Creation from Nothing Revisited: Landscape from Cosmological Bootstrap

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Creation from Nothing Revisited Landscape from
Cosmological Bootstrap

• A.O.Barvinsky
• Theory Department, Lebedev Physics Institute,
  Moscow
• and
• A.Yu.Kamenshchik
• Landau Institute for Theoretical Physics, Moscow
• and
• Dipartimento di Fisica and INFN, Bologna, Italy

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Introduction
Motivation search for selection rule restricting
landscape of stringy vacua quantum
cosmology and Euclidean quantum gravity
Euclidean spacetime
Lorentzian spacetime
Infrared catastrophe
Cosmology debate no-boundary vs tunneling
Wheeler-DeWitt equation
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Outline
Density matrix vs pure state in Euclidean quantum
gravity Back reaction of hot (radiation-like)
quantum matter Conformal anomaly and
ghost-avoidance renormalization Effective
(modified Friedmann) and bootstrap
equations Elimination of infrared catastrophe
of small ? Bounded cosmological landscape of
instanton garlands Shrinking stringy landscape?
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From pure state to statistical ensemble
density matrix
instanton bridge mediates density matrix
correlations
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Density matrix of pure Hartle-Hawking state
Main effect back reaction of quantum matter
destroys HH instanton by radiation that prevents
half-instantons from closure and maintains
thermal nature of physical state
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Calculation of partition function toroidal
instanton with periodically identified Euclidean
time
Bootstrap back reaction of radiation supports
instanton background on top of which this
radiation exists
Bounded cosmological landscape
Boundedness of on-shell gravitational action in
Euclidean QG
Infinite sequence of 1-parameter families of
garland-type instantons saturating ?max sound
link between gravitational tunneling and
renormalization theory
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Effect of radiation
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Density matrix
effective action
integration over periodic fields on a torus
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Back reaction nature of approximation
minisuperspace background
quantum matter cosmological perturbations
nature of approximation
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Conformal anomaly and ghosts
Conformally invariant quantum matter
Conformal transform to static Einstein universe
conformal time
Weyl tensor
Euler density
ghosts (BAD!)
Coefficient of conformal anomaly
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Finite ghost-avoidance renormalization
Euler density coefficient in conformal anomaly
For low spins
scalar Weyl spinor vector (e-m field)
zeta-functional and point-separation
regularizations
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Effective action on static Einstein instanton
vacuum energy
free energy
ghost avoidance renormalization
coefficient of
in anomaly
modified vacuum energy
Important universality
Euler density coefficient in anomaly
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Effective Friedmann and bootstrap equations
lapse function
conformal time
? turning points of solutions
Total effective action
classical
anomaly
vacuum energy
thermal
nonlocality (polylocality) breezing of instanton
in ?-direction
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Effective equation (via variation of N(?) or a(?))
anomaly contribution
radiation term
Bootstrap equation
On-shell action
thermal part
geometric part
!
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Effect of anomaly and bootstrap beginning of
landscape
The same two turning points
provided
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Elimination of infrared catastrophe
bootstrap
bootstrap
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One-parameter family of instantons
Upper (hyperbolic) boundary static Einstein
Universe with hot equilibrium gas of temperature
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Instanton garlands
k- folded garland, k2,3,
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k-folded conformal time
k2 garland
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sequence of garlands
no additivity in k !
Increasingly long ?0 log k2, increasingly
static and more and more cold garlands saturating
upper bound of landscape
Consequence of universality relation between
vacuum energies and conformal anomaly sound
link of renormalization theory and Euclidean
quantum gravity
Final bounds of landscape for scalar and vector
matter
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Conclusions some like it hot
Bounded cosmological landscape
Lorentzian evolution, expansion, radiation
dilution, inflation, usual structure formation
scenario

?lt?min ruled out by ?1
boundedness of on-shell gravitational action in
infrared domain of Euclidean gravity nonlocal
effect of anomaly and nonlocal bootstrap
Beyond conformal quantum matter? Instantons are
nearly static. Universality relation can be
broken C0ltB/2 sequence of garlands becomes
hot BgtC0gtB/2 -- sequence of garlands is
truncated C0gtB infrared catastrophe develops
Normalizability of partition function sum over
instantons. Measure and prefactors.
Semiclassical validity scaling behavior with N
number of fields
1/N-expansion
Climbing up phenomenology energy scale and higher
spins, Bgtgt1
Shrinking stringy landscape?
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This is how cosmological landscape comes out of
Nothing, if some like it hot