Dark Matter

# The Standard Model + General Relativity

<br>

<div style="text-align: center; float: left; width: 50%">
              <img
                src="https://upload.wikimedia.org/wikipedia/commons/2/2b/Standard_Model_of_Elementary_Particles_dark.svg"
                width="95%">
              <font size="3"> Credit: Cush [Wikimedia Commons]</font>
            </div>

<div style="text-align: left; float: right; width: 47%">
              <h2>Tested with extraordinary precision</h2>
              <br>
              <h3>   • e.g., electron magnetic moment, Higgs boson</h3>
              <h3>   • gravitational lensing, gravitational waves</h3>
              <br><br><br>
              <h2>However...</h2>
              <br><br><br>
              <div class="fragment">
                <h2>Several deep inconsistencies</h2>
                <h2>with the observed universe</h2>
              </div>
              
            </div>

# Unexplained mysteries

<br>

<h2>Why is there so much more matter than anti-matter?</h2>
                <h3> • CP-violation in the Standard Model is too small</h3>
              </div>

<h2>Quantum theory for gravitation?</h2>

</div>

<h2>No explanation for dark energy</h2>
                <h3> • Explain accelerated expansion of universe
                  • Cosmologists: Why is Λ so large?
                  • Particle theorists: Why is Λ so small?
                </h3>

</div>

<h2>No explanation for dark matter...</h2>

</div>

# Focus: dark matter

<br>

<div style="text-align: center; float: left; width: 35%">
              <br><br><br>
              <h3>Coma Cluster</h3>
              <br>
              <img
                src="https://upload.wikimedia.org/wikipedia/commons/7/7d/Ssc2007-10a1.jpg"
                width="95%">
              <font size="3"> Sloan Digital Sky Survey + Spitzer Space
                Telescope
                [NASA / JPL-Caltech / L. Jenkins]</font>
            </div>

<div style="text-align: left; float: right; width: 47%">
              <h2>First major hints: galaxy clusters</h2>
              <br>
              <h3>Fritz Zwicky: clusters too fast. <br>
                • Termed phrase "dark matter"</h3><br>
              <p>(And some even earlier hints)</p>

<br>
              <div class="fragment">
                <h3>Then: Vera Rubin, along with Kent Ford</h3>
                <br>
                <img src="img/vera-rubin.jpg" width="60%"><br>
                <font size="3">
                  [AIP Emilio Segrè Visual Archives, Rubin Collection]
                </font>

</div>
            </div>

# Galactic Rotation Curves

<div style="text-align: center; float: left; width: 70%">
              <br><br>
              <img
                src="https://upload.wikimedia.org/wikipedia/commons/c/cd/Rotation_curve_of_spiral_galaxy_Messier_33_%28Triangulum%29.png"
                width="95%"><br>
              <font size="3">[Mario De Leo, Wikimedia Commons]</font>
            </div>

<div style="text-align: left; float: right; width: 30%">
              <br><br>
              <h2>Missing Matter?</h2>
              <br>
              <p data-markdown>• Not a small correction</p>
              <br>
              <p data-markdown>• 80 - 95% of mass is "missing"</p>
              <br>
              <div data-markdown class="fragment fade-in">
                <p data-markdown>• Implies <font color="orange">dark matter</font></p><br>
                \[a = \frac{G \, [M(r) + {\color{orange}\delta M(r)}]}{r^2} \]
                <br>
                <p data-markdown>   • Simulations + observations: DM "halo"</p>
              </div>
              <br>
              <p data-markdown class="fragment fade-in">• ... or <font
                  color="green">modified
                  gravity</font><br><br>
                \[a = \frac{[G + {\color{green}\delta G(M,r)}] \, M(r)}{r^2} \]
              </p>
              <br>
            </div>

# Bullet Cluster

<div style="text-align: left; float: left; width: 65%">
              <br>

<div class="r-stack">
                <div class="fragment fade-out" data-fragment-index="0">
                  <img
                    src="https://upload.wikimedia.org/wikipedia/commons/e/ea/Bullet_cluster.jpg"
                    width="100%"><br>
                  <font size="3">Chandra X-ray Observatory [NASA]</font>
                </div>

