PHY323:Lecture 10 the Death of Baryonic Dark Matter

Home , Baryonic dark matter, Cold dark matter, Hot dark matter, Mirror matter, Warm dark matter

PHY323:Lecture 10 The Death of Baryonic Dark Matter

•Neutrinos •The New Particle Zoo •Cold, Warm and Hot Dark Matter •SUSY and Extra Dimensions - introduction

Candidates for Dark Matter II Can Neutrinos be Dark Matter? Worked Example (1) Neutrino mass upper limit in the hot big-bang cosmology one expects about as many cosmic ”black-body neutrinos” as there are microwave photons. 3 sum extends over the masses of all "v = n# %m$ 11 sequential neutrino ﬂavours

present-day density in microwave from earlier background photons $# "# = $c 2 m$ ! "0h # ρc = 3Ho2/8πG %100eV

taking h to be between 0.6-0.7 we get (for all three families) ! 2 "0h <# 0.4 !m " # 40eV

! ! Can Neutrinos be Dark Matter? Worked Example (1) Neutrino mass lower limit It is also interesting to ask for a lower limit on Ωh2 which the dominant dark-matter component must obey. Allowing for a signiﬁcant baryon fraction indicates that particle

dark matter (PDM) should obey Ων > 0.2 Taking h > 0.5 as a lower limit for the expansion rate implies

2 0.05 " #$ h " 0.4 So a reasonable range where this dark matter candidate could be all of the nonbaryonic dark matter, therefor neutrinos with mass ABOUT: ! 4eV " m# " 40eV could represent all of the dark matter

! Energy Density and Neutrinos Worked Example The amount of energy in radiation in today's universe can be estimated with the Stefan-Boltzmann Law, considering that the universe is ﬁlled with blackbody radiation at 2.7 K. The energy density in this equilibrium radiation is given by:

you should know this equation from this work out the number density of gammas you expect in the Universe u(T) ANS: given in lecture ... use n = " kT

! Notes work out the number density of gammas you expect in the Universe u(T) = const " T 4 u(T) n = Know these useful equations " kT !

What is the number density of neutrinos? ! Death of Neutrino Dark Matter The SNO solar (1) The new neutrino experiments neutrino the latest experiments looking for neutrino experiment oscillations suggest that ∑mν < ~1 eV.

(2) Large scale structure with neutrinos N-body simulations show that neutrinos tend to smooth out small scale structure

simulations simulations with Neutrino with Cold Hot Dark Dark Matter Matter

more next lecture A Brief Review The observed motions of stars and clusters due to the force of gravity on other known massive bodies are inconsistent with the predictions of the currently accepted laws of gravitation. Low luminosity stars ? NO - not enough microlensing events from MACHO, OGLE, etc Anything made out of protons and neutrons ? - NO - abundances of the light elements give estimate of the baryon fraction and it’s not high enough.

Neutrinos ? - NO - too light and too relativistic at the time of formation of galaxies and clusters.

That is all there is in terms of stable particles in standard model particle physics. The New Particle Zoo The Wild, Wild West of particle physics: Some possible particle dark matter candidates 1. LSP (Lightest SUSY Particle), m ~ 100 − 1000 GeV 2. Heavy leptons, m ~ 2 GeV 3. Ultraheavy, quasi-stable particles, m ~ 1013 GeV 4. Axion, m ~ 10-5 eV? 5. LKP (Lightest KK Particle), from extra dimensions 6. PBH, M ≥ 1016 g (primordial black holes) 7. Mirror matter,strongly interacting dissipating dark matter 8. Non-topological solitons, Q-ball 9. QCD nuggets 10. WIMPzillas, SuperWIMPS 11. Gravatinos The New Particle Zoo Masses and interaction strengths span many, many orders of magnitude. But independent of cosmology, we expect new particles. Most Important dark matter candidates

Supersymmetry theory Weakly (1) Neutralino Particles Interacting (2) Kaluza-Klein Particles Massive Extra Dimension Particles theory

(3) Axions CP violation theory Hot, Cold and Warm Dark Matter We can divide the candidates into three types (HDM, CDM and WDM) useful for understanding the influence they have of structure formation in the Universe: The difference reflects how fast the particles were moving at the time they decoupled from the baryonic matter (i.e. when they stopped interacting with it as the Universe cooled). This distinction is important because whether dark matter is in the form of CDM or HDM critically influences how we would expect the Universe to form. Remember which ever it is (CDM or HDM) it dominates the Universe so its bound to affect the structure of the visible bit we can see (galaxies etc.).

