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astro-ph/9410065 20 Oct 94 Astrophysical MeV Fermi National Accelerator Lab oratory Batavia IL c Enrico Fermi Institute The University ofb Chicago Chicago IL University of Chicago Chicago IL a Geza Gyuk pro ducts the must b e less than Irresp ective of decay mo de for or less than provided interesting less than trinos to the massother density things and through their ra interactions number of types and so on but also interesting astrophysical and cosmological scenarios how type I I sup ernovae agreement b etween the cold dark theory of structure formation and observations and helping to explain relic velocity time magnetic and transition p er novae which o ccur at a rate of ab out sec of around one p er the atmosphere rain downtheir on p ower the in earth at a rate the has b een used to obtain imp ortant constraints to the ordinary of NASA Astrophysics Center Department of Physics Departments of Physics and of Astronomy Astrophysics Terrestrial Neutrinos are ubiquitous in the cosmos Because energy INTRODUCTION prop erties observable These limits follow from considering among sp ecies abundance density of stars  of astrophysical a c of propagation  MeV Ma jorana keV Dirac and order all the cosmic contribution of neu and and Michael S Turner and 4 of neutrinos like He mass fraction or high greater than from Heavenly this 6 cm type the and sec MeV our Neutrino the explo de the m number sec and sun II  Cosmological secret pro duce Neutrinos pro duced heavenly big core MeV p er cosmological radiate including mass life exp eriments  of neutrino bang moments charge Exploring  ie explosion collapse sec the mass of the must b e either approximately A ab out lab MeV Ma jorana or Dirac provided is b tau additional c neutrinos cm can consequences severely the MeV mass range not only prob es fundamental neutrino sp ecies sup er Their Even Constraints and If the dominant decay mo de includes electromagnetic daughter in in of constrain allowing of mass relaxing and primordial nucleosynthesis diative decays Universe cluded is shown inregions Figs of the masslifetime planeCherenkov that detectors can b e ex I I and IrvineMichiganBrookhaven IMB water from SN A detected by thecay Kamiokande mass I I charge K and sowhite on on dwarf the stars neutrino trino burst the emission up on eects the of evolution of radiative red de giant and neutrinos including neutrino structure of account additive to improve the agreement b etween the 4 deuterium abundance improving signicantly the Neutrinos mass b etween the bigbang cosmological and mass the for eV sp ecies in the Universe and and the Mischief MeV bigbang nucleosynthesis the and can to to more additional CBR bulk  lifetime eV of the diuse implications have  and mass nucleosynthesis recently A partial summary of the of has MeV  imp ortant the of neutrino eV the the eects b een to and an mass 12 accommo date a can MeV eects sec keV Dirac the neutrino suggested to For physics density have astrophysical sp ecies b ound formation of eV tau background example of a neutrino massive of neu MeV sp ecies host of would to as a up on the low the an of a

Figure Excluded region of the masslifetime Figure Excluded region of the masslifetime

plane for a neutrino that decays radiatively plane based up on the contribution to the cosmic

from Ref mass density from Ref

cold dark matter picture of structure formation just ab ove MeV in the foreseeable future the

and observations Sciama has emphasized that tauneutrino mass sensitivity may b e improved

a neutrino of mass eV and radiative lifetime to MeV or lower Constraints from primor

of around sec would explain how the bulk of dial nucleosynthesis and SN A allow the mass

the matter in the present Universe b ecame ion limit for a longlived sec tau neutrino to



ized as well as accounting for the dark matter b e lowered to around MeV Ma jorana and

