Density%20matrix%20of%20the%20Universe%20reloaded:%20origin%20of%20inflation%20and%20cosmological%20acceleration

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Density matrix of the Universe reloadedorigin
of inflation and cosmological acceleration
A.O.Barvinsky Theory Department, Lebedev Physics
Institute, Moscow
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Cosmological constant problem
Introduction
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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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 )
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From the pure Hartle-Hawking state to a
statistical ensemble the density matrix
instanton bridge mediates density matrix
correlations
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EQG density matrix
D.Page (1986)
Effective action statistical sum
integration over periodic fields on a torus
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Euclidean FRW metric
3-sphere of a unit size
scale factor
lapse
gravitons
quantum matter cosmological perturbations
minisuperspace background
quantum effective action of ? on
minisuperspace background
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nature of approximation
Effective Friedmann equation
Assumption of Ncdf conformally invariant free,
Ncdf À 1, quantum fields
exactly solvable model, 1/Ncdf -- expansion
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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, k1
k- folded garland, k1,2,3,
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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
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LQG density matrix
-- conjugated momenta
Representation of three-metric and matter fields
includes gauge fixing factor
constraints
lapse and shift functions
Range of integration over
Wheeler-DeWitt equations
Microcanonical density matrix
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Sum over Everything
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
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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
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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
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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
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Recovery of GR
Cosmological acceleration and Big Boost
singularity
Assumption of growing ?
Big Boost singularity
inflation
acceleration
t
t1
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Hiearchy problem, strings and extra dimensions
We need time dependent and presently huge ?,
of conformal fields
Planck
EW
Hubble
1019 GeV
TeV
10-33 eV
Ncdf 1032 (Dvali, 2007)
Ncdf 10120
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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
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Dual description via AdS/CFT correspondence
Randall-Sundrum
model
RS model 5D SUGRA vs 4D N4 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
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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
0
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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