CDM HDM Hot Dark Matter Hot Dark Matter (HDM) is a massive particle species that decouples, or freezes out when its interaction rate drops below the Hubble expansion rate when the particles velocity is still relativistic

An example of HDM is a neutrino with mass m ~ eV. On small scale, neutrinos are moving too quickly (hot) to participate in gravitational clustering. But on larger scales they can cluster just like heavy matter. The transition occurs around the size of clusters of galaxies ~ 10 Mpc (or 1012Mo). So HDM tends to smooth out structure such that large scale structure (i.e. super clusters of galaxies) to persists but small scale structure (galaxies and smaller size stuff) is less likely. To fit observation this suggests a top-down scenario for the formation of the Universe. i.e. large scale structure would have to form first and break up into small scale structure. Cold Dark Matter CDM is the reverse. The particles hardly move after they have decoupled and their masses are large. Thus this favours formation of small scale structure (galaxies etc.) first. We have a bottom-up scenario. Cold Dark Matter (CDM) is non-relativistic when it freezes out, and so is more massive. If its physics is neutrino-like, the number m / M density is exponentially suppressed n ~ me " freeze and so has mass m » 100GeV. The current prime candidate for CDM is the lightest supersymmetric particles, the neutralino.

Warm Dark! Matter Warm Dark Matter (WDM) freezes out early, but with 100x more degrees of freedom and is still relativistic, and has mass M È 10keV. There are no major contenders for WDM. Notes e.g. Explain the difference between HDM, CDM and WDM... HDM ---> low mass particles, relativistic at decoupling, favours large scale structure CDM ----> high mass particles, non-relativistic at decoupling, favours small scale structure

Remember the simulation shown in the lecture HDM, CDM Structure Formation Cosmologists perform N-body simulations of the Universe to determine which scenario is the best ﬁt. For CDM we expect a hierarchical clustering scenario where small structure forms ﬁrst and then collects into larger structure. So we need to compare the spatial distribution of masses in the Universe predicted by the simulation with that actually observed. Are the clustering properties of the simulations like that observed for real galaxies? The best way to quantify this to use a so called the two-point spatial Galaxy correlation function. Suppose N point are distributed in a volume V. The density is then n=N/V. If the points are randomly distributed in the sky then the probability that a given point has a neighbour in a surrounding volume "P = n"V

! HDM, CDM Structure Formation distance from the ﬁrst point If there is correlation between the points: n"V[1+ #(r)] two-point correlation function if points clustered: "(r) > 0 if points random: "(r) = 0

This can be calculated for galaxies! and clusters leading to a plot of density ﬂuctuation vs. scale. Two main problems: ! ! (1) difﬁcult to get the distance to galaxies - problem of the distance scale and peculiar velocities (2) don’t really know if the non-baryonic dark matter, baryonic dark matter and visible matter are distributed in the same way. It may be for instance the DM is more clustered than the visible matter. This is called biased galaxy formation. HDM, CDM Structure Formation

Increasing the neutrino mass above 0 rapidly pushes the predicted power spectrum curve to the left CONCLUSION: CDM wins Notes e.g. Explain the previous plot and how structure in the Universe depends on the amount of CDM or HDM http://nedwww.ipac.caltech.edu/level5/Guzzo/Guzzo5.html

qualitatively how is the power spectrum of density in the Universe derived (the previous plot) A few Problems with CDM extra note There may be a few problems with CDM.... 1. Missing satellites: CDM predicts an order of magnitude more galactic satellites than observed. 2. Destruction of galactic disk: Even if the number of the satellites is reduced by star formation winds, many smaller tightly bound DM systems would survive and destroy galactic disk by gravitational heating. 3. Central cusps: expected singularity in galactic centers while ﬂat proﬁles are observed. 4. Excessive angular momentum: CDM predicts smaller galactic angular momentum than observed.

