Constraints on cosmic charge asymmetry and neutrino charge from the microwave background

4 Pages·0.06 MB·English

by  Sujan Sengupta

January 1995 IIA-NAPP-95-1
Constraints on cosmic charge asymmetry and
neutrino charge from the microwave background
Sujan Sengupta and Palash B. Pal
∗ †
Indian Institute of Astrophysics, Bangalore 560034, INDIA
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Abstract
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1 Considering the observed anisotropy in cosmic microwave background radiation
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(∆T/T 10−4) an upper limit on the electric charge asymmetry over a cosmologi-
≤
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cal scale is found which is several orders more stringent than those found earlier. The
v
1 same argument constrains the charge of massless, degenerate neutrinos.
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1 PACS numbers : 98.80.-k, 98.70.Vc, 95.85.Ry One possibility which has excited particular inter-
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5 est over the years is the question of whether matter in particular and the Universe in general have
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absolute charge symmetry. Interest in the subject was aroused following the suggestion by Bondi
/
h
p and Littleton [1] that if the electron and proton charge differed by a part in 1018 it would account
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p for the expansion of the Universe. This was followed by the experiment of Hillas and Cranshaw [2].
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h Afterwards the work gained general acceptance by the scientific community and there were several
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v experiments (see for example Ref. [3]) to detect charge asymmetry in matter. All these experi-
i
X ments put definite upper limits on the charge asymmetry although they are much lower than that
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a required by Bondi and Littleton. However, since the strength of the electromagnetic interaction is
1039 times stronger than the gravitational interaction any small asymmetry could have a profound
consequence. Recently it has been suggested [4] that a net charge asymmetry could generate chaotic
magnetic field on astronomically interesting scales.
In thiscontext we show inthis letter that aslight excess inelectric chargeover a cosmic scale can
have severe consequence on the observed isotropy in the cosmic microwave background radiation
and hence put a limit on the net charge asymmetry of the Universe which is several orders more
stringent than the existing limits. Following the same arguments a stringent upper limit on the
electric charge of massless, degenerate neutrinos is obtained.
Let n be the present excess number density of particles with charge e over the particles of
Q
opposite charge. Then n e is the present charge density which gives rise to the charge asymmetry
Q
over cosmic scales. Consider now a sphere of significantly large radius R. The electric forces will
∗e-mail: [email protected]
†e-mail: [email protected]
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generate peculiar velocities in the particles in very much the same way the gravitational density
perturbations do. Thus, just as the gravitational density perturbations induce temperature fluc-
tuations in the microwave background (the Sachs-Wolfe effect [5]), the electrical forces will induce
the same. To estimate the effect, we first note that the electric self-energy of the particles in this
sphere can be written as
16π2
(el) = n2αR5, (1)
ER 15 Q
where α = 1/137 is the fine structure constant. On the other hand, the gravitational self-energy of
the same sphere due to the uniform background mass density ρ is given by
16π2
(gr) = Gρ2R5. (2)
ER 15
The ratio of these two gives the temperature fluctuation in the background radiation:
∆T (el) n2α
ER = Q . (3)
T ≈ (gr) Gρ2
ER
This provides an upper limit on n given by
Q
G ∆T
n ρ . (4)
Q
≤ sα ×(cid:18) T (cid:19)obs
Considering the universe to have critical density given by
ρ = 104h2 eV/cm3, (5)
c 0
where h is the Hubble parameter in units of 100kms−1Mpc−1, we thus obtain
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n 9.6 10−26h2 cm−3, (6)
Q ≤ × 0
using ∆T/T 10−4 [6, 7]. Equivalently, one can write
≤
n
Q 3.2 10−29h2, (7)
s ≤ × 0
where s is the entropy density of the microwave background radiation, whose value at the present
epoch is 2970 cm−3 for T = 2.75◦K.
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The above limit is several orders more stringent than the existing limit n /s 10−27 [1]. It is
Q
≤
