научная статья по теме COSMOLOGY AND NEUTRINO PROPERTIES Физика

Текст научной статьи на тему «COSMOLOGY AND NEUTRINO PROPERTIES»

ЯДЕРНАЯ ФИЗИКА, 2008, том 71, № 12, с. 2189-2201

ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ

COSMOLOGY AND NEUTRINO PROPERTIES

© 2008 A. D. Dolgov

Institute of Theoretical and Experimental Physics, Moscow, Russia; University of Ferrara and INFN, Italy Received March 21, 2008

A brief review for particle physicists on cosmological impact of neutrinos and on restrictions on neutrino properties from cosmology is given. The paper includes discussion of upper bounds on neutrino mass and possible ways to relax them, methods to observe the cosmic-neutrino background, bounds on the cosmological lepton asymmetry which are strongly improved by neutrino oscillations, cosmological effects of breaking of spin-statistics theorem for neutrinos, bounds on mixing parameters of active and possible sterile neutrinos with the account of active-neutrino oscillations, bounds on right-handed currents and neutrino magnetic moments, and some more.

PACS: 04.90.+e

1. INTRODUCTION

Neutrino is the weakest of all known elementary particles, but despite that, or maybe because of that, cosmological impact of neutrinos is significant. Neutrinos are important for cosmology and, vice versa, astronomy allows to measure neutrino properties with precision which is in many cases higher than the precision of direct experiments.

Neutrinos are the second most abundant particle in the Universe (after photons of cosmic microwave background (CMBR)), their total number density, with antineutrino included, is

j

(nv + nv) & 340/cm3

(1)

almost equally shared between all three active neutrino species ve, vM, and vT. For comparison the average cosmological number density of the normal baryonic matter is

he « 2.5 x 10"7/cm3. (2)

The average momentum of cosmic neutrinos is very low, about 6.1 K ~ 5.3 x 10"4 eV. The cosmic neutrino background (CvB) is not observable directly at the present time, because of the very weak interactions of these low-energy neutrinos. Still their cosmological impact is profound.

In this paper I will consider cosmological effects produced by neutrinos and cosmological bounds on neutrino properties. More detailed discussion can be found in the review paper [ 1], but presentation here contains some recent development.

The paper concerned with the (i) cosmological bounds on neutrino masses, mv; (ii) possibility of

direct registration of CvB; (iii) restriction on the number of neutrino species from Big-Bang nucleosynthesis (BBN) and CMBR; (iv) neutrino statistics and cosmology; (v) neutrino oscillations, BBN, and cosmological lepton asymmetry; (vi) right-handed currents and magnetic moment of neutrinos.

2. THERMAL HISTORY OF NEUTRINOS

AND GERSTEIN-ZELDOVICH BOUND

In the early Universe at T > 1 MeV neutrinos were in thermal equilibrium with electron-positron pairs and photons. Correspondingly, their number density was

Hv = (3/8)h7 (3)

for each left-handed neutrino flavor, ve, vM, vT, under assumption of vanishing asymmetry between neutrinos and antineutrinos, i.e.,

Hv = Hi,. (4)

The condition for thermal equilibrium is found by comparing the neutrino reaction rate, r = an ~ ~ gft5, with the cosmological expansion rate, H = = a/a ~ T2/mPl. If r > H, thermal equilibrium is established. This took place at T > 1 MeV.

More accurate treatment based on solution of the kinetic equation governing neutrino distribution [1] shows that ve decoupled from the electron—positron pairs at T k> 2 MeV, while v^T decoupled at T k> ^ 3 MeV. Interactions between neutrinos maintain their kinetic equilibrium down to lower temperatures, Tve = 1.3 MeV and Tv^vT = 1.5 MeV for Ve and v^T, respectively. Below these temperatures neutrinos practically decoupled from the plasma and free

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streamed with the speed of light till they became nonrelativistic.

At smaller temperatures, T < me, photons were heated by e+e- annihilation, while v were not, because they had already decoupled from the electromagnetic component of the primordial plasma. The increased number density of photons had led to the decrease of the neutrino-to-photon ratio:

nv + n = (3/11)nY = 112/cm3

(5)

The coefficient 3/11 is obtained from the entropy conservation and the numerical value of the neutrino + antineutrino number density is presented for the present-day Universe and obtained from the measured number density of photons in CMBR, nY = = (410.5 ± 0.5)/cm3.

As a result of the photon heating, the temperature of neutrinos dropped down with respect to the photon temperature:

Tv = 0.714T7 = 1.945 K = 1.68 x 10-4 eV, (6)

where the second equality is written for the present-day neutrino temperature calculated from the known value of TY = 2.725 K. One should remember, however, that for massive neutrinos the distribution function has the form

fv = [exp(p/T) + 1]

-1

(7)

It is not equilibrium distribution because in the equilibrium one there should be the neutrino energy E instead of momentum p as in Eq. (7). So, strictly speaking, parameter T here is not temperature. The difference, however, is essential only at low temperatures, T ~ mv.

