Cold Dark Matter the Newtonian Result of Classical Mechanics

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Science Café Research by KIAS Visitors Newsletter Vol 3 The KIAS Research by KIAS Visitors Cold Dark Matter the Newtonian result of classical mechanics. References The entropy increases again, adiabatically, 1. Verlinde, E., 2010, hep-th/1001.0785 by the same amount whenever the passenger 2. Bekenstein, J.D., 1981, Phys. Rev. D., 23, 287 Paolo Gondolo KIAS Visitor (University of Utah) goes down to the ground floor, whereby any 3. Thorne, K.S., in Magic without Magic, ed. J. Klauder (Freeman, San Francisco, 1972), pp. 231- net residual entropy creation is associated only 258 with the actuation of the elevator, not in the 4. Bekenstein, J.D., 1973, Phys. Rev. D., 7, 2333; ibid. Earth-passenger system. 1974, Phys. Rev. D., 9, 3292 5. van Putten, M.H.P.M., 2006, PNAS, 103, 505 Open problems 6. Schwarzchild, K., 1916, Sitzber. Deut. Akad. Wiss., Clearly, we are only beginning to elucidate 1, 189; Einstein, A., & Rosen, N., 1938, Phys. Rev. The nature of more than 80% of the matter in the D., 48, 73; Lindquist, R.W., 1963, Phys. Rev. D, 4, entropic gravity in some illustrative examples. Universe is unknown. At present, we have evidence 938; Brill, D.R., & Lindquist, R.W., 1963, Phys. Rev. Yet, the implications may be important is D, 131, 471 that this matter is not made of any known elementary ways unforeseen, including a new approach 7. van Putten, M.H.P.M., 2010, Class. Quant. Grav., particle, but we are still in the exploratory stage to to understanding the cosmological constant 27, 075011 figure out its nature. Many ideas have been considered, problem [11], that may ultimately lead to 8. Hawking, S.W., Commun. Math. Phys.75, 199 both theoretically and experimentally, and more are consistent holographic representations [12,1]. 9. Penrose, R., 1965, Phys. Rev. Lett., 14, 57 expected to come. Three examples of current interest In developing these directions, including a 10. van Putten, M.H.P.M., 2010, under review are: dark matter particles of mass around 10 GeV/c2 , generalization of entropic forces between 11. Jacobson, T., 1995, Phys. Rev. Lett., 75, 1260; dark matter particles of mass around 1 TeV/c2 , and the Padmarabhan, T., 2010, Rep. Prog. Phys. 73, elementary particles (with no direct recourse recently developed topic of dark stars. 046901; Eason, D.A., Frampton, P.H., & Smoot, at hand to apparent event horizons), we are G.F., 2010, hepth-th/1002.4278 Figure 1. The current content of the Universe as measured potentially on an exciting path to see gravity in 12. ‘t Hooft, G., 1993, gr-qc/940908; Susskind, L., The evidence for cold dark matter comes from in precision cosmology an entirely new light, that may also lead to new 1994, hep-th/940908 observational cosmology, a field that has made giant computational algorithms for evolving multi- leaps in the past ten years. For the first time in history, hole solutions in de Sitter space. there is now a cosmological model based on scientific from those that eventually contract. The current data rather than mere speculation. Of great interest to measurements1 are summarized in Figure 1, where a Maurice H.P.M. Van Putten received his Ph.D. from the California Institute of Technology in -24 1992. He has held postdoctoral positions at the Institute for Theoretical Physics at the University of physics are the measurements of the mass and energy yoctogram (yg) is 10 grams. The distinction between Santa Barbara and the Center for Radio Physics at Cornell University. He then joined the faculty of content of the Universe. Not only these measurements dark energy (cosmological constant), radiation the Massachusetts Institute of Technology and became a member of the new Laser-Interferometric are precise (the current precision is of a few percent1, (photons), and matter (ordinary matter, neutrinos, and Gravitational-wave Observatory (MIT-LIGO). Professor van Putten’s research in theoretical 2 astrophysics has spanned a broad range of topics in relativistic magnetohydrodynamics, hyperbolic and more precise observations are under way ), but cold dark matter) is based on their respective equation formulations of general relativity, and radiation processes around rotating black holes and their also the mass and energy densities are measured in of state, namely the relation between pressure p and prospects for long durations bursts