Non-particle Proposals for Dark Matter Will Bunting California Institute of Technology Ph 199 Seminar Presentations May 28, 2014 Overview 1 What is the dark matter problem? Experimental discrepencies Proposed solutions 2 Exotic Candidates Exotic particles Hidden sector particles Black hole remnants Modified gravity Geons 3 Conclusion Astrophysical evidence for dark matter • Galactic rotation curves • Gravitational lensing on cluster scales • Cosmic microwave background • Large scale structure formation (Vera Rubin's original Andromeda rotation curve) Astrophysical evidence for dark matter • Galactic rotation curves • Gravitational lensing on cluster scales • Cosmic microwave background • Large scale structure formation (Abell 2744 cluster lensing) Proposals Particle Dark Matter Non-particle Dark Matter • WIMP • Black hole remnant • Axion • Modified Gravity • Majorana fermion • Modified Newtonian Dynamics (MOND) • Tensor-vector-scalar gravity (TeVeS) • Sterile neutrino • Moffat gravity • Q-Ball • Topological Geons • Hidden sector particles Proposals Particle Dark Matter Non-particle Dark Matter • WIMP • Black Hole Remnant • Axion • Modified Gravity • Majorana fermion • Modified Newtonian Dynamics (MoND) • Tensor-vector-scalar gravity (TeVeS) • Sterile neutrino • Moffat gravity • Q-Ball • Topological Geons • Hidden sector particles Einstein Gravity • Our current best theory of gravity is General Relativity • Governed by an action principle for the gravitional field gµν 1 Z p Z p S = d4x R −g + d4xL −g (1) EH 8πG M • Varying the action gives the Einstein Equations 1 G := R − g R = 8πGT (2) µν µν 2 µν µν • Completely in agreement with astrophysical observations if cosmological constant is included • If dark matter is a particle and contributes to Tµν Hidden sector particles • It is easily possible that there are some quantum fields which do not couple to the Standard Model • If that were the case we would expect to see the effects of the fields only gravitationally (since gravity seems to be universally coupling) • This idea does not seem to make any falsifiable predictions • String theory does (at least currently) predict hidden sectors • There could be a whole zoo out there, although we have some constraints on self-interacting dark matter Black hole remnants • Hawking showed that black holes have a temperature and radiate away (given enough time) • Unclear what happens at the very end of a black hole's evaporation • May be unable to emit Hawking particles because have quantized energy levels • However, would probably need an inordinatley large number of internal states • Full explanation would certainly involve quantum gravity Modifying Einstein Gravity • There are several reasons one may want to modify Einstein gravity • String Theory • Asymptotic Saftey in quantum gravity • "Dark Matter" - observed lensing and galaxy rotation curves • BUT, differnet problems want different modifications! • String theory hints that SEH is only approximate • Asymptotic saftey attempts to modify SEH to make gravity renormalizeable • Dark matter could possibly be explained by modifying the long range behavior of gravity to account for astrophysical observations First Attempt: MOND • The simplest attempt to modify a gravity theory to account for astrophysical observations was Modified Newtonian Dynamcis (MOND) by Milgrom [1] • Proposed modification to Newton's second law where small accelerations give deviation from direct proportionality of force to acceleration (see homework) (Mordechai Milgrom) • Can choose a suitable modification to match galactic rotation curves Making MOND Relativistic: TeVeS • Obvious problem with MOND: not a relativistic theory! (don't get observed cluster lensing) • Bekenstein proposed a relativisitic generalization of MOND called Tensor-vector-scalar gravity (TeVeS) [2] • Adds three extra fields to GR: • A non-dynamical scalar field σ • A dynamical scalar field φ • A unit four-vector field u (Jacob Bekenstein) Making MOND Relativistic: TeVeS • The aciton for the scalar fields is: 1 Z p 1 G S = − d4x −g σ2hαβφ φ + σ4F kGσ2 (3) s 2 ,α ,β 2 l2 • The action for the unit four-vector field uµ is: K Z p h S = − d4x −g g αβg µνu u (4) v 32πG [α,µ] [β,ν] 2λ − (g µνu u + 1) K µ ν • The theory has three parameters K, k, and l, and a function F TeVeS Limits • It is important to be able to show that modified theories like TeVeS reproduce correct limiting behavior of GR and MOND • Milgrom showed that in the K ! 