2 : critical coupling² / c2 : critical coupling
Low cutoff phaseLow cutoff phase, below :, below :
R_min = 2 c1 ( R_min = 2 c1 ( ΛΛ^4 / v ^4 / v κκ² ) ln ( c2 ² ) ln ( c2 κκ² / ² / ΛΛ² ) ² )
High cutoff phaseHigh cutoff phase : :
R_min = 0R_min = 0 : : flatflat
2 phases : flat and strongly curved space-time2 phases : flat and strongly curved space-time
Condensation of metric tensorCondensation of metric tensor
Running Newton constant Running Newton constant
κκ² ( R ) = ² ( R ) = κκ² - ( R / v ) ² - ( R / v ) γγ1 ( R )1 ( R )
G ( R ) = 1 / ( 16 G ( R ) = 1 / ( 16 ΠΠ κκ² ( R ) )² ( R ) )
Infrared Landau pole in low-cutoff phaseInfrared Landau pole in low-cutoff phase : :
R_L = R_min /2 :R_L = R_min /2 :
Confinement of gravitons Confinement of gravitons ( experiments )( experiments )
G ( R ) increasing in high-cutoff phaseG ( R ) increasing in high-cutoff phase
Savvidy vacuumSavvidy vacuum
Induced cosmological constant Induced cosmological constant
ΓΓ [g] = [g] = κκ²_eff ∫ dx √g (x) F ( R (x) )²_eff ∫ dx √g (x) F ( R (x) )
F ( R ) = R – 2 F ( R ) = R – 2 λλ – g R² – g R²
κκ_eff = _eff = κκ
λλ = c1 ( = c1 ( ΛΛ^4 / 2 v ^4 / 2 v κκ² ) ln ( c2 ² ) ln ( c2 κκ² / ² / ΛΛ² )² )
ΛΛ > 0 : curved phase > 0 : curved phase
ΛΛ < 0 : flat phase < 0 : flat phase
Or running GOr running G
Stability and matter fields Stability and matter fields
λλ_bare -> 2D _bare -> 2D phase diagramphase diagram
stabilitystability
include matter fieldsinclude matter fields : :
1.1. scalarscalar
2.2. strong interaction : strong interaction :
influence of confinement in gauge andinfluence of confinement in gauge and
gravitational sectors on each othergravitational sectors on each other
gravitational waves gravitational waves