Leung Center for Cosmology and Particle Astrophysics, National Taiwan University
Dong-han Yeom
2015. 7. 10.
Phantom of the instanton:a phantom dark energy modelinspired by theHartle-Hawking wave function
Based on- Chen, Qiu and DY, 1503.08709
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Cosmological parameters from Planck 2015
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Phantomness, as well as the violation of the Null Energy Condition (NEC) can be easily
explained by assuming a ghost field. For example, a quintom (quintessence + phantom)
model is as follows:
However, usually a negative kinetic term causes instabilities up to small perturbations.
One may resolve such an instability by using some strange assumptions, e.g., introducing
non-local relations, but these models seem to be very ugly.
Phantomness and violation of NEC
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Phantomness, as well as the violation of the Null Energy Condition (NEC) can be easily
explained by assuming a ghost field. For example, a quintom (quintessence + phantom)
model is as follows:
However, usually a negative kinetic term causes instabilities up to small perturbations.
One may resolve such an instability by using some strange assumptions, e.g., introducing
non-local relations, but these models seem to be very ugly.
Perhaps, the only known legal way to violate the null energy condition comes from quantum
field theory in curved spacetime: e.g., Hawking radiation.
Phantomness and violation of NEC
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Hartle and Hawking in 1976
Hartle and Hawking interpreted Hawking radiation as a particle tunneling. Then for a certain
hypersurface of the bulk region, there is a particle that moves backward in time, though there is
no such an exotic behavior at the future infinity.
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Hartle and Hawking in 1976
This process can be approximated by the Euclidean analytic continuation.
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Phantomness, as well as the violation of the Null Energy Condition (NEC) can be easily
explained by assuming a ghost field. For example, a quintom (quintessence + phantom)
model is as follows:
However, usually a negative kinetic term causes instabilities up to small perturbations.
One may resolve such an instability by using some strange assumptions, e.g., introducing
non-local relations, but these models seem to be very ugly.
Perhaps, the only known legal way to violate the null energy condition comes from quantum
field theory in curved spacetime: e.g., Hawking radiation.
Can we justify the phantomness from the Euclidean analytic continuation?
Phantomness and violation of NEC
Hartle-Hawking wave function
and classicality
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To resolve the singularity problem, we can quantize the gravity and solve the Wheeler-
DeWitt equation.
As a boundary condition of the ground state wave function, Hartle and Hawking suggested
the Euclidean path integral:
Hartle-Hawking wave function
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Let us consider a model with Einstein gravity and two canonical scalar fields:
By assuming O(4) symmetry, we can construct a minisuperspace model:
The Euclidean path integral can be approximated by summing over on-shell histories: so-
called instantons
Hartle-Hawking wave function
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Typical instantons
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Typical instantons
In general, complex-valued around here.
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In order to assign a sensible probability, we require the classicality at infinity:
This condition can be obtained if all field values approach to be real at infinity.
If there remains an imaginary part of the scalar field at infinity, it behaves as a ghost.
Classicality
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In order to assign a sensible probability, we require the classicality at infinity:
This condition can be obtained if all field values approach to be real at infinity.
If there remains an imaginary part of the scalar field at infinity, it behaves as a ghost.
What if (1) we are not observing at infinity and (2) a very subdominant scalar field is not
classicalized yet?
Classicality
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In order to assign a sensible probability, we require the classicality at infinity:
This condition can be obtained if all field values approach to be real at infinity.
If there remains an imaginary part of the scalar field at infinity, it behaves as a ghost.
What if (1) we are not observing at infinity and (2) a very subdominant scalar field is not
classicalized yet?
We may see phantomness from this non-classicalized scalar field, where this is a non-
perturbative effect from the entire wave function, and hence a kind of residue of quantum
gravity.
Classicality
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Let us assume that there are two scalar fields.
One is an inflaton field and the other is a qunitessence field.
We further assume that
(1) in the beginning, the energy amount of the quintessence field is negligible (hence, the
qunitessence field does not make physical effects during inflation) and
(2) the quintessence field is still slow-roll even though the universe approaches the dark
energy dominated era.
Now the quintessence model can be embedded to a quintum model.
Hartle-Hawking inspired quintom model
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Example: classicalized instanton
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Example: classicalized instanton
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Example: classicalized instanton
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Example: classicalized instanton
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Robustness of classicality of the inflaton field
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Quintessence dynamics
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Evolution of dark energy
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This model has the following properties.
(1) Even though it shows a phantom behavior, this can be justified from the entire path
integral: a ghost-like field is an effect emergent from the entire path integral.
(2) This phantom model does not cause a big rip singularity, since the model towards local
minimum, not only for the real part but also for the imaginary part.
Conclusion: Hartle-Hawking inspired quintom model
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Can we see ‘residue’of quantum gravity in the Universe?
(1) As we see, if there is phantomness, then this can be a candidate.
Future topics: evidence of quantum gravity?
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Can we see ‘residue’of quantum gravity in the Universe?
(1) As we see, if there is phantomness, then this can be a candidate.
(2) For some ‘bias’ from the LCDM model in the power spectrum of CMB, this can be
explained by assuming a phantom equation of state for the earlier stage of inflation. Note that
this can be a quite universal behavior.
Future topics: evidence of quantum gravity?
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Future topics: evidence of quantum gravity?