Neutrino oscillations provide a very attractive so to around keV Dirac On the other hand

lution to the solarneutrino problem and have for b etween MeV and MeV there are

even b een suggested as a means for explaining lifetimes and decay mo des that led to very in

how sup ernovae explo de teresting astrophysical and cosmological conse

The topic of neutrinos astrophysics and cos quences relaxing the bigbang nucleosynthesis

mology is a very rich one indeed and it is not b ound to the baryon density and to the num

our intent to try to summarize it here excellent b er of neutrino sp ecies allowing bigbang nucle

reviews exist Rather we will discuss recent osynthesis to accommo date a low less than

work concerning the astrophysical and cosmolog He mass fraction or high greater than

ical constraints to and interesting consequences deuterium abundance improving signicantly the

of an MeV tau neutrino This work is timely for agreement b etween the cold dark matter theory of

two reasons The current lab oratory mass limit is structure formation and observations and help

cussing on nal states containing ve The

CLEO data set has such decays and the AR

GUS data set has such decays By searching

for events close to the kinematic endp oint they

are able to set the following CL upp er lim

its to the tauneutrino mass

MeV ARGUS MeV CLEO

Detector and accelerator upgrades at CLEO as

well as the study of other decay mo des eg

nal states with should lead to improved

mass sensitivity p erhaps as low as MeV or

so In addition the LEP collab orations are b e

ginning to study tau physics including the tau

neutrino mass Finally up coming exp eriments at

Bfactories and taucharm factories if built may

b e helpful

A b eamdump exp eriment at CERN using the

BEBC set a very restrictive limit to the decay

of tau neutrinos to channels that include electro



magnetic daughter pro ducts e and

The absence of such electromagnetic interactions

in the BEBC excludes a radiative decay rate in

the interval

m m

Figure Excluded region of the masslifetime

sec  sec

rad

 

MeV MeV

plane for a neutrino that decays radiatively based

As we will describ e this limit together with those

up on type I I sup ernovae white dwarf co oling and

based up on SN A and primordial nucleosyn

red giant evolution from Ref

thesis all but exclude a tau neutrino that is more

massive than ab out MeV and that decays pri

marily through radiative mo des

ing to explain how type II sup ernovae explo de

SN A

While the theoretical motivation for an MeV

When the core of a massive star exhausts its

mass tau neutrino is not strongthere are some

nuclear fuel and collapses to form a star

mo delswe wish to stress that exploring the MeV

most of its binding energy ab out  erg is

mass range allows tests of intriguing astrophysi

released in thermal neutrinos of all three sp ecies

calcosmological scenarios

A neutron star is so dense that neutrinos b ecome

trapp ed and are emitted from a neutrinosphere

MASSLIFETIME CONSTRAINTS

whose temp erature is ab out MeV In all more

than neutrinos p er sp ecies of average en Lab oratory

ergy around MeV are emitted during the ini There are two very imp ortant lab oratory con

tial sec to sec of co oling The detection of straints that to the mass based up on the kine

neutrino events asso ciated with SN A by the matics of tau decays and that to the radia

IMB and KI I detectors provided dramatic conr tive lifetime based on the Big Europ ean Bubble

mation of this picture The enormous ux of neu Chamber BEBC b eamdump exp eriment

trinos emitted the b eautiful KI I and IMB data The CLEO and ARGUS collab orations have

and our theoretical understanding of type I I core studied the decays of millions of tau fo

collapse sup ernovae make SN A a wonderful gammaray detectors which were in op eration at

lab oratory for probing neutrino prop erties as has the time Since the neutrino uence on earth was

b een summarized elsewhere nearly cm and that of gammarays dur

So far as tau neutrinos are concerned there ing the sec interval at the time of the neutrino

are three imp ortant SN A constraints The burst was less than ab out cm this leads to a

rst involves Dirac neutrinos b ecause of the mis very stringent constraint Additional con

match b etween and helicity for a mas straints of this type have b een obtained recently

sive neutrino neutrino scattering deep from GRO Comptel observations of SN A at

inside a hot young neutron star can transform late times and of SN J

a prop erhelicity neutrino into a wronghelicity Given the tauneutrino mass lifetime and ux

neutrino whose interactions are weaker by a fac from a hot neutron star it is a simple matter to

tor of m E These wronghelicity neutri derive the constraints that follow from SN A

nos are emitted copiously from the core where There is a slight hitch in getting the tauneutrino

temp eratures reach MeV or higher and sim ux for masses in the MeV range the neutri

ply stream out For a Dirac mass b etween ab out nosphere temp erature is only MeV for a mass

keV and MeV and lifetime greater than ab out less neutrino sp ecies so that suppression of the

sec m MeV they quickly rob the core of neutrino ux should b ecome imp ortant for masses

its thermal reserves leading to a burst of prop er ab ove MeV Recently the neutrinosphere tem

helicity neutrinos from the neutrinosphere that p erature and neutrino ux for a massive neutrino

is to o short to b e consistent with the KI I and sp ecies has b een calculated using a simple but

