Cosmic Connections

A National Research Council study on connecting quarks with the cosmos has recently posed a number of the more important open questions at the interface between particle physics and cosmology. These questions include the nature of dark matter and dark energy, how the Universe began, modifications to gravity, the effects of neutrinos on the Universe, how cosmic accelerators work, and whether there are new states of matter at high density and pressure. These questions are discussed in the context of the talks presented at this Summer Institute. ∗ c © 2003 by John Ellis. 1 Connecting Quarks with the Cosmos My task in this closing lecture is to preview possible future developments at the interface between particle physics on one side, and astrophysics and cosmology on the other side. Though these cosmic connections may benefit from some theoretical advice, they must rely on the firm facts provided by accelerator experiments, as well as non-accelerator experiments and astronomical observations. To guide the discussion, I structure this talk around a report with the same title as this section, published recently by the U.S. National Research Council, that poses eleven major cosmological questions for the new century: • 1: What is the dark matter? • 2: What is the nature of dark energy? • 3: How did the Universe begin? • 4: Did Einstein have the last word on gravity? • 5: What are the effects of neutrinos on the Universe? • 6: How do cosmic accelerators work? • 7: Are protons unstable? • 8: Are there new states of matter at high density and pressure? • 9: Are there additional space-time dimensions? • 10: How were heavy elements formed? • 11: Do we need a new theory of matter and light? The last two questions primarily concern nuclear physics and plasma physics, respectively, and I do not discuss them here. A particle physicist’s answer to the fourth question about the completeness of general relativity is inextricably linked to the ninth question about extra dimensions. Likewise, the fifth and seventh questions about neutrinos and protons, respectively, are linked in grand unified theories. Therefore, I treat these questions in pairs. 1: What is the dark matter? We have heard repeatedly at this institute that dark matter is necessary for the formation of structures in the Universe. The latest data from the Sloan Digital Sky Survey, shown here by Kent, are very consistent with the power spectrum measured in the CMB and by previous sky surveys, weak lensing and the Lyman-α forest. At the level of galaxy clusters, as we heard here from Henry, some resemble train wrecks and are still forming today, whereas others have relaxed and are good probes of the dark matter content. Even before the combination of Type-1a supernovae and the CMB, cluster data indicated that Ωm ≪ 1: current cluster data yield: Ωm = 0.30 +0.04 −0.03 (1) after marginalizing over Ωb and h. Moreover, as discussed here by Dekel, the motion of luminous matter in the neighbourhood of our galaxy provides a detailed profile of the local dark matter density. Is this dark matter composed of particles or of larger objects such as white dwarfs or black holes? The recently-demonstrated concordance between the values of Ωb extracted from Big-Bang Nucleosynthesis and the CMB confirms that the dark matter cannot be composed of baryons, excluding a dominant white dwarf component and implying that any substantial black hole component must have been primordial. Microlensing searches exclude the possibility that our own galactic halo is composed of objects weighing between <∼ 10 −3 and >∼ 10 +3 times the mass of the Sun. Therefore, in the following, we concentrate on particle candidates for the dark matter. Is this dark matter hot, warm or cold? The recent WMAP, 2dF and SDSS data are very consistent with the standard cold dark matter paradigm. In particular, the combination of WMAP with other data implies that ΩHDMh 2 < 0.0076, (2) corresponding to Σνmν < 0.7 eV. Moreover, the early reionization of the Universe recently discovered by WMAP requires some structures to have started forming very early, which is evidence against warm dark matter. However, there are problems with the cold dark matter paradigm. For one thing, the density profiles of galactic cores appear less singular than calculated in some cold dark matter simulations but these may be changed by interactions with ordinary matter and by mergers and black hole formation. For another thing, there is little observational evidence for the halo substructures predicted by cold dark matter simulations but the formation of stars may be dynamically inhibited in small structures near larger galaxies. Therefore, we continue to focus on cold dark matter candidates. Generally speaking, these might have been produced by some thermal mechanism in the very early Universe, or non-thermally. A good example of the latter is the axion, which is my second-best candidate for cold dark matter. Recent data from the LLNL axion search, reported here by Nelson, excludes the possibility that a KSVZ axion weighing between 1.9 and 3.4 μeV could constitute our galactic halo. Another example of non-thermally produced cold dark matter could be a superheavy particle produced around the epoch of inflation, called by Kolb the ‘wimpzilla’. A natural example of a wimpzilla is a metastable ‘crypton’ from the hidden sector of some string model. If metastable, a wimpzilla could be the orgin of the ultra-high-energy cosmic rays discussed here by Ong. The classic thermally-produced cold dark matter candidate is the lightest supersymmetric particle (LSP), but another possibility proposed recently is the lightest Kaluza-Klein particle (LKP) in some scenarios with universal extra bosonic dimensions (UED). The spectra in some UED models are strikingly similar to those in supersymmetric models, but with bosons and fermions switched around. During this institute, there was an important