Ferromagnetic Instability in PAAI in the Sky
487
Since the domain structure is completely random we expect zero large-scale
magnetic field on the average. Residual departure from this average can be estimated
by assuming that the deviation from the mean grows as
√
N as we include N
domains. Thus if the X-magnetic field in individual domains has the value B dom ,
then on the scale of galactic clusters L gal it possesses a root mean square value
ΔB ≡ B dom (L/L gal ) 3/2 .
Assuming U(1) X field mixes kinetically with standard electromagnetism through
term of the form ξF μν F X
μν , the ξ is well constrained from Supernova 1987A data to
[32] 10 −7 < ξ < 10 −9 . The exact value of the seed required depends on the epoch
being studied and other model dependent factors [33]. We consider the possibility
of a seed of 10 −30 T with a coherence length of 0.1 kpc ∼ 3 × 10 18 m obtained with
ξ = 10 −8 .
ΔB seed = 10
−30 T ∼ 10
−8
×
m M
eV
2
e
e
β
3
L
m
3/2
× 10
−40 T
(11)
From this, representative values for L for β = 0.1 are in the range 10 11 to
10 13 m which is solar system size. A detailed treatment to estimate the residual
fluxes on large coherence length scales could trace the statistics of flux values in
near neighbour domains and the rate at which the magnetic flux could undergo
percolation, providing perhaps a smaller value for L, which should tally with above.
6 Conclusions
We have proposed the possibility of a negative pressure medium as arising from
nothing more radical than a peculiar ground state of a pair of asymmetric fermion
species interacting through an unbroken abelian gauge force. In an attempt to highlight the potential utility of the PAAI to cosmology, specifically to DE and to cosmic
ferromagnetism, we have been agnostic about the earlier history of this sector. A
study of temperature dependence of this phenomenon as also phenomenological
inputs from the cosmic dawn data would help to sharpen this scenario.
7 Questions from the Audience
Here we address two of the more important questions raised variously by several
members of the audience, which we take the liberty to recapitulate and freely
paraphrase. We gratefully acknowledge these inputs as having sharpened our
understanding of our proposal.
Q1 The condensed state of the magninos seems to define a special frame of
reference. Does that not conflict with the standard cosmology?
487
Since the domain structure is completely random we expect zero large-scale
magnetic field on the average. Residual departure from this average can be estimated
by assuming that the deviation from the mean grows as
√
N as we include N
domains. Thus if the X-magnetic field in individual domains has the value B dom ,
then on the scale of galactic clusters L gal it possesses a root mean square value
ΔB ≡ B dom (L/L gal ) 3/2 .
Assuming U(1) X field mixes kinetically with standard electromagnetism through
term of the form ξF μν F X
μν , the ξ is well constrained from Supernova 1987A data to
[32] 10 −7 < ξ < 10 −9 . The exact value of the seed required depends on the epoch
being studied and other model dependent factors [33]. We consider the possibility
of a seed of 10 −30 T with a coherence length of 0.1 kpc ∼ 3 × 10 18 m obtained with
ξ = 10 −8 .
ΔB seed = 10
−30 T ∼ 10
−8
×
m M
eV
2
e
e
β
3
L
m
3/2
× 10
−40 T
(11)
From this, representative values for L for β = 0.1 are in the range 10 11 to
10 13 m which is solar system size. A detailed treatment to estimate the residual
fluxes on large coherence length scales could trace the statistics of flux values in
near neighbour domains and the rate at which the magnetic flux could undergo
percolation, providing perhaps a smaller value for L, which should tally with above.
6 Conclusions
We have proposed the possibility of a negative pressure medium as arising from
nothing more radical than a peculiar ground state of a pair of asymmetric fermion
species interacting through an unbroken abelian gauge force. In an attempt to highlight the potential utility of the PAAI to cosmology, specifically to DE and to cosmic
ferromagnetism, we have been agnostic about the earlier history of this sector. A
study of temperature dependence of this phenomenon as also phenomenological
inputs from the cosmic dawn data would help to sharpen this scenario.
7 Questions from the Audience
Here we address two of the more important questions raised variously by several
members of the audience, which we take the liberty to recapitulate and freely
paraphrase. We gratefully acknowledge these inputs as having sharpened our
understanding of our proposal.
Q1 The condensed state of the magninos seems to define a special frame of
reference. Does that not conflict with the standard cosmology?