IMB data the timing argument For accurate mo del based up on the diusion approx

masses larger than around MeV the wrong imation Ab ove a mass of MeV the neu

helicity states b ecome trapp ed and are radiated trinosphere temp erature slowly rises with mass

from a wronghelicity neutrinosphere whose tem reaching ab out MeV for a mass of MeV

p erature b ecomes close to that of the ordinary This means that the neutrino ux falls more

neutrinosphere for a mass of MeV for lifetimes slowly than a naive estimate using the Boltzmann

shorter than ab out sec m MeV they de factor for T MeV would suggest The su

cay inside the neutron star p ernovae constraints based up on our uxes for a

If Dirac neutrino decays pro duce massive tau neutrino are shown in Fig

or neutrinos or antineutrinos and their

lifetime is b etween sec m MeV and 

Bigbang nucleosynthesis

sec m MeV then masses as low as keV

Bigbang nucleosynthesis is one of the great

are excluded on the basis of the very highenergy

successes of the standard cosmology Provided

of order MeV events they should have pro

that the baryontophoton ratio is b etween 

duced in the KI I and IMB detectors and appar

and  the predictions for the pri

ently didnt

mordial abundances of D He He and Li

The second and third constraints involve radia

which span nine orders of magnitude are con

tive decay of tau neutrinos emitted from the neu

sistent with their measured abundances

trinosphere Decays inside the progenitor star

Nonstandard assumptions ab out the physics of

radius of ab out  cm will b e absorb ed by

the early Universe eg additional light particle

the star and pro duce energy that is visible ei

sp ecies such as neutrinos an MeVmass tau neu

ther thermalized and radiated from the photo

trino or a slight change in the gravitational con

sphere ab out erg is actually seen as the su

stant can upset this success and primordial nu

p ernova reworks or in the bulk motion of the

cleosynthesis has b een used often as a heavenly

expanding shell ab out erg is seen De

lab oratory to study physics b eyond the standard

cays outside the progenitor that pro duce a pho

mo del

ton lead to a ux of highenergy gamma rays

An unstable MeVmass tau neutrino aects

that could have b een seen by the SMM and PVO nucleosynthesis in three dierent ways dep ending

the decays o ccur around the time of nucleosynthe

sis then for a xed predecay baryontophoton

the baryontophoton ratio at the time of nucle

osynthesis is smaller leading to decreased He

pro duction and increased D pro duction

The third and most interesting eect o ccurs if

tauneutrino decays pro duce electron neutrinos

and antineutrinos Through the weak interac

tions n $ p e and n e $ p these

e e

neutrinos can aect the neutron fraction which

in turn controls the amount of He synthesized

essentially all the wind up in He so

the He mass fraction pro duced Y ' In

P n

the standard picture the weak interactions that

regulate the neutron fraction cease o ccurring on

a cosmological timescale when the temp erature

of the Universe is ab out MeV thereafter the

neutron fraction no longer tracks its equilibrium

value and remains roughly constant until nucle

Figure Excluded regions of the masslifetime

osynthesis commences T  MeV at a value

plane for a MeV neutrino that decays radia

X '