comparable with the stringent bound onthe net excess of charge per baryon constrained to be below
10−30 from arguments involving the isotropy of cosmic rays, i.e., anisotropy induced by electric field
[8]. In these arguments for isotropy of high energy cosmic rays of energy E, one requires the product
of the coherence length and the field to be less than E giving the limit of 10−30.
We now turn our attention to the bounds on the electric charge of the neutrino. Considering
the bunching in time of the neutrinos detected from SN1987A in LMC, Barbiellini and Cocconi [9]
found the upper limit of the neutrino electric charge to be 10−17e. This limit is substantially smaller
than the limit 10−13e obtained from arguments on solar energy losses [10]. Assuming the bulk of
the dark matter in galactic halos and clusters constituted by non-zero rest mass neutrinos a more
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stringent limit (10−26e) is found [11]. Considering the galactic magnetic field B 10−6G at a
G
≃
cosmic scale R = 10kpc and the virial velocity of neutrinos in the galactic magnetic field to be 300
kms−1 the same author found the limit of the neutrino electric charge to be 2 10−32e. Although
×
this is a very stringent limit, its derivation does not have any strong observational support as it
depends on the hot dark matter hypothesis. Further, the numerical value of the charge is highly
sensitive to the rest mass of neutrino which is rather uncertain (only the electron neutrino mass is
considered in this work without taking into account the opposite charge of antineutrinos).
Our argument from temperature fluctuations can be applied to constrain the electric charge of
massless neutrinos if they are degenerate. Let µ be the chemical potential of the neutrinos where i
i
implies electron, muon andtauneutrinos. Inthedegenerate limit ( µ T ) the massless neutrinos
i ν
| | ≫
contribute an amount [12]
1 3
ρ [ µ4] (8)
ν+ν ≃ 8π2 i
i=1
X
to the present energy density of the Universe. Requiring ρ ρ , we obtain
ν+ν c
≤
1/4
3
µ4 8.9 10−3 h eV. (9)
i! ≤ × 0
Xi=1 q
Assuming all flavors of neutrinos are equally degenerate, this gives
µ µ µ
1 2 3
| | = | | = | | 53 h , (10)
0
T T T ≤
ν ν ν q
◦
using T = 1.96 K.
ν
The net lepton number density contributed by neutrinos is given by [13]
3 1 3
n (n n ) = [π2µ T2 +µ3] (11)
Q ≡ i − i 6π2 i ν i
i=1 i=1
X X
where n denotes the number density of antineutrinos. Thus, if the neutrinos have a charge q, this
i
will produce a net charge density of the magnitude qn . The argument leading to Eq. (6) now gives
Q
q 3
[π2µ T2 +µ3] 4.8 10−25h2 cm−3, (12)
e i ν i ≤ × 0
i=1
X
where e = √α in our natural units where h¯ = c = 1. This is a strong correlated limit on the possible
values of neutrino charge and degeneracy. In the specific case when the neutrinos are maximally
degenerate as given by Eq. (10), we obtain the following bound on neutrino charge:
q 5.2 10−33e h . (13)
0
| | ≤ × ×
q
This is more stringent than any other limit derived so far. The derivation of the above limit assumes
complete degeneracy of neutrino with zero rest mass. However if the chemical potential of neutrino
is zero then there would be no net charge excess and the above argument is not applicable.
In conclusion, we would like to point out that the constraints we derived here are direct con-
sequences of the observed anisotropy in cosmic microwave background radiation, and hence they
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are more stringent than the other limits derived earlier. Our limit from the anisotropy of CMBR
implies that it is very unlikely to have any other profound consequences due to the electric charge
asymmetry of the Universe or the electric charge of neutrinos since such consequences require much
higher asymmetries than are allowed by our limit.
We thank C. Sivaram for discussions.
References
[1] R. A. Lyttleton and H. Bondi, Proc. Roy. Soc. (London) A252 (1959) 313.
[2] A. M. Hillas and T. E. Cranshaw, Nature 184 (1959) 892.
[3] H. F. Dylla and J. G. King, Phys. Rev. A7 (1973) 1224.
[4] A. Dolgov and J. Silk, Phys. Rev. D47 (1993) 3144.
[5] R. K. Sachs and A. M. Wolfe, Ap. J 147 (1967) 73.
[6] E. B. Fomalont, R. B. Partridge, J. D. Lowenthal and R. A. Windhorst, Astrophys. J. 404
(1993) 8.
[7] S. J. E. Radford, Astrophys. J. Lett. 404 (1993) L33.
[8] S. Orito and M. Yoshimura, Phys. Rev. Lett. 54 (1985) 2457.
[9] G. Barbiellini and G. Cocconi, Nature 329 (1987) 21.
[10] J. Bernstein and M. Ruderman, Phys. Rev. 132 (1963) 1227.
[11] C. Sivaram, Prog. Theor. Phys. 82 (1989) 215.
[12] S. Weinberg, Gravitation and Cosmology, Ch. 15 (John Wiley, New York 1972).
[13] E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, Redwood City 1990).
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