Theory Department, Lebedev Physics Institute, Moscow Density matrix of the Universe reloaded: origin of inflation and cosmological acceleration A.O.Barvinsky Theory Department, Lebedev Physics Institute, Moscow

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

& A.Kamenshchik, arXiv: hep-th/0801.2063 ) cosmological wavefunctions baby universes BH thermodynamics Problems: indefiniteness of the Euclidean gravitational action; infrared catastrophe of small cosmological constant , cosmology debate of the no-boundary vs tunneling proposals EQG elimination of the infrared catastrophe of small  ensemble of universes in a limited 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] EQG density matrix of the Universe 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 D.Page (1986) Effective action: statistical sum integration over periodic fields on a torus:

Euclidean FRW metric 3-sphere of a unit size lapse scale factor gravitons quantum “matter” – cosmological perturbations minisuperspace background quantum effective action of  on minisuperspace background

Effective Friedmann equation 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: coefficient of the Gauss-Bonnet term in the total conformal anomaly primordial cosmological constant amount of radiation constant instanton period in units of conformal time --- inverse temperature Casimir energy thermal energy Solutions --- set of tubular periodic garland-type instantons with oscillating scale factor Tree-level version: Halliwell & Myers (1989); Fischler, Morgan & Polchinski (1990) 1- fold, k=1 k- folded garland, k=1,2,3,…

bounded range of the cosmological constant amount of radiation constant cosmological constant selection rule for string landscape? bounded range of the cosmological constant elimination of the infrared catastrophe (anomaly effect) new quantum gravity scale (anomaly effect) of quantum fields: 1/N-approximation

LQG density matrix Representation of three-metric and matter fields -- conjugated momenta includes gauge fixing factor lapse and shift functions constraints Range of integration over Wheeler-DeWitt equations Microcanonical density matrix

Sum over Everything Sum over Everything (closed cosmology) Statistical sum Physical reduction in the unitary gauge, physical Hamiltonian Canonical Faddeev-Popov integral in terms of physical variables: chronological ordering In a static gauge (use on-shell gauge-independence) (closed cosmology) Sum over Everything

Gaussian integration over momenta gives a Lagrangian path integra over Lorentzian variables (L) Gaussian integration over momenta gives a Lagrangian path integra over minisuperspace LQG path integrals with real integration variables 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 imaginary lapse integration contour:

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 with initial conditions set by the saddle-point instanton Analytic continuation of the instanton solutions: Casimir energy does not weigh Decay of a composite  in the end of inflation and particle creation of conformally non-invariant matter: matter energy density Modified Friedmann equation Dimensionless coefficient of the Gauss- Bonnet term in conformal anomaly:

Cosmological acceleration and Big Boost singularity Recovery of GR: Cosmological acceleration and Big Boost singularity Assumption of growing : Big Boost singularity: inflation acceleration t t1

Hiearchy problem, strings and extra dimensions We need time dependent and presently huge , # of conformal fields Hubble EW Planck 10-33 eV TeV 1019 GeV Ncdf» 1032 (Dvali, 2007) Ncdf» 10120

Mechanism of variable B from string/Kaluza-Klein theory indefinitely growing with evolving size of X-tra dimension(s) --- coefficient of the Gauss-Bonnet term in the total conformal anomaly; number of conformally invariant massless modes --- KK and winding modes Masses of KK and winding modes: approximate masslessness and 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-sided RS model with a bulk BH 4D thermal gas dual to 5D bulk BH brane tension

Anomaly driven cosmology and the DGP model Vacuum (=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

Density Matrix Reloaded: Minimum set of assumptions --- an ultimate equipartition in physical phase space in the form of 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-domination stages 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