Possible solutions: 1. Insufﬁcient accuracy of numerical simulation. 2. Dissipative and self-interacting DM component may help 3. WDM, or better, a mixture of WDM and CDM. Thermal vs. non-Thermal An important distinction in DM particle candidates is between those created thermally in the Early Universe or non-thermally in a phase transition. There is a different relationship between abundance and mass/ coupling for thermal and non-thermal cases WIMPs are produced thermally In early (hot) Universe the number density of WIMPS is approximately equal to the number density of photons As the Universe expands and cools below a temperature equivalent to the WIMP mass the particles cease to be produced and are spaced out too far to annihilate with each other

The abundance is then frozen out (ﬁxed). Why Like Relic CDM Particles? Another reason to like CDM: If you postulate existence of a massive weakly interacting particle (WIMP) in the early Universe then: " + " # " + " There will be equilibrium while reaction rate is larger than expansion rate Γ >> H but! “Freeze-out” occurs once H drops below Γ € leaving a relic density

How big€ is this relic € density? Why Like Relic CDM Particles?

Indicates Weak Scale

So cosmology indicates generic WIMPs at W&Z scale that give about the correct value of Ω we need for dark matter: Candidate 1 (SUSY WIMPs, LSP, Neutralino) Candidate 2 (UED WIMPs, LKP) Notes Explain Freeze Out of relic DM particles The ﬁrst reason to like Weakly Interacting Particles as dark matter

It turns out that in the early universe, if a particle was produced having a rest energy around the ‘electroweak scale’ of the W rest energy (90GeV), then the standard production mechanisms predict that the present day abundance of these particles would be about right to solve the dark matter problem. This argument just requires the electroweak energy scale as input, NOT the particle candidate. But we just said the W and Z are unstable. They have the right mass, but they can’t be dark matter. What other new physics comes in at roughly the electroweak energy scale (90GeV) that could supply a stable dark matter candidate? WIMP Candidate 1 Supersymmetric Dark Matter

Each particle gets a “sparticle” counterpart. Bosons get fermions and vice versa. e.g. Photon Photino W Wino Z Zino etc The Lightest Supersymmetric Particle (LSP) is predicted to be stable. This is called the NEUTRALINO. Supersymmetry Theory and the Higgs To make things simpler, it would be nice if all the forces of nature were uniﬁed under the same theoretical framework. The energy at which this is likely called the Planck energy (1019 GeV). This was started in the 1970s - the result is the electroweak theory. The theory is intricate and complicated, partly because the photon is massless, but the W & Z are heavy. The electroweak theory posits that the very different carriers, and therefore properties, of these forces at energy scales present in nature today are actually the result of taking a much more symmteric theory at higher energies, above the ‘electroweak scale’ of 90GeV (the W and Z rest energy) and ‘spontaneously breaking’ it. The theoretical mechanism for spontaneous symmetry breaking requires yet another new particle, a spin zero particle called the HIGGS BOSON. Supersymmetry Theory What we are aiming to do, e.g.:

At higher energies, where symmetries are unbroken, you might expect a uniﬁed theory should have a single coupling constant The “Higgs” is unstable, so it can’t be the dark matter itself The Higgs endows the carriers of the weak force with their high mass, resulting in a feeble force with a short range. But now the standard model contains another particle, and when you look in to the properties of the Higgs, you hit problems. For example, the Higgs in electroweak theory has a coupling to two electrons and a four Higgs self-coupling.

Because of the Higgs mechanism, the standard model of particle physics is internally inconsistent. To remove the inconsistencies, extensions to the theory are needed. SUPERSYMMETRY is a popular candidate extension. Higgs Self Energy

The quantum mechanical amplitude for a Higgs to travel from A to B, summed over all contributing processes is...

H Fixing Higgs Self Energy Problem In supersymmetry, each particle in the standard model has a supersymmetric partner with spin angular momentum differing by hbar/2. So for every fermion there is a supersymmetric partner boson and vice-versa. The extra diagrams for the Higgs self energy where virtual superpartners are formed and destroyed cancel the divergent diagrams in the standard model sector, rendering the Higgs self- energy ﬁnite. In fact, it’s more complicated than this. The supersymmetric partners, none of which have been detected, mix together quantum mechanically, so that the actual supersymmetric objects we might detect in the LHC will be MIXTURES of the supersymmetric partners of the known particles. Supersymmetric Partner Mixing Lots of very clever people are working very hard on detecting the supersymmetric partners of ordinary particles, and if they do then they will sort out the mess of what supersymmetric states are actually observed in nature, and what their properties are.

Possibility of very exciting new physics if supersymmetry is detected at the LHC. Dan Tovey, Stathes Paganis, Davide Costanzo here at Shefﬁeld. The Neutralino The neutralino is a possibility for the lightest supersymmetric particle, and hence WIMPs. What is it? Well, it’s quite complicated. The neutralino is a quantum mechanical superposition of the bino, wino and two higgsinos