n

tively based up on nondetection of rays from

If decayproduced electron neutrinos and an

SNA region lab eled SMM light and ki

tineutrinos have high energies ie E 

netic energy seen in SNA b elow curve la

T m m  MeV corresp onding to a tau

n p

b eled SNL CLEOARGUS mass limit and the

neutrino mass greater than ab out MeV then

BEBC b eam dump b elow curve These results

the probability to convert a neutron to a

are for a Dirac neutrino Ma jorana results are

is roughly equal to that to convert a proton to a

similar from Ref

neutron However there are seven times as many

as neutrons so the net eect is to pro

duce more neutrons than protons increasing the

neutron fraction and ultimately He pro duction

up on its mass lifetime and decay mo des First

In the other extreme where the decay

the energy density of it and its daughter pro d

pro duced neutrinos and antineutrinos have low

ucts contribute to the total energy density which

energies corresp onding to a tauneutrino mass

aects the expansion rate of the Universe Be

less than ab out MeV the conversion of protons

cause neutrinos cease interacting on a cosmolog

to neutrons but not that of neutrons to protons

ical timescale ab out the time of nucleosynthesis

is suppressed by the neutronproton mass dier

b egins t  sec the energy density of an MeV

ence and there is a net reduction in the neutron

mass tau neutrino can exceed that of a massless

fraction leading to decreased He pro duction see

neutrino sp ecies after their annihilations freeze

Fig

out the number of massive tau neutrinos remains

We have mo died the standard bigbang nucle

constant so that their energy density decreases as

osynthesis co de to accommo date all three eects

R while that of a massless sp ecies decreases

Briey our assumptions and changes to the

as R R is the cosmicscale factor The main

co de are

eect of the energy density is on the yield of He

higher energy density leads to more He

Second if the daughter pro ducts include pho The abundance of tau neutrinos p er co



tons or e pairs tauneutrino decays pro duce en moving volume is assumed to b e constant

tropy which lowers the baryontophoton ratio If and determined by their electroweak annihi

lation channels ! e e Tau neutrino decays to daughter pro ducts

e e

The assumption that annihilations have that include sterile and particles

ceased b efore nucleosynthesis and the ne that interact electromagnetically eg !

glect of inverse decays has b een studied and For this mo de b oth the energy den

is well justied for the masses and lifetimes sity of the tau neutrino and its daughter

m MeV In of interest sec pro ducts and entropy pro duction aect nu



Ref the regime of very short lifetimes is cleosynthesis

addressed for the decay mo de !

Tau neutrino decays to daughter pro ducts

that include electron neutrinos eg !

Electromagnetic daughter pro ducts eg



or For this mo de b oth

e pairs and photons are assumed to

e e e e

the energy density of the tau neutrino and

rapidly thermalize and thereby increase the

its daughter pro ducts and the change in the

entropy density

weak rates aect nucleosynthesis

Sterile daughter pro ducts ie those with

Tau neutrino decays to daughter pro ducts

weak interactions or weakermuon neutri

that include electron neutrinos and parti

nos or NambuGoldstone b osons are as

cles that interact electromagnetically eg

sumed to b e relativistic and noninteracting



! e For this mo de all three ef

e

The phase space distribution of electron fects come into play

and muon neutrinos and antineutrinos is

followed by integrating the Boltzmann

equations including all the usual elec

 

troweak interactions e $ e $

e e $ as well as the decays

of tau neutrinos

The weak rates that control the neutron

toproton ratio n e $ p n $

e e

p e n $ p e are mo died to take

e

into account the p erturb ed phasespace dis

tribution of and antineu

trinos

The eect of a decaying tau neutrino on pri

mordial nucleosynthesis dep ends up on its decay

mo de Based up on the three ways in which nu

cleosynthesis is aected we have identied four

generic decay mo des that bracket the larger

range of p ossibilities

Figure The eect of a neutrino that decays

! on He pro duction from Ref

e

Tau neutrino decays to daughter pro ducts

that are sterile eg ! or

sterile

for lifetimes greater than a few sec

Figures and show the eect of tau neutrinos onds it is a go o d approximation to treat

of dierent masses and dierent decay mo des on muon neutrinos as noninteracting For this

the pro duction of He as a function of lifetime mo de the only eect on nucleosynthesis is

Because the He abundance is so well known through the energy density of the tau neu

Y ' it oers the most leverage trino and its daughter pro ducts P

Figure Regions of the masslifetime plane that

Figure The eect of a neutrino on He pro

are excluded on the basis of nucleosynthesis to

duction for the generic decay mo des !

the right of the curves for the four generic decay

denotes the all sterile decay mo de from Ref

mo des Dirac Our results are not reliable in the

region denoted by NA from Ref

When the eect of a decaying tau neutrino up on

the yields of primordial nucleosynthesis are sig

ucts include electron or muon neutrinos and

nicant they are almost always deleterious and

 sec m MeV A mass



large regions of the masslifetime plane can b e

of approximately MeV is allowed as the

excluded The excluded regions for the dierent

nucleosynthesis b ounds cut out around

generic decay mo des are shown in Figs and

MeV

Conuence of constraints

For the sp ecic decay mo de !