in gravitational wave and radio emissions. His theory describes physical units, i.e. mass or energy per unit volume. energy density r. “Radiation” is a gas of massless a unique link between gravitational waves and Kerr black holes, two of the most dramatic predictions of general relativity. His research has appeared in the Physical Review Letters and on This was impossible more than a decade ago, when particles, like black body photons, for which p=r/3. the covers of Science (2002) and PNAS (2006), and his graduate course “Gravitational Radiation, one could only determine ratios to the so-called “Matter” is a gas of very heavy particles (mc2@@ kT), Luminous Black Holes and Gamma-Ray Burst Supernovae” has been published by Cambridge University Press (2005). critical energy density, defined as the energy density for which one neglects the pressure, p=0. Matter is Contact information: Department of Physics, KIAS. E-mail: [email protected] separating cosmological models that expand forever further divided into “ordinary matter”, which interacts

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electromagnetically with photons, “hot dark state the total kinetic and potential energies into present-day galaxies. Cold dark matter instead supersymmetric particles (in supersymmetric matter”, which was relativistic at the time of should be comparable, but measurements show can start contracting earlier, at the matter-radiation solutions to the hierarchy problem - why is gravity galaxy formation and does not form small a kinetic energy much higher than the potential equality, and has enough time to form galaxies. The so weak?), and Kaluza-Klein particles (in solutions galaxies, and “cold dark matter”, which was energy. A possible solution is to augment the amount of baryons at recombination is measured via to the hierarchy problem invoking extra space-time non-relativistic at galaxy formation and is the potential energy by the gravitational energy the height of the CMB acoustic peaks and via baryon dimensions). main contributor to galaxies. Finally, “dark created by invisible dark matter. Numerous acoustic oscillations (BAO) in the matter power A general class of dark matter candidates called energy” is here a fluid with equation of state and varied measurements exist today: rotation spectrum. The total amount of matter is measured WIMPs, for weakly interacting massive particles, p=-r, which mimicks Einstein’s cosmological velocity of gas in spiral galaxies; velocity using the distribution of luminous red galaxies. includes supersymmetric and Kaluza-Klein dark constant and which, as Zeldovich pointed out, dispersion of stars in dwarf and elliptical Comparison of the two quantities gives the remarkable matter. WIMPs are interesting because (i) WIMPs in is the equation of state of a quantum vacuum. galaxies; kinetic energy, gas density, gas result that more than 80% of the matter in the Universe chemical equilibrium in the early Universe naturally temperature, and gravitational lensing of does not have electromagnetic interactions, i.e. is non- have the right density to be cold dark matter, and It is interesting to note that the cosmic clusters of galaxies; correlation function of baryonic dark matter.4 (ii) the same physical processes that give the right density of neutrinos is currently bracketed to the distribution of galaxies on large distances, density make WIMP detection possible, so one can within an order of magnitude. This impressive and its Fourier transform, the matter power What is non-baryonic cold dark matter? Going experimentally test the WIMP hypothesis. result is due to the combination of precision spectrum; distortion of galaxy images by weak through the list of known elementary particles soon cosmological measurements and the discovery gravitational lensing; distance to supernova brings up a problem (see Figure 2). Photons are not In the first nanoseconds after the Big Bang, WIMPs of neutrino oscillations. Cosmology (i.e. explosions; fluctuations in the temperature dark. Electrons, gluons, and up- and down-quarks are are produced in ordinary matter-antimatter collisions Cosmic Microwave Background (CMB) of the CMB. All these observations can “baryonic” matter. The weak gauge bosons and the in the hot primordial soup, and are annihilated in fluctuations, Luminous Red Galaxies (LRGs) be explained consistently within a single other quarks and leptons decay too quickly to have the inverse reactions. When the expansion rate of the distribution, and the Hubble constant) places cosmological model that includes cold dark survived some 13 billion years from matter-radiation Universe becomes faster than the collision rate, WIMP an upper bound of 0.44 eV/c2 on the sum of the matter in the amount mentioned above. equality to the present time. And the neutrinos are hot production ceases and the number of WIMPs is neutrino masses,1 giving an upper bound of dark matter. Thus no known particle 0.08 yg/m3 on their cosmic density. Neutrino Further support for the existence of cold can be cold dark matter. This is the oscillation measurements of ⁄Dm2 place a lower dark matter comes from the theory of galaxy dark matter problem. bound of 0.048 eV/c2 on the heaviest neutrino formation. Galaxies can start to form out of mass,3 leading to a lower bound of 0.009 yg/ the highly-uniform primordial plasma only Many new particles have been m3 for the cosmic neutrino density. The same when the expansion of the Universe slows proposed as dark matter candidates. lower bound also implies that neutrinos were down at a plasma temperature of ~1.28 eV/k The most attractive ones belong to relativistic when galaxies formed, that is (matter-radiation equality). However, particles theories that originate from genuine neutrinos are hot, not cold, dark matter. with electromagnetic interactions (like particle physics questions and are protons, neutrons, and electrons, collectively in principle disconnected from the Cold dark matter was introduced in the 1980’s called “baryons” in cosmology) continue to dark matter problem. Among these to explain a discrepancy between the kinetic oscillate acoustically with the plasma until its candidates are axions (arising in and potential energies of stars in galaxies and temperature lowers to ~0.26 eV/k, at which solutions to the strong-CP problem of galaxies in clusters (for the latter there was point they decouple (recombination and CMB of quantum chromodynamics - also a prescient study by Zwicky in the 1930’s). formation). After recombination, there is simply why is the electric dipole moment Figure 2. No known particle can be cold dark matter (Table of elementary According to the virial theorem, in a steady not enough time for the baryons to contract of the neutron so small?), lightest particles by Fermilab)

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explanations involving pulsars or reacceleration at introduction of a new idea to probe dark matter at the cosmic ray sources are reasonable, many authors have time when the first stars form, about 13 billion years entertained the possibility that the excesses may be ago.8 According to the original authors,6 the first stars due to the annihilation or decay of heavy dark matter. would initially be sustained by the annihilation of The absence of a corresponding excess in cosmic the dark matter that was gravitationally attracted into ray positrons, and the relatively strong positron flux, them while they formed. For about a million years has made the most popular dark matter candidates or so they would be dark-matter powered stars, or for non-viable, and has prompted the introduction of short dark stars (see Figure 5 for an artist’s conception new particle models with annihilation cross sections of these objects). Despite their name, dark stars shine strongly enhanced at low energy either via resonance like a million suns and might be detectable by the Figure 3. Principle of direct dark matter detection Figure 4. Principle of indirect dark matter detection effects or via novel initial state interactions.6 A upcoming James Webb Space Telescope (JWST), (Background figure courtesy of the CRESST collaboration) (Background drawing by J. Lomberg) conclusion on this case has not been reached yet, and although with the help of the magnifying power of much is expected from the AMS detector scheduled to a cluster-of-galaxies gravitational lens. Dark stars conserved in any region that expands with the technique. (3) Indirect detection, in which fly to the International Space Station (ISS) in 2011. might also help explaning the anomalous chemical Universe. For the final WIMP density to be that dark matter particles transform into ordinary composition of old halo stars and the rapid formation of cold dark matter, the WIMP annihilation particles which are then detected or inferred Light WIMPs with