update for the accelerator constraints on supersymmetry, with a re-analysis of the ee data used to estimate the Standard Model contribution to the anomalous magnetic moment of the muon, gμ − 2. These now bring the Standard Model prediction to within 2 σ of the experimental value, leaving less room for a supersymmetric contribution. The direct searches for LSP dark matter were reviewed here by Spooner. As he mentioned, the long-running DAMA claim to have observed a possible annual modulation signal for cold dark matter scattering has recently been reinforced by new data from the same experiment that show the annual modulation persisting for seven years. However, several other experiments, including CDMS, EDELWEISS and most recently ZEPLIN 1 exclude a spin-independent scattering cross section in the range proposed by DAMA. This range is also far above what one calculates in the CMSSM when one takes into account all the constraints. More worryingly, the ICARUS collaboration has recently measured a large annual modulation in the neutron flux in the Gran Sasso laboratory where DAMA is located. What are the prospects for detecting dark matter at a particle accelerator? First at bat is the Fermilab Tevatron collider, which, as we heard here from Thomson, now aims at an integrated luminosity of 2 pb by 2007 and 4 pb by 2009. This will enable it to search for squarks and gluinos with masses considerably heavier than the present limits. Next at bat will be the LHC, which is scheduled to start making collisions in 2007. With a centre-of-mass energy of 14 TeV and a luminosity of 10 cms, it will be able to find squarks and sleptons if they weigh <∼ 2.5 TeV. 31 If the squark and gluino masses are relatively low, measurements at the LHC may fix the supersymmetric model parameters sufficiently accurately to enable Ωχh to be calculated with an accuracy comparable to the uncertainty currently provided by WMAP. The LHC will also address many other issues of interest to cosmology, such as the origin of mass, which may be linked to the mechanism for inflation, the primordial plasma in the very early Universe, and the cosmological matter-antimatter asymmetry. Most analyses of supersymmetric dark matter assume that the lightest supersymmetric particle (LSP) is the lightest neutralino, a mixture of spartners of Standard Model particles. However, another possibility, discussed here by Feng, is that the LSP is the supersymmetric partner of the graviton, the gravitino. This possibility is severely constrained by the concordance between Big-Bang nucleosynthesis and CMB. However, the possibility remains of a deviation from standard Big-Bang nucleosynthesis calculations and/or a distortion of the CMB spectrum. 2: What is the nature of dark energy? The necessity of dark energy became generally accepted when data on high-redshift supernovae were combined with the CMB data favouring Ωtot ≃ 1. This conclusion has been supported by recent data extending the previous supernova samples to larger redshift z, in particular, but how robust is this conclusion? As has already been mentioned, the pre-existing data on dark matter in clusters have long favoured Ωmatter ≃ 0.3 which, combined with the CMB data, favour dark energy Λ with ΩΛ ≃ 0.7 independently from the supernova data. Moreover, as was discussed here by Kolb and Pinto, there are good reasons to think that the Type-1a supernovae are indeed good standard candles. Also, as discussed here by Wright, radical alternatives to the standard ΛCDM scenario such as modified Newtonian dynamics (MOND) do not agree with the CMB data. So it seems that we have to learn to live with dark energy. Supporting evidence for dark energy comes from the recent observation of the integrated Sachs-Wolfe effect, a correlation between galaxy clusters and features in the CMB that appears only if there is dark energy causing the space between clusters to expand. The next question is whether this dark energy is constant, or whether it is varying with time. The latter option offers the hope of understanding why the dark energy density in the Universe today is similar in magnitude to the density of matter, through some sort of ‘tracker solution’. In this case, the dark energy would have non-trivial dynamics described by an equation of state that can be parametrized by w(z) ≡ p(z)/ρ(z), where I emphasize that w(z) depends in general on the redshift z. Discarding this possibility for the moment, the present cosmological data favour w ≃ −1, corresponding to a cosmological constant, as discussed here by Kolb. The SNAP satellite project aims at increasing substantially the available sample of high-z supernovae, and offers the prospect of constraining w(z) much more tightly. This may enable a clear distinction to be drawn between time-varying ‘quintessence’ models and a cosmological constant. If the vacuum energy Λ is indeed constant, the next step will be to calculate it. This is surely the ultimate challenge for any pretender for a full quantum theory of gravity, such as string/M theory. For some time, the efforts of the string community were directed towards proving that Λ = 0. However, this was never achieved, despite searches for a suitable symmetry or dynamical relaxation mechanism. Presumably a non-zero value of Λ is linked to microphysical parameters such as mW , mt, msusy,ΛQCD, etc., and the challenge is to find the right formula . If, on the other hand, Λ is really varying, the next question is: what is the asymptotic value? Is it zero, a non-zero constant, or even −∞? Quintessence only postpones the problem. 