Bringing together all the constraints discussed

primordial nucleosynthesis has b een used to

ab ove the following general statements can b e

exclude masses less than ab out MeV and

made ab out a massive tau neutrino

lifetimes less than ab out sec

If the dominant decay mo de is radia

These b ounds derive in large measure from pri

tive and the lifetime is longer than 

mordial nucleosynthesis where in deriving the

sec m MeV the mass must b e less

abundance of massive tau neutrinos at nucleosyn

than MeV or less than keV for a Dirac

thesis it was assumed that tau neutrinos annihi

sec m MeV neutrino provided

late at the rate given in the standard electroweak



In the Dirac case the lower mass limit

theory If the tau neutrino has mass it will of

falls to ab out keV if the decay pro ducts in

course have additional interactions which could

clude electron or muon neutrinos and

signicantly enhance the annihilation cross sec



 sec m MeV

tion reducing their abundance at nucleosynthesis

and weakening the nucleosynthesis limits

Irresp ective of the decay mo de if the life

With regard to theoretical exp ectations for the

time is longer than ab out sec then the

lifetime of a massive tau neutrino in the stan

mass must b e either around MeV or less

dard electroweak theory an MeVmass tau neu

than MeV Ma jorana keV Dirac



trino can decay ! e with lifetime

e

As b efore in the Dirac case the lower mass

limit falls to ab out keV if the decay pro d G cos m sin

F

out that exp erimentalists searching for an MeV

mass tau neutrino are also exploring interesting

astrophysical and cosmological scenarios

Relaxing the b ound to

B

Bigbang nucleosynthesis constrains the contri

bution of to the mass density of the Uni

verse

h h

B

 

where h is the Hubble constant in units of

km s Mp c For h this b ounds the



fraction of critical density contributed by baryons

to b e less than ab out The case for non

baryonic dark matter hinges up on this decades

old b ound and for this reason many attempts

Figure Same as Fig for a Ma jorana neu

have b een made to circumvent it The most

trino from Ref

recent involved inhomogeneities in the baryonto

photon ratio pro duced in a strongly rstorder

QCD phase transition o ccurring at a temp erature

 sec

of less than ab out MeV However there is no

'

sin m MeV

set of parameters describing the inhomogeneity

that allows the b ound to b e signicantly lo osened

In mo dels with horizontal symmetries the tau

0

moreover current indications are that the QCD

neutrino can decay ! is the Nambu

phase transition is at b est weakly rstorder with

Goldstone b oson of horizontal symmetry with

transition temp erature MeV or higher

lifetime

The upp er b ound to traces to the under

B

sec f GeV

pro duction of D and overproduction of He and

 f m 

m MeV

Li The overproduction of He results b ecause

for high baryon density nucleosynthesis can b e

where f is the scale of horizontalsymmetry

gin earlier when fewer neutrons have decayed

breaking There are other p ossibilities eg de

The overproduction of Li and underpro duction

cay mediated by righthanded gauge interactions

of D results b ecause the neutron fraction at the

in this case the lifetime in Eq scales as

time of nucleosynthesis drops precipitously for

M These two examples serve to illus M

W W

R

high baryon density as nuclear reactions more ef

trate decay mediated by a massive gauge b oson

ciently gobble up free neutrons

and scalar mediated decay

Remarkably a tau neutrino of mass MeV to

MeV and lifetime of sec to sec whose

MISCHIEF

decays pro duce electron neutrinos can remedy

While the astrophysical and cosmological ar the problems with D He and Li simultane

guments discussed ab ove lead to very stringent ously p ermitting the bigbang b ound to b e re

and imp ortant limits there are some very inter laxed by a factor of ten and allowing baryons

