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Aspects of Neutrino Physics in the Early Universe

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Aspects of Neutrino Physics in the Early Universe Asp ects of Neutrino Physics in the Early Universe PhD Thesis Steen Hannestad Institute of Physics and Astronomy University of Aarhus Octob er Contents Preface v Intro duction Neutrinos Primordial Nucleosynthesis Thesis Outline Particle Dynamics in the Expanding Universe Global Evolution Equations The Boltzmann Equation Basic Big Bang Nucleosynthesis Theory Observations Dirac and Ma jorana Neutrino Interactions Denition and Prop erties of Neutrino Fields Neutrino Weak Interactions Mixed Neutrinos Decaying Neutrinos Neutrino decoupling in the Standard Mo del Fundamental Equations Numerical Results Discussion and Conclusions Massive Stable Neutrinos in BBN Numerical Calculations Mass Limits Decaying Neutrinos in BBN Necessary formalism Numerical Results Nucleosynthesis Eects Conclusion iii Neutrino Lasing The Basic Scenario The Level Laser Numerical Results Discussion Conclusions Outlo ok Acknowledgements A Mathematical Formalism A Dirac Matrices and Their Algebra A Dirac Spinors A Creation and Annihilation Op erators B Phasespace Integrals C English Resume Bibliography Preface The present thesis is a summation of the work carried out during my PhD study The bulk of the work has b een p erformed in collab oration with my su p ervisor Jes Madsen at the Institute of Physics and Astronomy at the University of Aarhus However some of the work has b een done during a six month stay at the Max Planck Institut fur Physik in Munich during the spring and summer of where I also had the pleasure of collab orating with Georg Raelt in the eld of sup ernova neutrino physics Chapters contain an intro duction to various key issues connected with neutrino physics and Big Bang nucleosynthesis Chapters are essentially reprints of pap ers as describ ed b elow Finally there is a thesis conclusion in Chapter and an outlo ok to p ossible future work in Chapter There are three app endices at the end app endices A and B contain various mathematical details and App endix C contains a brief summary of the thesis work Note that throughout I use natural units where c ~ k B List of Publications I S Hannestad and J Madsen Neutrino Decoupling in the Early Universe Published in Phys Rev D I I S Hannestad and J Madsen Nucleosynthesis and the Mass of the Tau Neutrino Published in Phys Rev Lett Erratum published in Phys Rev Lett I I I S Hannestad and J Madsen Nucleosynthesis and the Mass of the Tau Neutrino Revisited Published in Phys Rev D IV S Hannestad and J Madsen A Cosmological Three Level Neutrino Laser Published in Phys Rev D v vi Preface V S Hannestad Tau Neutrino Decays and Big Bang Nucleosynthesis accepted for publication in Phys Rev D VI S Hannestad Can Neutrinos be Majorana Particles hepph not intended for publication VI I S Hannestad and G Raelt Supernova Neutrino Opacity from Inverse NucleonNucleon Bremsstrahlung in preparation The contents of pap er I have b een describ ed in detail in Chapter pap ers II and III have b een summarised in Chapter pap er IV is contained in Chapter and nally Chapter describ es pap er V Some of the contents of pap er VI have b een included in Chapter Note that pap er VI I ab out sup ernova neutrino physics has not b een included in the thesis The eld it covers is somewhat disjoint from that of the thesis and for this reason I have left it out Chapter I Intro duction One of the most succesful areas of mo dern physics is the interface b etween parti cle physics and astrophysics This eld includes such phenomena as sup ernovae active galactic nuclei and p erhaps most notably the early Universe It is also a relatively new eld that has only existed for less than years so that there are still big white sp ots left on the map making it a very interesting eld of research The present thesis deals with dierent asp ects of the physics of the parti cles called neutrinos in the early Universe esp ecially in connection with the formation of light elements Neutrinos Neutrinos are chargeless spin fermions b elonging to the family of leptons There are three known sp ecies of neutrinos corresp onding to the three known charged leptons They are group ed together in three generations e e with corresp onding antiparticles These three generations corresp ond to the three quark generations u c t d s b It is not known whether there are additional generations of fermions but since the fermion masses increase with generation any new generation would likely b e extremely heavy In any case they would have to b e so in order not to have b een detected in accelerator exp eriments Neutrinos are unique among the known fermions in that they do not p ossess electric charge meaning that they have no electromagnetic interactions at tree level The only interactions that neutrinos have are weak interactions and since Chapter Intro duction the weak coupling constant G is very small neutrinos interact only very weakly F with the other fermions Neutrinos can b e pro duced on earth for example in nuclear reactors How ever the most constant neutrino source we have is the Sun where electron neutrinos are pro duced by the nuclear burning of hydrogen via the reaction p He e e yielding a neutrino ux of more than cm s on earth The most p owerful neutrino sources known are the core collapse typ e I I sup ernovae They emit a burst of neutrinos from the neutronisation reaction p e n e lasting a few seconds During this p erio d roughly ergs are emitted in neutrino radiation giving the sup ernova a neutrino luminosity comparable to the optical luminosity of the whole visible Universe Even though neutrinos are so abundant in the Universe their very weak interactions mean that they are extremely dicult to detect in the lab oratory Typically one needs many tons of detection material to achieve a detection rate of a few p er day even with the huge neutrino ux coming from the Sun For the same reason very little is known ab out the prop erties of neutrinos In the standard mo del of particle physics neutrinos are strictly massless However there is no a priori reason why this should b e so and in many extensions of the standard mo del neutrinos do indeed have mass A great numb er of exp eriments have b een made in order to constrain fundamental parameters like mass and magnetic moment of the dierent neutrino sp ecies However most of these exp eriments are inecient b ecause of the very low counting statistics and this is where indirect exp eriments enter the picture Neutrinos are thought to b e of fundamental imp ortance in triggering the sup ernova explosions for example Therefore observations of sup ernovae yield imp ortant information on neutrino prop erties The other lab oratory where fundamental neutrino physics can b e prob ed is the early Universe Here neutrinos are roughly as abundant as photons and should therefore contribute signicantly to for example the cosmic energy density This in turn leads to stringent limits on parameters like neutrino mass Neutrinos are also of fundamental imp ortance in the formation of light elements in the early Universe Constraints on neutrino prop erties coming from the study of light element formation form the bulk part of the present work and will b e describ ed in much more detail later Primordial Nucleosynthesis For many years cosmology was a research eld strongly lacking in observational input However during the last decade numerous improvements have b een made on this For example the cosmic microwave anisotropies were discovered in by the COBE satellite and small scale anisotropies are exp ected Primordial Nucleosynthesis to b e observed by the next generation of satellites exp ected to y within years time This has op ened up a completely new window on the physics of the early Universe since the physical comp osition of the Universe at the time of creation of the background radiation is imprinted in these anisotropies Thus a new precision determination of such essential parameters as the cosmological density parameter and the Hubble parameter H can b e exp ected Another eld under rapid development is that of large scale galaxy redshift surveys This is primarily due to new telescop e technology and observational techniques that automate the pro cesses that earlier had to b e done manually In this way redshifts of millions of galaxies can b e obtained and the physical structure of the Universe mapp ed out This again tells something ab out the matter content of the Universe b ecause that aects the way structures form If the content of the Universe is mainly in the form of very light m eV particles all imhomogeneities on small scales will have b een smeared out by the free streaming of these particles This means that the rst structures to form are very large roughly on the size of sup erclusters of galaxies Only subsequently
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