mass ~10 GeV/c2 have become of the first quasars. cross section must be of the order of the weak (Figure 4). To this broad category belong interesting through a couple of direct detection interaction cross section (about 10-36 cm2). searches for high-energy neutrinos produced experiments.7 For more than 11 years, the DAMA Specific models obtain this cross section when in the annihilation of dark matter inside the collaboration has been observing that the rate of the WIMP mass is in the range between a few Sun or Earth or around the black hole at the nuclear recoils in their NaI(Tl) crystals is modulated GeV/c2 and a few TeV/c2. Galactic Center, searches for gamma-rays, with a phase and a 1-yr period that no one has been Experimental tests of the WIMP hypothesis positrons, antiprotons, and antideuterons able to explain except in terms of dark matter particles. can be divided into three groups. (1) Production produced by dark matter annihilation in our The CoGeNT collaboration has recently reported an of new particles at accelerators like the Galaxy or in external galaxies, and searches “irreducible excess” of nuclear recoils in their very- Large Hadron Collider (LHC) at CERN, for exotic astrophysical objects that would exist low-threshold Ge detector. Some authors have claimed Geneva, which started continuing operations only in the presence of dark matter, like stars that the two signals may be due to the same dark in 2009. Here the electrically-neutral dark powered by dark matter annihilation instead of matter particles with mass ~7 GeV/c2 and cross section matter particles would leave no trace but nuclear fusion (dark stars). with nucleons ~10-40 cm2. The claim is controversial could be inferred through missing energy or because according to other analyses5 the XENON10 connected theoretically to charged particles In the past year or so, great attention has and XENON100 detectors should also observe nuclear Figure 5. Artist’s conception of a “dark star,” a brightly that are detected. (2) Direct detection in been paid to WIMPs with mass ~1 TeV/ recoils due to such particles, but no recoils have shining star powered by the annihilation of dark matter low-background underground laboratories, c2, as a way to explain an excess in cosmic been recorded. Also controversial is the theoretical instead of nuclear fusion (image credit: University of Utah) when dark matter particles “kick” nuclei ray positrons observed by the PAMELA explanation for the existence of such particles, because in a crystalline, gaseous, or liquid detector collaboration and an excess in the flux of different studies reach opposite conclusions even Without doubt, the nature of cold dark matter is transferring part of their energy to the nuclear cosmic ray electrons+positrons observed by within the same theories. one of the biggest mysteries in the physical sciences. recoil (Figure 3). Dozens of such experiments the Fermi Gamma-Ray Observatory and the Precision cosmology has brought new insight into the worldwide are using and improving this HESS collaboration.5 Although astrophysical Finally, the past couple of years have seen the amount and distribution of dark matter, and numerous

26 Korea Institute for Advanced Study | 27 Research by KIAS Visitors Newsletter Vol 3 The KIAS Research by KIAS Visitors

26 Korea Institute for Advanced Study | 27 Research by KIAS Visitors Research by KIAS Visitors Newsletter Vol 3 The KIAS Research by KIAS Visitors

experimental searches and theoretical studies the understanding that cold dark matter is not Black holes in all have been put forward to detect dark matter made of any known particle. However, the particles. More than twenty years of research nature of cold dark matter remains elusive. And have allowed the separate measurements of a doubt still lingers: might we be searching for the amount of hot and cold dark matter, and something analogous to the 19th-century ether? Maria J Rodriguez KIAS Visitor (Max Planck Institute for Gravitational Physics)

1 E. Komatsu et al. (WMAP Collaboration), arXiv:1001.4538 (2010). 2 Planck mission, http://sci.esa.int/science-e/www/area/index.cfm?fareaid=17. Black holes are the most elementary and fascinating process, so the most common black hole formed this 3 Talk by P. Vahles (MINOS collaboration) at Neutrino 2010, Athens, Greece. objects of General Relativity (GR). The fact that the way should be a rotating black hole. These black 4 M. Tegmark et al. (SDSS Collaboration), Phys. Rev. D74, 123507 (2006). effects of the space-time curvature are dramatic in holes have their theoretical realization in the rotating 5 O. Adriani et al. (PAMELA Collaboration), Nature 458, 607 (2009), Phys. Rev. Lett. 102, 051101 (2009), arXiv:1007.0821 (2010); A.A. Abdo et al. (Fermi-LAT Collaboration), Phys. Rev. Lett. 102, 181101 (2009); D. Grasso et al. (Fermi-LAT Collaboration), Astropart. their presence explains why it is relevant studying black hole solution of Roy Kerr [2], a description Phys. 32, 140 (2009); P. Blasi, Phys. Rev. Lett. 103, 051104 (2009); F. Aharonian et al. (HESS Collaboration), Astron. Astrophys. 508, these systems. Recent developments in String/M providing an absolutely exact representation of all 561 (2009). Theory -expected to be a truly unified theory of the black holes that exist. The black hole solution of 6 M. Ibe, H. Murayama, T.T. Yanagida, Phys. Rev. D79, 095009 (2009); N. Arkani-Hamed, D.P. Finkbeiner, T.R. Slatyer, N. Weiner, Phys. all interactions- and in the application to the study Kerr is characterized only by two parameters (called Rev. D79, 015014 (2009); L. Bergstrom, J. Edsjo, G. Zaharijas, Phys. Rev. Lett. 103, 031103 (2009). 7 P. Gondolo, G. Gelmini, Phys. Rev. D71, 123520 (2005); F. Petriello, K. Zurek, JHEP 0809, 047 (2008); Z. Ahmed et al. (CDMS of strongly coupled field theories via the AdS/CFT charges in this context): mass and angular momentum, Collaboration), Science 327, 1619 (2010); R. Bernabei et al. (DAMA Collaboration), Eur. Phys. J. C67, 39 (2010); C.E. Aalseth et al. correspondence -stating that a gravitational solution something colloquially referred to as that black holes (CoGeNT Collaboration), arXiv:1002.4703 (2010); E. Aprile et al. (XENON100 Collaboration), arXiv:1005.0380; C. Savage, G. Gelmini, P. in the bulk is dual to a non-gravitational conformal have no hair. Conversely, according to uniqueness Gondolo, K. Freese, arXiv:1006.0972 (2010); D. Hooper, J. Collar, J. Hall, D. McKinsey, arXiv:1007.1005 (2010). field theory- have prompted our interest in black holes theorems, the most general four dimensional, neutral, 8 D. Spolyar, K. Freese, P. Gondolo, Phys. Rev. Lett. 100, 051101 (2008). in more than four space-time dimensions. Bearing in asymptotically flat, stationary black hole is Kerr’s. mind the transcendental impact of the connections These objects have a theoretical counterpart in higher between GR and other non-gravitational theories, we space-time dimensions. Unlike in four, in higher will describe here the different species of black holes dimensions there is more room and black hole solutions in D space-time dimensions. display richer features. In fact, the four-dimensional It is now commonly accepted that black holes (in four uniqueness theorems break down for D > 4. dimensions of space-time) are not only an intellectual Paolo Gondolo is a Professor of Physics and Astronomy and the Director of the High Energy possibility but do indeed exist in our Universe, usually The first black holes Astrophysics Institute at the University of Utah. He received his Ph.D. from the University of California at Los Angeles in 1991 and was a post-doctoral fellow at the Universities of Uppsala, lying at the centre of galaxies, including the Milky In the 18th century it was already proposed [3] Paris, and Oxford, and at the Max Planck Institute for Physics. He was on the faculty of Case Way. The actual formation of objects with such special that very massive celestial objects could deflect Western Reserve University. Paolo Gondolo works in particle astrophysics, especially on the dark matter problem. He was a Visiting Professor at KIAS during the Summer of 2010. properties remains a quiz, but they are believed to light and drag it back due to self-gravitational correspond to the final stage in the evolution of a effects. In 1916, a gravitational object with these Contact information: Department of Physics and Astronomy, University of Utah, 115 South 1400 star that undergoes a catastrophic, self-gravitational characteristics was shown by Karl Schwarzschild East, Salt Lake City, UT 84112-0830, USA. E-mail: [email protected]. collapse [1]. Stars usually rotate and the angular [4] to be possible within the framework of momentum ought to be preserved along the collapsing General Relativity. Schwarzschild’s solution

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