esting islands in the masslifetime plane Before to close the Universe see Fig It works

describing the tantalizing astrophysical and cos like this The overproduction of He is avoided

mological consequences of an MeVmass tau neu b ecause the abundance of tau neutrinos is su

trino we wish again to disclaim any strong the ciently low that the equivalent number of mass

oretical motivation for the masses lifetimes and less neutrinos is ab out two The D and Li prob

decay mo des required Our purp ose is to p oint lems are solved by protons capturing antielectron

sho ck that is initiated by the core b ounce stalls neutrinos which pro duce neutrons preventing the

after traveling only a km or so Since each neutron fraction from dropping precipitously

neutrino sp ecies carries erg xes involving

neutrino physics have b een suggested The

tricky part is getting weakly interacting neutri

nos to transfer enough energy to the matter

There is a new solution involving a MeV

MeV tau neutrino It works like this Be

yond the tau neutrinosphere at a temp erature

of around MeV tau neutrinos continue to an

nihilate pro ducing highenergy electron muon

neutrinos and electronp ositron pairs In total

residual tauneutrino annihilations dep osit ab out

erg around km from the core ab out the

right amount of energy and correct lo cation to

help p ower the sho ck see Fig Provided the

lifetime is greater than ab out sec the life time and decay mo de are irrelevant

Energy Deposited

0

Figure Deuterium and Li pro duction as a

-2

function of baryon to photon ratio in the stan

dard scenario solid and with a neutrino that

decays ! broken from Ref

e

-4

The lo osening of the bigbang b ound to Log(Edep/E0)

B -6

works for a wide range of tauneutrino mass and

lifetime However it requires that the abundance of tau neutrinos around nucleosynthesis b e ab out

-8

a factor of ten less than the standard value which

requires that the annihilation cross section b e ab out a factor of ten larger than that in the elec

-10 If neutrinos have mass they nec

troweak mo del 20 40 60 80 100

have additional interactions and so the

essarily Mass (MeV)

annihilation cross section could well b e larger

Explo ding sup ernovae

Figure Energy dep osited b eyond the neutri

While only a small fraction ab out of the

nosphere by residual annihilations in units

energy released in a type I I sup ernova is needed

of E ergs from Ref

to blow up the progenitor star creating the sp ec

tacular reworks and preventing the formation of

a black hole numerical simulations have yet to

succeed in blowing up a massive star The

CDM This is b ecause the Universe underwent a tran

The cold dark matter theory of structure for sition from radiation domination at early times

mation motivated by ination is probably the t  yr to matter domination at late times

most attractive theory of structure formation the which imp oses a feature on the sp ectrum at the

most studied theory of structure formation and scale that crossed the horizon at matterradiation

the most ruled out theory of structure formation equality ab out Mp c see Fig This imp or

Its basic elements are a critical Universe com tant scale dep ends up on the level of radiation in

p osed of ab out baryons and cold dark the Universe the fraction of critical density con

matter slowly moving relic particles such as ax tributed by matter as opp osed to the vacuum

ions or with scaleinvariant density energy asso ciated with a cosmological constant

p erturbations The very precise measurement of and the Hubble constant the critical density de

temp erature uctuations on the tendegree scale p ends up on the Hubble constant In CDM it is

by COBE provides the normalization for the sp ec the radiation level that diers from the standard

trum of density p erturbations scenario The scale imp osed by the transition

There are now ten or so detections of CBR from radiation to matter domination is roughly

anisotropy spanning angular scales from ab out

 

 