<div class="fragment fade-in" data-fragment-index="0">
                  <img
                    src="https://upload.wikimedia.org/wikipedia/commons/a/a8/1e0657_scale.jpg"
                    width="90%">
                  <font size="3">NASA/CXC/M. Weiss - Chandra X-Ray Observatory</font>
                </div>
              </div>

</div>

<div style="text-align: left; float: right; width: 35%">
              <br>
              <h3>• Colliding galaxy clusters ~ 4 Gyr</h3>
              <br>
              <h3>• X-ray emission image:<br> distribution of gas (baryons)</h3>
              <br>
              <br>
              <div class="fragment fade-in" data-fragment-index="0">
                <h3>• Composite image: X-ray + lensing</h3>
                <br>
                <h3>• Pink = gas (X-ray)</h3>
                <h3>• blue = mass (gravitational lensing)</h3>
                <br>
                <h3 class="fragment fade-in" data-fragment-index="1">
                  • Frictionless dark matter: <br>
                  passes straight through
                </h3>
              </div>
            </div>

# Dark Matter: What we know

<br>
            <h3> There's lots of it</h3>

<h3> It gravitationally clusters in halos around galaxies</h3>
            <h4> (really, galaxies gravitationally cluster around DM)</h4>

<div style="text-align: left; float: left; width: 50%"
              class="fragment">
              <br><br>
              <h2>Very strong evidence:</h2>
              <br>
              <h3>• Rotation curves, gravitational lensing, CMB </h3>
              <br>
              <h3>• Also: large scale structure, BAO etc. </h3>
              <br>
              <h3>• It's not strange for particles to not interact with
                light (e.g., neutrinos)</h3>
              <br>
              <br>
              <h3 class="fragment">• ΛCDM model works extremely well
                <br>  • Ωc =
                0.2589(57) [Planck] </h3>
              <h3 class="fragment">• (Just need to work out the Λ and CDM parts)</h3>
            </div>

# Dark Matter: What we don't know

<br>
            <div class="fragment" data-fragment-index="0">
              <h2> ... everything else</h2>
            </div>

<br>

<div class="r-stack">
              <img class="fragment" data-fragment-index="1"
                src="img/DM_masses2.png" width="80%">
              <img class="fragment" data-fragment-index="3"
                src="img/DM_masses3.png" width="80%">
            </div>
            <div class="fragment" data-fragment-index="1">
              <font size="3">US "Cosmic Visions" report [arXiv:1707.04591]</font>
            </div>

<div class="fragment" data-fragment-index="1">
              <h3>• Possible mass range: 90 orders of magnitude!</h3>
            </div>
            <div class="fragment" data-fragment-index="2">
              <h3>• Fundamental particle: 50 orders (de Broglie to Planck)</h3>
            </div>

<br>

<div class="fragment">
              <h3> • Vast majority of focus on WIMPs, but field is very wide</h3>
            </div>

# WIMP miracle

<!-- <div class="r-stack">
              <img class="fragment fade-out" data-fragment-index="0"
                src="img/DM_masses2.png" width="80%">
              <img class="fragment current-visible" data-fragment-index="0"
                src="img/DM_masses3.png" width="80%">
            </div>

<div style="text-align: left; float: left; width: 30%">
              <br><br>
              <img src="img/Feynman.png" width="95%">
              <br><br>
              <h3> • Early universe: hot and dense</h3>
              <h3> DM + SM in thermal equilibrium</h3>
              <br>
              <h3 class="fragment fade-in" data-fragment-index="0">
                • Universe cools: <br>
                Boltzmann suppression
              </h3>
              <br>
              <h3 class="fragment fade-in" data-fragment-index="1">
                • Universe expands: <br>
                Shuts off annihilation
              </h3>
              
            </div>

<div style="text-align: center; float: right; width: 65%">
              <div class="r-stack">
                <img class="fragment fade-in" data-fragment-index="0"
                  src="img/YDM/Yeq.png" width="90%">
                <img class="fragment fade-in" data-fragment-index="1"
                  src="img/YDM/YDM1.png" width="90%">
                <img class="fragment fade-in" data-fragment-index="2"
                  src="img/YDM/YDM2.png" width="90%">
              </div>
              <h3 class="fragment fade-in" data-fragment-index="3">
                • Weak interaction ($G_F \simeq 10^{-5}\,{\rm
                GeV}^{-2}$): new physics scale<br>
                • $m_{\rm weak} \simeq 100\,{\rm GeV}$ <br>
              </h3>
              <h3 class="fragment fade-in" data-fragment-index="4">
                • $\langle\sigma v\rangle_{\rm weak} \simeq
                3\times10^{-26}\,{\rm
                cm}^3/{\rm s}$ !!!
              </h3>
            </div>

# WIMP Searches: XENON

<div style="text-align: left; float: left; width: 60%">
              <div class="r-stack">
                <div class="fragment fade-out" data-fragment-index="1">
                  <br><br><br>
                  <img src="img/Feynman.png" width="65%">
                  <br><br>
                  <h3 class="fragment highlight-red" data-fragment-index="0">•
                    Direct detection
                    (scattering)</h3>
                  <h3>• Indirect detection (annihilation)</h3>
                  <h3>• Collider searches (production)</h3>
                </div>
                <div>
                  <div class="fragment fade-in" data-fragment-index="1">
                    <br>
                    <h3>Excluded cross-section for WIMPs:</h3>
                    <img
                      src="img/WIMP-constraints.png" width="100%">
                  </div>
                  <h3 class="fragment fade-in" data-fragment-index="2">
                     • Mass below nuclear mass: energy threshold
                  </h3>
                  <h3 class="fragment fade-in" data-fragment-index="2">
                     • High mass: fewer particles
                  </h3>
                </div>
              </div>
            </div>

# En*light*ening the search for Dark Matter?
            ## Atomic Physics!

<br>

<h2> Mass drops below nuclear mass:</h2>
                <h3> • No nuclear recoils
                   • Instead: electron recoils + ionisation</h3>
              </div>
              <br>

<h2> Mass drops below electron mass:</h2>
                <h3> • No electron recoils
                   • Instead: absorption (dark photoelectric effect)</h3>
              </div>
              <br>

<h2> Mass drops below eV:</h2>
                <h3> • Classical DM field
                   • Quantum sensing (atomic clocks)</h3>
              </div>
              <br>

</div>

<div style="text-align: center; float: right; width: 40%">
              <br>
              <img class="fragment" data-fragment-index="0"
                src="img/atom.png" width="40%">
              <br><br>
              <div class="r-stack">
                <div class="fragment" data-fragment-index="2">
                  <img
                    src="img/laser-JILA.jpg" width="90%"><br>
                  <font size="3">[JILA]</font>
                </div>
                <div class="fragment" data-fragment-index="3">
                  <img
                    src="img/Ye_UCBolder-SrLattice.jpg" width="80%"><br>
                  <font size="3">[Ye/UCBolder]</font>
                </div>
              </div>
            </div>

# Light "WIMPs": electron ionisation

<div>
              <br>
              <div style="text-align: center; float: left; width: 40%">
                <img src="img/ionisation.svg" width="65%"><br>
                <font size="2">[nagwa.com/]</font>
              </div>

<div style="text-align: center; float: right; width: 60%">
                <br>
                <h2>Mass drops below nucleus: no nuclear recoils</h2>
                <br>
                <h2>Instead: electron recoils - ionisation $R\propto K$</h2>
                <br>
                <img class="fragment fade-in" src="img/K-approx2.png"
                  width="65%">
              </div>
            </div>

* Ashlee R. Caddell, **BMR**,
            [arXiv:2305.05125](http://arxiv.org/abs/2305.05125)
            * **BMR**, V. V. Flambaum, [Phys. Rev. D **100** 063017
            (2019)](https://link.aps.org/doi/10.1103/PhysRevD.100.063017)
            * **BMR**, Flambaum, Gribakin, [Phys. Rev. Lett **116** 023201
            (2016)](http://link.aps.org/doi/10.1103/PhysRevLett.116.023201)

# Light and Ultralight Dark Matter

$$ \Huge
            \rho_{\rm DM}\simeq 0.3 ~ \frac{\rm GeV}{{\rm cm}^3}
            $$

<br>

## Mass decreases $\implies$ number density increases:
            ## Classical boson field (e.g., axions, scalars)

<br>

<div style="text-align: left; float: right; width: 70%">
              <div class="fragment fade-in">
                <h3>
                  1. No interaction: oscillation: $\phi = \phi_0 \cos(m_\phi
                  t)$
                </h3>
                \[\phi_0^2\propto \rho_{\rm DM}\]
              </div>

<h3 class="fragment fade-in">
                2. Interactions: clumps
              </h3>
              <br>
              <h3 class="fragment fade-in">
                3. Also: constant build-up (local over-densities)
              </h3>
            </div>

<h2 class="fragment fade-in">
              Classical field: quantum sensors (clocks)
            </h2>

# Atomic Clocks 101:

<br>

### Clock: frequency reference
            <div class="fragment fade-in">
              <h3>
                Best atomic clocks approach accuracy: $\delta f/f \sim
                10^{-20}$
              </h3>
            </div>

<div class="fragment fade-in"
              style="text-align: center; float: left; width: 32%">
              <img src="img/Bohr.png" width="70%"><br>
              <font size="3"> JabberWok [Wikimedia Commons]</font>
              <br>
              <h3>
                Atomic transition: "perfect*" frequency reference
              </h3>
            </div>

<div class="fragment fade-in"
              style="text-align: center; float: left; width: 32%">
              <img src="img/Wcislo2016.png" width="95%">
              <font size="3"> Wcislo, Science 2016</font>
              <br>
              <h3>
                Compare frequency of oscillator to atomic transition
              </h3>
            </div>

<div class="fragment fade-in"
              style="text-align: center; float: right; width: 32%">
              <img src="img/Al+Choi2010.png" width="95%">
              <font size="3"> Choi, Phys. Rev. Lett. 2018</font>
              <br>
              <h3>
                Lock on: Adjust local oscillator to maximum transition rate
              </h3>
            </div>

# "Listen" for DM field using atomic clocks

<br>

<div style="text-align: left; float: left; width: 50%">
              <br> <br>
              <img src="img/NHanacek_NIST.png" width="90%"><br>
              <font size="3">[N Hanacek/NIST]</font>
            </div>

<div style="text-align: left; float: right; width: 50%">
              <br>
              <div>
                <h3>
                   • DM scalar field has small interaction with matter
                </h3>
                <h3>
                   • Shift atomic energy levels and frequencies
                </h3>
              </div>
              <br>
              <div class="fragment fade-in">
                <h3>Observable shift:</h3>
                
                <br>
                \[\huge
                \frac{\delta f}{f} = \kappa \, \phi_{\rm DM}(\vec{r},t)
                \]
              </div>
              <br>
              <div class="fragment fade-in">
                <h4>
                   • $\kappa$ - model dependent parameter
                </h4>
                <h4>
                   • Calculated: high-precision atomic theory
                </h4>
              </div>

<br>
              <div class="fragment fade-in">
                <h3>Example: variation of constants</h3>
                
                <br>
                \[\huge
                \mathcal{L} = \phi F_{\mu\nu}F^{\mu\nu}
                \implies \alpha\to\alpha+\phi_{\rm DM}(\vec{r},t)
                \]
                \[\huge
                \kappa = \frac{{\rm d} f}{{\rm d} \alpha}\frac{\alpha_0}{f_0}
                \]
              </div>