3: How did the Universe begin? By now, the standard answer to this question is: inflation. But this answer is far from being established. Simple models predict a near-scale-invariant spectrum of nearGaussian perturbations with a model-dependent ratio of tensor and scalar modes. Some of these predictions are successful: for example, the spectral index of the scalar perturbations seen so far is consistent with being scale-invariant, with an accuracy of a few % when WMAP data are combined with data on large-scale structure. However, one can never ‘prove’ that a statistical distribution is Gaussian: one can apply various tests, but if they are passed, one can never be sure that the distribution will not fail some future test. And there are some puzzles in the WMAP spectrum, for example glitches around l ≃ 100, 200 and 340, as discussed here by Wright. As for the possible tensor modes, the first CMB polarization measurements have been published by DASI and WMAP, whose sensitivity is close to expectations in some inflationary models, but far above some predictions, as discussed here by Winstein. ∗String theorists are also worried that, whether Λ is constant or not, the existence of an event horizon appears inevitable. In this case, it is never possible to make exact predictions because of information loss across the horizon. Assuming the validity of the basic inflationary paradigm poses a new series of questions. Was inflation driven by some simple field-theoretical mechanism, such as an mφ or λφ potential, or was some more subtle (quantum-gravitational? stringy?) mechanism responsible? a‘string plasma’? The WMAP measurements strongly disfavour the simplest λφ potential, but the mφ potential survives for now. If inflation was driven by some scalar inflaton φ, how can it be related to the rest of particle physics? The most suitable candidate in the present particle menagerie appears to me to be the supersymmetric partner of the heavy neutrino in a seesaw model of light neutrino masses. Even if inflation was driven by a scalar inflaton field, the CMB might reveal some traces of Planckian physics in the form of some effects suppressed by powers of mP . However, to answer the question in the title of this section, one must look beyond inflation, which presumably occurred when the energy density in the Universe was (∼ 10 GeV), back to when it approached the Planck energy density (∼ 10 GeV). At this epoch, perhaps the Universe was described by some form of string cosmology or pre-Big-Bang scenario. How to test such an idea? One possibility might be provided by gravitational waves from this epoch. 4/9: Does completing Einstein’s theory of gravity require extra dimensions? Einstein certainly did not have the last word on gravity. His General Theory of Relativity was one of the greatest physics achievements of the first half of the twentieth century, the other being Quantum Mechanics. Combining them into a true quantum theory of gravity was the greatest pieces of unfinished business of twentieth-century physics: in particular, how to make sense of the uncontrollable infinities encountered when gravitational interactions are treated perturbatively, and how to deal with the loss of information apparently inherent in non-perturbative gravitational phenomena such as black holes? Presumably the answers to these questions involve modifying either General Relativity, or Quantum Mechanics, or both. The best/only candidate we have for a quantum theory of gravity is string/M theory, which relies heavily on the existence of extra dimensions. These include fermionic dimensions, in the form of supersymmetry with its accompanying superspace, as well as ‘conventional’ extra bosonic dimensions. If they are to aid in stabilizing the mass hierarchy, provide the cold dark matter and facilitate unification of the particle interactions, the fermionic dimensions should appear at the TeV scale, within reach of colliders. But what might be the scales of the extra bosonic dimensions? Consistency of string theory at the quantum level requires extra dimensions at the scale of ∼ 10 cm, and unification of gravity with the other interactions suggests they might appear at ∼ 10 cm. Colliders can probe distance scales down to ∼ 10 cm, but there is no particular reason to expect that extra dimensions will show up at such a large scale. What other signatures might there be for a quantum theory of gravity? One possibility might be gravitational waves, or there might be signatures in the CMB, as discussed earlier. It could even be that the inflation now being probed by the CMB was produced by some stringy effect. As also discussed earlier, the value of the vacuum energy should be calculable in a complete quantum theory of gravity. Other possible tests of models of quantum gravity include the propagation of energetic particles which might be retarded by space-time foam, as could be probed by measurements of photons from AGNs or GRBs or their interactions, as could be probed by UHECRs. Modifications of quantum mechanics could be probed by laboratory studies of K mesons, B mesons and neutrons. There are plenty of ways in which theories completing Einstein’s theory of gravity can be tested. 5/7: What are the effects of GUTs on the Universe? The direct upper limits on neutrino masses: mνe <∼ 2.5 eV, mνμ <∼ 190 keV, mντ <∼ 18 MeV, have left open the possibility that neutrinos might be an important contribution to the dark matter. However, the combination of WMAP data with previous astrophysical and cosmological data provides the more stringent upper limit: Σνmν < 0.7 eV ↔ Ωνh 2 < 0.0076, (3) implying that neutrinos can provide only a small fraction of the dark matter. On the other hand, neutrino oscillation experiments tell us that neutrinos do have masses and mix. The minimal renormalizable model of neutrino masses requires the introduction of weak-singlet ‘right-handed’ neutrinos N . These will in general couple to the conventional weak-doublet left-handed neutrinos via Yukawa couplings Yν that yield Dirac masses mD = Yν〈0|H|0〉 ∼ mW . In addition, these ‘right-handed’ neutrinos N can couple to themselves via Majorana masses M that may be ≫ mW , since they do not require electroweak summetry breaking. Combining the two types of mass term, one obtains the seesaw mass matrix: