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