Knowing the number density of neutrinos in the present-day Universe we can calculate their energy density and from the condition that the latter does not exceed the measured energy density of matter we obtain the cosmological bound on neutrino mass:

E

mh

< 94Qmh2 eV,

(8)

where h = #/(100 km s" -1 Mpc ) is the dimension-less Hubble parameter and üm is the fraction of the energy of matter relative the critical energy density, pc = 3H2mpx/8n. This bound was derived by Gerstein and Zeldovich (GZ) in 1967 [2].

Using the observational data, üm < 0.25 and h = = 0.7, we find:

E

mh

< 11.5 eV.

(9)

This bound can be further improved by factor ^3 because too large energy density of neutrinos would inhibit large-scale structure (LSS) formation at relatively small scales and at high red shifts, z > 1. In simple words, neutrinos are fast and reluctant to form gravitationally bound systems. To eliminate such an undesirable property the mass density of hot dark matter, created by cosmic neutrinos should not exceed ^30% of the total matter density. Correspondingly,

mUa < 1.2 eV. (11)

This is a robust and quite strong bound, stronger than that obtained in the direct experiments.

The best bounds on neutrino mass, obtained from tritium decay experiments (Troitsk and Mainz) is [3]:

mVe < 2-3 eV. (12)

Though this bound is usually presented as a bound on the mass of electronic neutrino, it is inaccurate because, as we know from the measured neutrino oscillations, mass eigenstates are strongly different from the flavor eigenstates, i.e., from . Neutrino oscillations allow to measure only two mass differences of three mass eigenstates, but not the absolute value of the mass. Neutrino oscillation data are best fitted with [3]

moiar = (5.4-9.5) x 10-5 eV2, (13)

'atm

ömlm = (1.2-4.8) x 10"3 eV2.

For almost equal masses of neutrinos (as we know from neutrino oscillations)

mv

< 3.9 eV.

(10)

Presently telescopes allow to weight neutrinos more accurately than direct experiments. Astronomy can be sensitive to

mv - (a few) x 10-1 eV, (14)

based on combined data on LSS and CMBR (see Section 5).

Historical remark: the paper by Gerstein and Zeldovich "Rest mass of muonic neutrino and cosmology" was published in 1966 [2]. Six years later a similar paper by Cowsik and McClelland [4] "An upper limit on the neutrino rest mass" was published. In many subsequent works the cosmological bound on neutrino mass is quoted as "Cowsik—McClelland bound". This is not just, however, firstly, because the GZ paper was much earlier and, secondly, in the paper by Cowsik and McClelland the effect of photon heating by e+e- annihilation was disregarded and both helicity states of neutrinos, left-handed and right-handed, were assumed to be equally populated. This incorrectly gives rise to 7 times stronger bound.

We know that only left-handed neutrinos participate in weak interactions. If neutrino mass is nonzero, the other, right-handed state, must exist. However, right-handed neutrinos could be in equilibrium only

a

a

a

a

a

at very high temperatures and even if they were abundantly created at some early cosmological stage, they would be strongly diluted by entropy released in massive particle annihilation and so their number density would normally be negligible at T~ MeV.

2.1. Is It Possible to Relax the GZ Bound?

Let us critically discuss essential assumptions used in the derivation of the GZ bound and check if they can be modified in such a way that the present-day number density of CvB would be noticeably smaller than the standard one (5) and thus would allow for a larger neutrino mass.

The obtained upper bound on mv is based on the following:

1. Thermal equilibrium in the early Universe.

It is surely true in the standard cosmology. Neutrinos would not be produced in equilibrium amount if the primeval plasma temperature were never larger than a few MeV [5]. It could be realized in inflationary models with anomalously low (re)heating temperature. However, a smaller number density of neutrinos during BBN would distort successful predictions for light-element abundances. The problems with baryo-genesis would be also serious.

2. Nonvanishing lepton asymmetry. We assumed that number density of neutrinos is equal to that of antineutrinos. If the primeval plasma has a nonzero lepton asymmetry, this equality would be broken. However, in thermal equilibrium the total number density nv + h„ would be larger in asymmetric case and the upper bound on mv would be stronger. Moreover, as we see below, the cosmologi-cal lepton asymmetry is strongly bounded from above and cannot noticeably change the neutrino number density.

3. Conservation of the ratio nv/nY from 1 MeV to the present day. If there are some extra sources of heating of the photon plasma below MeV, the ratio nv/nY would be smaller than (5). This can be achieved, e.g., by electromagnetic decays of new ligh

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