</div>

# Oscillating signals

<div style="text-align: left; float: left; width: 50%">
              <br>
              <h3>Case: oscillating field:</h3>
              \[\huge
              \phi_{\rm DM} = \phi_0 \cos({m_\phi t})
              \]
              <br>
              \[\huge
              \frac{\delta f}{f} = \kappa \phi_0 \cos({m_\phi t})
              \]
              <br>
              <br>
              <div class="fragment fade-in">
                <h3>• Constraints from clock-clock comparisons</h3>
                <br>
                <h3>• ~ $10^{-2}$ Hz (optical clocks)</h3>
                <h4>
                    • e.g., Wcislo et al
                  <a
                    href="https://advances.sciencemag.org/content/4/12/eaau4869">
                    Science Advances <b>4</b>, 4869 (2018)</a>
                </h4>
                <br>
                <h3>• ~ $10^{-6}-10^{-2}$ Hz (microwave clocks)</h3>
                <h3>• $\implies m = 10^{-21}-10^{-18}$ eV</h3>
                <h4>
                    • e.g., Hees et al
                  <a
                    href="http://link.aps.org/doi/10.1103/PhysRevLett.117.061301">
                    Phys. Rev. Lett. <b>117</b>, 061301 (2016)</a>
                </h4>
              </div>
            </div>

<div style="text-align: left; float: right; width: 50%">
              <br> <br>
              <div class="fragment fade-in">
                <h3>The DAMNED experiment:</h3>
                <img src="img/damned.png" width="90%"><br>
                <p>(DArk Matter search using Non-Equal Delay lines)</p><br>
                <div class="fragment fade-in">
                  <h3>• Modifies length + refractive index</h3>
                  <h3>• 10-100 kHz range ($m=10^{-10}$ eV)</h3>
                  <h3>• Led by Etienne Savalle (SYRTE Paris)</h3>
                  Savalle, Hees, Frank, Cantin, Pottie, <b>BMR</b>, Cros,
                  McAllister,
                  Wolf, <br>
                  <a
                    href="https://link.aps.org/doi/10.1103/PhysRevLett.126.051301">
                    Phys. Rev. Lett. <b>126</b>, 051301
                    (2021)</a>
                </div>
              </div>
            </div>

# GPS.DM

<div style="text-align: left; float: left; width: 35%">
              <br>
              
              
              <h3>• 30 Cs, Rb atomic clocks</h3>
              <br>
              <h3>• Over 20 years of high-quality data</h3>
              <br>
              <h3>• Publicly available (JPL)</h3>
              <br>
              <h3>• 50,000 km Dark Matter observatory</h3>
              <br>
              
              <div class="fragment fade-in">
                <video width="75%" data-autoplay muted>
                  <source src="img/GPSDM.mp4"></video><br>
                <font size="3">[Video: Conner Dailey (honors student)]</font>
              </div>
            </div>

<div style="text-align: center; float: right; width: 65%">
              
              <img div class="fragment fade-in" src="img/gps-data.png"
                width="45%">
              <br>
              <br>
              <br>
              <div class="fragment fade-in">
                <img src="img/GPSDM-results.png" width="98%">
                <b>BMR</b>, Blewitt, Dailey, Murphy, Pospelov, Rollings,
                Sherman,
                Williams, Derevianko, <br>
                <a
                  href="http://www.nature.com/articles/s41467-017-01440-4">
                  Nature Comms.
                  (2017)</a>

</div>

# Super-massive black hole at the Galactic Centre

<div style="text-align: left; float: left; width: 50%">
              <h3>• with UCLA Galactic Centre Group</h3>
              <h4>   • Observations led by Tuan Do</h4>
              <h4>   • Andrea Ghez: Awarded 2020 Nobel
                prize for discovery of black hole</h4>
              <br>
              <h3>• Keck telescope in Hawaii</h3>
              <br>
              <h3>• Motion of ∼1000 stars tracked</h3>
              <h4>   • Precise spectroscopy for many stars</h4>
              <br>
              <br>
              <div class="fragment fade-in">
                <h3>• High gravitational potential</h3>
                <h3>• Possibly large concentration of dark
                  matter </h3>
                <h3>• (also other "exotic" physics)</h3>
              </div>
            </div>