rad

to They prob e the sp ectrum of den

 h Mp c

EQ

h

sity p erturbations on length scales from ab out

radstd matter

Mp c to ab out Mp c Mp c corresp onds to

the scale of galaxies and Mp c corresp onds to

the size of the observable Universe In addition

the distribution of matter to day more precisely

light in the form of bright galaxies has b een

prob ed by redshift surveys CfA slices of the Uni

verse IRAS survey APMStromolo survey and

others on scales from ab out Mp c to Mp c

or so While these data conrm the general shap e

of the p ower sp ectrum predicted by CDM viewed

more carefully they seem to indicate a signicant

problem with the simplest version of CDM the

shap e of the sp ectrum is not quite right and the

level of inhomogeneity on small scales is to o high

A number of variants of CDM have b een pro

p osed to remedy this problem They com

prise the CDM Family of Mo dels hot eV to

eV neutrino cold dark matter CDM

tilted cold dark matter TCDM CDM with

a Hubble constant of km s Mp c cold

dark matter cosmological constant CDM

Figure COBE normalized p ower sp ectra for

and CDM which involves an MeVmass tau

standard CDMMCDM and CDM The data

neutrino The last three variants rely up on

p oints are from the IRAS Jy redshift survey

the same x a lower ratio of matter to radiation

from Ref

While the primeval sp ectrum of p erturbations

predicted by ination is scale invariant more

precisely uctuations in the gravitational p oten

tial that are indep endent of scale the sp ectrum

In the standard scenario the radiation con

of density p erturbations we see to day is not tent to day consists of a thermal bath of photons

at temp erature T  K and three at a higher value and thereby to more He pro

massless or nearly massless neutrino sp ecies at duction

temp erature T T K The As just mentioned a tau neutrino that decays

three massless neutrino sp ecies contribute ab out and pro duces electron neutrinos around or shortly

of what photons do In order to t the after the neutron fraction freezes out depresses

largescale structure data b etterin fact very the neutron fraction and He pro duction thereby

wellthe scale should b e ab out a factor of making ro om for additional light particle sp ecies

EQ

two smaller than in the standard case around The eect can b e enormous the equivalent of

h Mp c to h Mp c This can b e accom additional neutrino sp ecies can b e tolerated

plished by decreasing h by a factor of without overproducing He see Fig Relax

matter

which can b e done with a lower Hub ing this bigbang limit could resurrect interesting

ble constant or smaller matter density or by in particlephysics theories that were discarded b e

creasing by a factor of In terms of cause they predict to o many additional light de

rad

additional light neutrino sp ecies the latter corre grees of freedom

sp onds to N which is clearly ruled out

by bigbang nucleosynthesis see b elow and mea

surements of the Z resonance which imply that

N 

An MeVmass tau neutrino can lead to in

creased radiation without violating either b ound

Supp ose the tau neutrino has a mass of b etween

MeV and MeV decays with electron neu

trinos as daughter pro ducts and has a lifetime

of around sec to sec Tau neutrino decays

do two things First they pro duce additional

electron neutrinos and p ossibly other relativistic

particles by virtue of the fact that the decays o c

cur when the tau neutrino is very nonrelativistic

the energy density pro duced is equivalent to many

neutrino sp ecies thereby raising the energy den

sity in radiation by the required amount Second

the electron neutrinos pro duced depress the neu

tron fraction and ultimately the He abundance

thus preventing overproduction of He that would

results from the higher energy density

Figure Additional massless sp ecies ex

pressed in equivalent number of massless neutrino

Relaxing the b ound to N

sp ecies p ermitted for the ! decay mo de

e The constraint to the number of light mass

from Ref

less than ab out MeV particle sp ecies based

up on bigbang nucleosynthesis is probably the

b est known of all the imp ortant astrophysical

and cosmological limits Expressed in equivalent

Saving bigbang nucleosynthesis itself number of neutrino sp ecies the limit is N 

The agreement b etween the predicted light The limit is based up on the overproduction

element abundances and their measured abun of He additional light particle sp ecies lead to an

dances is p erhaps the most stringent test of the increase in the energy density at xed temp er

standard cosmology The agreement has b ecome ature in turn leading to more expansion This

more impressive with time Shortly after the dis leads to an earlier freeze of the neutron fraction

covery of the CBR the main success was the ex the NASA through grant NAGW at Fermi

planation of the large primeval He abundance lab GG was supp orted by an NSF predo ctoral

by the mid s it was realized that the big fellowship

bang was the only plausible source for D and in

the s b oth He and Li were added to the

REFERENCES

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At present bigbang nucleosynthesis can ac