0, l ! 1 limit the scalar and vector fields decouple from the metric, thus reproducing General Relativity • Beckenstein showed that in the weak field and quasistatic situation MOND dynamics are reproduced, thus explaining the galactic rotation curves • TeVeS has gravitational lensing (unlike MOND) and it is in agreement* with cluster lensing observations Moffat Gravity • In 1979 John Moffat proposed a new theory of gravity called Nonsymmetric gravitational theory [3, 4] • He made the observation that the gravitational field takes the form of a symmetric tensor and one could possibly introduce a new force (like (John Moffat) EM) that has an antisymmetric tensor as the field • This ’fifth’ force would be responsible for the galactic rotation curves, as it would only affect galactic and cosmic scales Moffat Gravity • Nonsymmetric gravitational theory had problems: • No black holes • May not be stable? • In 2005, Moffat realized a more elegant formulation of his theory in Scalar-tensor-vector gravity (STVG) [5] • This theory replaces the antisymmetric (NGT) or skew (MSTG) tensor field with a four-vector field and promotes the gravitational constant to a scalar field • Is claimed to fit all observed rotation curve and cluster data as well as possibly the CMB power spectrum [6, 7] Scalar-tensor-vector gravity The action for STVG is a modified Einstein-Hilbert term (the G is now a dynamical field) plus four-vector field, scalar field, and matter terms. SSTVG = Sg + Su + Ss + SM (5) Z p 1 S = − d4x −g φ BµνB + V (u) (6) u 4 µν u Z p 1 1 S = d4x −g r Gr G − V (G) (7) s G 3 2 µ v G 1 1 + g µνr φr φ − V (φ) (8) G 2 µ ν φ 1 1 + g µνr σr σ − V (σ) (9) µ2G 2 µ ν σ Modified Gravity fits to Data (Moffat’s fits to galactic rotation curves [6]) Problems with modified gravity theories • Bullet cluster observation • Collision has appeard to separate dark matter from ordinary matter • Claim by observers to rule out modified gravity theories [8] • Moffat and Milgrom have published refutations of this claim [7] (Lensing observed in the bullet cluster [8]) Topological Geons • John Wheeler originally proposed the idea of a geon as a confined configuration of a gravitational wave • They were extended to the idea that the space-time manifold may actually have localized topological defects • It was shown that General Relativity does not admit such defects (they are unstable) • However, we expect modifications to the Einstein-Hilbert action with higher order curvature terms, and then geons are admitted into the theory [9] • They would behave sort of like elementary particles in this case Conclusion • There are several proposals on the table for how to deal with the dark matter problem • On the left hand side, we can modify gravity by either adding new fields or including exotic solutions to the Einstein equations to get agreement rotation curve and lensing data • On the right hand side, we can modify the stress energy, potentially with hidden sector particles or exotic objects like Q-balls and hidden sector particles • It is possible that both of these things happen to some extent! References Mordechai Milgrom (1983) A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis The Astrophysical Journal 270: 365-370 Jacob Bekenstein (2005) Relativistic gravitation theory for the MOND paradigm astro-ph/0403694v6 John W. Moffat (1979) New theory of gravitation Phys. Rev. D. 19: 3554 John W. Moffat (1994) Nonsymmetric Gravitational Theory gr-qc/9411006v3 John W. Moffat (2005) Scalar-Tensor-Vector Gravity Theory gr-qc/0506021v7 References J.R. Brownstein and John W. Moffat (2005) Galaxy Rotation Curves Without Non-Baryonic Dark Matter astro-ph/0506370 J.R. Brownstein and John W. Moffat (2007) The Bullet Cluster 1E0657-558 evidence shows Modified Gravity in the absence of Dark Matter astro-ph/0702146v3 D. Clowe et. al. (2006) A Direct Emperical Proof for the Existance of Dark Matter astro-ph/0608407v1 Dan N. Vollick (2008) Gravitational Geons in 1+1 Dimensions gr-qc/0807.0611v2.