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Cosmological constant problem Introduction Cosmological constant problem Hubble constant energy density Two aspects of the problem: Early Universe: constraints from large-scale structure formation Present Universe: cosmological acceleration or dark energy Problem of landscape in string theory of string vacua
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Density matrix of the Universe reloaded:origin of inflation and cosmological acceleration
A.O.Barvinsky Theory Department, Lebedev Physics Institute, Moscow
Cosmological constant problem
• Early Universe: constraints from large-scale structure formationTwo aspects of the problem:
• Present Universe: cosmological acceleration or dark energy
Hubbleconstant
energydensity
Introduction
Problem of landscape in string theory
of string vacua
EQG
cosmological wavefunctions
baby universes
BH thermodynamics
Problems: indefiniteness of the Euclideangravitational action;
infrared catastrophe of smallcosmological constant ,
cosmology debate of the no-boundary vs tunneling proposals
EQG density matrix of the Universe
elimination of the infraredcatastrophe of small
ensemble of universes in alimited range of
selection mechanism for string landscape
A.B. & A.Yu.Kamenshchik,JCAP, 09, 014 (2006)[hep-th/0605132];Phys. Rev. D74, 121502 (2006)[hep-th/0611206]
Justification of these results from Lorentzian quantum gravity (LQG) and a new mechanism of dark energy (A.B., PRL 99, 071301 (2007); A.B., C.Deffayet& A.Kamenshchik, arXiv: hep-th/0801.2063 )
From the pure Hartle-Hawking state to a statistical ensemble – the density matrix:
instanton bridge mediates density matrix correlations
EQG density matrix
Effective action:statistical sum
integration over periodic fields on a torus:
D.Page(1986)
minisuperspace background
quantum “matter” – cosmological perturbations
Euclidean FRW metric 3-sphere of a unit size
scale factorlapse
gravitons
quantum effective actionof on minisuperspacebackground
nature of approximation
Effective Friedmann equation
Assumption of Ncdf conformally invariant free, Ncdf À 1, quantum fields
exactly solvable model, 1/Ncdf -- expansion
Euclidean effective equation of motion:
k- folded garland, k=1,2,3,…1- fold, k=1
amount of radiation constant
Solutions --- set of tubular periodic garland-type instantons with oscillating scale factor
Tree-level version:Halliwell & Myers(1989);Fischler, Morgan& Polchinski(1990)
coefficient of the Gauss-Bonnet term in the total conformal anomaly
instanton period in units of conformal time --- inverse temperatureCasimir energy thermal energy
primordialcosmologicalconstant
bounded range of the cosmological constant
elimination of the infrared catastrophe (anomaly effect)
new quantum gravity scale (anomaly effect)
amount of radiation constant
cosmologicalconstant
selection rule forstring landscape?
of quantum fields: 1/N-approximation
LQG density matrix
Representation of three-metric and matter fields -- conjugated momenta
lapse and shiftfunctions
constraints
Range of integration over
Wheeler-DeWitt equations
Microcanonicaldensity matrix
includes gaugefixing factor
Sum over Everything
In a static gauge (use on-shell gauge-independence)
Physical reduction in the unitary gauge,
Canonical Faddeev-Popov integral in terms of physical variables:
chronological ordering
Statistical sum
physicalHamiltonian
(closed cosmology)
Sum over Everything
No periodic solutions of Lorentzian effective equation in real time and real geometry! Saddle points of the Lorentzian path integral exist in Wick-rotated (Euclidean) geometry:
EQG path integral with the imaginarylapse integration contour:
Gaussian integration over momenta gives a Lagrangian path integra over
LQG path integrals with real integration variables
minisuperspace
Lorentzian variables (L)
Steepest decent integration contour for the Euclidean lapse --- conformal rotation in EQG
Deformation of the original contour of integration
into the complex plane to pass through the saddle point
Cosmological acceleration from the microcanonical state of the Universe
Lorentzian Universe withinitial conditions set by thesaddle-point instanton
Analytic continuation ofthe instanton solutions:
Decay of a composite in the end of inflation and particle creation of conformally non-invariant matter:
Modified Friedmann equation
Casimir energydoes not weigh
matter energy density
Dimensionless coefficient of the Gauss-Bonnet term in conformal anomaly:
Recovery of GR:
Cosmological acceleration and Big Boost singularity
Big Boost singularity:
Assumption of growing :
tt1
inflation acceleration
Hiearchy problem, strings and extra dimensions
We need time dependent and presently huge
PlanckEWHubble
1019 GeVTeV10-33 eV
Ncdf» 1032 (Dvali, 2007)
Ncdf» 10120
# of conformal fields
Mechanism of variable B from string/Kaluza-Klein theory
--- coefficient of the Gauss-Bonnet term in the total conformal anomaly;
number of conformally invariant massless modes --- KK and winding modes
indefinitely growing with evolving size of X-tra dimension(s)
Masses of KK and winding modes:
approximate masslessnessand conformal invariance
Growing tower of superhorizon KK modes
indefinitely decreases with
Growing tower of superhorizon winding modes
indefinitely decreases with
Dual description via AdS/CFT correspondence: Randall-Sundrum model
RS model: 5D SUGRA vs 4D N=4 SU(N) SYM
Small energy density
Friedmann equation in one-sidedRS model with a bulk BH
4D thermal gas dualto 5D bulk BH
branetension
Anomaly driven cosmology and the DGP modelVacuum (=0) DGP model with a 5D cosmological constant and bulk BH
is equivalent to the anomaly driven cosmology under the identifications
Only one (non-accelerating) branch is induced --- no Boulware-Deser ghost instability!
Big Boost scenario in the DGP model with 5 --- no need for running rc
0
Density Matrix Reloaded:
Minimum set of assumptions --- an ultimate equipartition in physical phase space in the formof the microcanonical state of closed quantum cosmology
Constraining the ensemble of (and possibly landscape of string vacua)
A new dark energy mechanism transcending the inflationary and matter-dominationstages as a quasi-equilibrium decay of the initial microcanonical state
``Nothing comes from Nothing”
Sidney Coleman: ``There is Nothing rather than Something”
Something (rather than Nothing) comes from Everything