See eg Kolb et al The Early Universe Ad

count for the measured primordial abundances of

dison Wesley Redwoo d City CA Chp

all four light elements provided that the baryon

G G Raelt Phys Rep

tophoton ratio lies in a very narrow interval

S Bludmar Phys Rev D

    With time the

Q Sha and F W Stecker Phys Rev Lett

concordance interval has shrunkand could even

M Davis F Summers and

disapp ear For example should the primeval

D Schlegel Nature A van

He abundance b e shown to b e or less He

Dalen and R K Schaefer Astrophys J

would push out of the interval required for the

A A Klypin et al ibid

other three elements some have argued that the

primeval He abundance is this small Like

D Sciama Phys Rev Lett

wise the recent tentative detection of deuterium

L Wolfenstein Phys Rev D

in a hydrogen cloud at red shift z seen in

S P Mikheyev and A Yu Smirnov Sov J

absorption in the sp ectrum of a QSO at red shift

Nucl Phys

z forces outside the aforementioned con

G Sigl and M S Turner Phys Rev D in

cordance interval At the moment neither

press

p oses a serious threat to the standard picture

D Cinabro et al CLEO Collab oration

However should that change either could b e ex

Phys Rev Lett H Albrecht

plained by an MeVmass tau neutrino Either

et al ARGUS Collab oration Phys Lett B

could also b e explained by a change in our under

standing of the chemical evolution of He The

J Ellis and D N Schramm Phys Rev D

lower limit to is based up on the overproduc

tion of D He and hinges up on the fact that

A Burrows et al Phys Rev Lett

known stars cannot eciently destroy He

R Mayle et al Phys Lett B

If this argument is wrong then the lower b ound

to b ecomes less stringent and low He or high

S Do delson J A Frieman and M S Turner

deuterium could b e accommo dated

Phys Rev Lett

As previously mentioned a tau neutrino of

S W Falk and DN Schramm Phys Lett B

mass MeV to MeV and lifetime sec to

sec whose decays pro duce electron neutrinos

E Kolb and M S Turner Phys Rev Lett

can depress He pro duction Likewise a tau neu

F Feilitzsch and L Ob erauer

trino of mass MeV to MeV and lifetime

Phys Lett B L Ob erauer

sec to sec whose decays pro duce electron

et al Astropart EL Chupp

neutrinos can enhance D pro duction even for

WT Vestrand and C Reppin Phys Rev

large values of While it is unlikely that big

Lett

bang nucleosynthesis will need such assistance an

R S Miller et al work in preparation

MeV tau neutrino could provide it

C Copi D N Schramm M S Turner Sci

ence in press

S Do delson G Gyuk and MS Turner

Acknowledgments

Phys Rev D

This work was supp orted in part by the Depart M Kawasaki et al Nucl Phys B

ment of Energy at Chicago and Fermilab and by

R Mayle DN Schramm MS Turner and

J Wilson Phys Lett B

G Mathews and R Malaney Phys Rep

and references therein

G Gyuk M S Turner Phys Rev D in press

See eg A Burrows Ann Rev Nucl Part

Sci W D Arnett et al Ann

Rev Astron Astrophys and

references therein

G M Fuller Phys Rep

See eg J A Peacock and S J Do dds Mon

Not R astron Soc

A R Liddle and D H Lyth Phys Rep in

press

R Davis et al Phys Rev Lett

A Liddle and D Lyth Phys Lett

B F Lucchin et al Astro

phys J L J Gelb et al ibid

L R Cen et al ibid L

J G Bartlett A Blanchard J Silk and

M S Turner astroph

M S Turner G Steigman and L Krauss

Phys Rev Lett M Turner

Physica Scripta T P J E Pee

bles Astrophys J G Efs

tathiou et al Nature

G Gyuk S Do delson and MS Turner

Phys Rev Lett

G Steigman DN Schramm and J Gunn

Phys Lett B VF Shvarts

man JETP Lett T P Walker

et al Astrophys J

G J Mathews R N Boyd and G M Fuller

Astrophys J G M Fuller

R N Boyd and J D Kalen ibid L

A Songaila et al Nature

R F Carswell et al Mon Not R astron

Soc L

J Yang MS Turner G Steigman

DN Schramm and K A Olive Astrophys

J