On Wednesday, June 30, 2021 at 6:24:32 PM UTC-5 Bruce wrote:
> On Thu, Jul 1, 2021 at 7:13 AM Lawrence Crowell <goldenfield...@gmail.com>
> wrote:
>
>> On Tuesday, June 29, 2021 at 5:24:06 PM UTC-5 Bruce wrote:
>>
>>> On Wed, Jun 30, 2021 at 4:50 AM Lawrence Crowell <
>>> goldenfield...@gmail.com> wrote:
>>>
>>>> The argument is a bit difficult, but the dS vacuum has positive energy
>>>> and there is some probability of it tunneling to a lower value.
>>>
>>>
>>> In order for this to be possible, there must be some "landscape" of
>>> possible values for the vacuum energy. There is no evidence for any such
>>> thing. The data are best described by a cosmological constant -- that is, a
>>> fixed constant function. In order for there to be some "landscape", or some
>>> lower possible value for the vacuum energy, there must be some function
>>> that describes this. That would require a dynamical origin for vacuum
>>> energy, and be the opposite of a simple constant.
>>>
>>> Any theory that goes in this direction is necessarily unevidenced
>>> speculation, no matter how arcane the mathematics might be.
>>>
>>
>> It is tied to inflationary cosmology, which has some empirical support.
>>
>
>
> Eternal inflation is not a generic prediction of inflationary cosmology.
> It all depends on the inflaton potential. The best fits to the cosmological
> data come from slow roll potential models with finely adjusted parameters.
> These do no give eternal inflation.
>
Eternal inflation is just field locality and the tunneling of the inflaton
field to a new configuration that propagates in a region bounded by null
geodesics. Non-eternal inflation is trickier in that the inflaton tunnels
into a lower energy configuration globally.
>
> It does give predictions on the CMB and ΛCDM, which has a fair amount of
>> empirical support. The B-modes for gravitational waves induced by inflation
>> seemed a good bet back in 2015, but the problem is that polarization from
>> galactic dust leaves a similar signature. So the data fell from 6-sigma to
>> 3-sigma. The situation though is improving. It is turning into a very
>> difficult signal processing issue.
>>
>
> Whether inflation occurred or not is not the issue. The problem is with
> the assumption that inflation is eternal.
>
>
Eternal inflation is less problematic to assume than to assume the inflaton
field quantum tunnels globally on the de Sitter (like) manifold of
inflation.
>
> Inflationary cosmology implies the sort of multi-cosmogony or multiverse
>> (I never liked that term) model. If B-modes are found this will gives some
>> support for that. In that case we will have some data to support work on
>> different vacua for cosmogonies.
>>
>
> The question of multiple vacua is like that of eternal inflation. It all
> depends on the inflaton potential, and we have no direct way of determining
> that.
>
This is complicated, but the sum over all fields in an inflationary bubble
may not necessarily be equivalent and this reflects different physical
vacuum configurations for the inflaton scalar field. How this works in the
swampland setting is less clear. The landscape requires an AdS vacuum, and
we of course are not in that sort of spacetime. Inflationary bubbles occur
on a de Sitter vacuum and how the huge diversity of vacuum configurations
in string/M-theory work in this picture is not at all clear. As I have
said, the local spacetime between two near colliding black holes is AdS_4
and this in a BPS bound will define string/M-theory fields. This means
string theory may have something to do with vertex functions for quantum
black holes and how they generate gravitons. However, this has a weak or
nonexistent connection with the spectrum of elementary particles. So there
are a lot of open questions here.
It is a bit to get stringy people to think my way, and they are reluctant.
However, the weak connection to the spectrum of elementary particles may
have to do with black holes. Arkani-Hamed wrote an interesting paper on how
the Kerr black hole has elementary particle properties. The vacuum
configuration is such that the masses of elementary particles are very
small compared to the the Planck mass. I think the gravitation coupling
constant should be thought of as (m_h/m_p)^2 ~ 10^{-34}, and this value may
be local. The mass of the Higgs particle may be tied to the mass of the
inflaton and some general and as yet unknown theory of scalar fields. This
may be some unified theory of phase transitions, which is a program in
solid state physics.
In general though, to assume there is a single global configuration for the
inflaton is more troubling. Now if we take the black hole AdS duality, and
say that even outside the BPS bound of a black hole in the AdS, then maybe
the nonlocality in the AdS confers a nonlocality to the scalar field.
However, the CFT boundary is still local, and this is where we might expect
scalar fields to live. in fact an elementary theory of such scalar fields
is CFT_3 which would suggest locality.
LC
>
> Where things go from there is uncertain. I tend to think that alternate
>> cosmologies with Λ >> Λ_obs may in fact be a form of off-shell condition.
>> These may then not in fact be real worlds as such. I also think this might
>> be a way to do radiative corrections in general, not just cosmology, that
>> avoids a lot of redundancies in Feynman diagram approaches and that further
>> avoids confusions over virtual states.
>>
>>
>>>
>>> It may do this "drip by drip" with Gibbon-Hawking radiation.
>>>
>>>
>>>
>>> I think Gibbon-Hawking radiation is rather like Unruh radiation. -- a
>>> test body in the expanding universe will experience radiation, but the
>>> vacuum energy does not decay, since the whole of spacetime is not filled
>>> with such radiation -- it is only in the presence of a test body that it is
>>> observable. Just like with Unruh radiation. The spacetime surrounding the
>>> accelerating body is not filled with radiation since the inertial observer
>>> does not see radiation. All he sees is the accelerated body emitting the
>>> occasional thermal particle.
>>>
>>> Bruce
>>>
>>
>> It is similar to Unruh radiation in that the cosmological horizon is a
>> particle horizon. It is though also similar to Hawking radiation, and an
>> inertial observer in principle can observe it.
>>
>
> Any observer in deSitter space can observe the radiation because they
> constitute a test particle. However, the space is not filled with such
> radiation in such a way that the cosmological constant itself decays.
>
> Bruce
>
On that I disagree. The GH radiation has a wavelength on the scale of low L
moments in the CMB. This radiation will pass across the cosmological
horizon and be lost. This at least suggests the curvature of the FLRW
spacetime adjusts in response and is reduced.
LC
> The practical problem of course is the quanta emitted have wavelength that
>> is comparable to the horizon distance L = √(3/Λ). If one wants hold to the
>> analogue with Unruh radiation then the cosmological constant does induce an
>> accelerated frame dragging of particles.
>>
>> I ponder whether in this multiple cosmogony perspective that all other
>> vacua have transition amplitudes to the lowest energy vacuum. These other
>> vacua the correspond to what we might call virtual cosmogonies or off-shell
>> states. The vacuum we are in would then be the lowest with the Λ_obs the
>> physical vacuum that has a fundamental mass-gap with zero energy or T^{00}
>> = 0. The internal emission of Gibbon-Hawking radiation might be the only
>> way the vacuum can transition to zero. If so there would be a restriction
>> on the number of physical cosmogonies, maybe down to just the one we
>> observe.
>>
>> LC
>>
>>
>>>
>>> It could also transition into an anti-de Sitter vacuum. In that case the
>>>> vacuum energy is negative, but there are conditions for regular
>>>> eigenvalued
>>>> orbits that define a minimum. That is a difficult subject involving the
>>>> moduli of hyperbolic geometries. So string theory is not needed to
>>>> understand this. In fact the de Sitter vacuum is "anti-string," and string
>>>> theory has nothing directly to do with the spectra of elementary particles
>>>> or the vacuum in the observable universe, That is except with colliding
>>>> black holes.
>>>
>>>
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