Jekyll2023-11-21T00:19:21+00:00http://wevbarker.com/feed.xmlDr. Will Barker (威廉 巴克尔) | theoretical physics, cosmologyThis site is for theoretical, high-energy and gravitational physics and cosmology (broadly defined). More specific topics might include differential geometry, geometric algebra, gauge theories of gravity. Blog-Mu-Nu is a blog which reviews interesting arXiv preprints from [gr-qc], [hep-th] and [astro-ph].Dr. Will E. V. BarkerarXiv Jul 22nd-27th 20232023-07-27T00:00:00+00:002023-07-27T00:00:00+00:00http://wevbarker.com/2023/07/27/gr-qc<head>
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<h2>A week on gr-qc</h2>
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<li><a href="https://arxiv.org/abs/2307.13939"><tt>2307.13939</tt></a> A gravitating global monopole gan be generated by breaking \(SO(3)\) to \(U(1)\).</li>
<li><a href="https://arxiv.org/abs/2307.13760"><tt>2307.13760</tt></a> An opportunity to get a basic understanding of Carrollian geometry; we were not really successful in our discussion so this is left to another day!</li>
<li><a href="https://arxiv.org/abs/2307.13803"><tt>2307.13803</tt></a> This one potentially looked very interesting. As is well known, there are significant problems in constructing nonlinear completions of massive gravity. The authors of this paper propose a massive graviton without introducing the Boulware-Deser ghost, requiring Vainshtein screening or even modifying classical GR. The (effective?) model they are using for the gravitational sector is \(S_{\text{eff}}=\int\mathrm{d}^4x\sqrt{-g}\left(M_{Pl}^2R/2-i\gamma\text{tr}\log |g_{\mu\nu}|\right)\). The motivation for this follows from assuming a non-trivial functional measure, whose effects are preserved by selecting a Gaussian regularisation scheme (see <a href="https://arxiv.org/abs/2102.10688"><tt>2102.10688</tt></a> for more details). Phenomenologically, \(\gamma\) is derived from a Wilsonian coefficient and is proportional to the graviton mass, with GR being recovered in the limit \(\gamma\to 0\). A key feature of this approach is that the GR limit is free from the vDVZ discontinuity. This is supposedly because the model with the logarithm is <i>already</i> a nonlinear completion of the theory, and in the field equations following it can be seen that the dynamics have a smooth massless limit. Separately, if the model is linearised then the Fierz-Pauli mass term appears in proportion to \(\gamma\). This argument isn't too clear to me, since I'd understood vDVZ to appear at the linear level anyway. There are some other curious features here; the square is purely imaginary, so the particle has to be virtual, and due to its origin in the functional measure it vanishes in the \(\hbar\to 0\) limit. Finally, despite the correction appearing to violate diffeomorphism invariance, the symmetry is restored by the modifications needed to variations in the presence of a non-trivial measure. In the final section of the paper, applications to the Newtonian potential are considered: this is interesting, you would typically expect a Yukawa-type potential for a massive graviton, but the imaginary nature of the mass leads to an oscillatory potential modulated by Yukawa decay.</li>
<li><a href="https://arxiv.org/abs/2307.13435"><tt>2307.13435</tt></a> I was not aware that there was a <a href="http://www.asc.rssi.ru/radioastron/">Russian space VLBI mission</a>.</li>
<li><a href="https://arxiv.org/abs/2307.11151"><tt>2307.11151</tt></a> By some excellent authors ;)</li>
</ol>Dr. Will E. V. BarkerarXiv Jul 17th-21st 20232023-07-21T00:00:00+00:002023-07-21T00:00:00+00:00http://wevbarker.com/2023/07/21/gr-qc<head>
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<h2>A week on gr-qc</h2>
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<li><a href="https://arxiv.org/abs/2307.10399"><tt>2307.10399</tt></a> We opened this just to learn that an anisotropic star is one in which the matter stress energy tensor is anisotropic, the spacetime is still spherically symmetric.</li>
<li><a href="https://arxiv.org/abs/2307.10199"><tt>2307.10199</tt></a> I'd heard of Einstein-Maxwell and Einstein-Proca, but who is working on Einstein-Yang-Mills? I had some vague notion that people would not be interested in this, because there is no meaningful classical limit in QCD. Actually \(SU(3)\) is not the issue, there is a big community of interest for \(SU(2)\). After some discussion, I learned that this is about gravitating exact solutions, not connected to sphalerons. We did not explore the paper very thoroughly, but there is some nice discussion of black hole-like solutions.</li>
<li><a href="https://arxiv.org/abs/2307.10899"><tt>2307.10899</tt></a> For the cosmologists. This looks somewhat like an extension of the `early dark energy' paradigm that was floating around a few years back. The authors propose to modify the cosmological constant by \(\Lambda\to\Lambda_{\text{s}}\equiv\Lambda_{\text{s0}}\ \text{sgn}[z_\dagger-z]\). Well, I think the conclusion we drew is that the approach might be useful in the functional parameterisation of \(w(z)\) reconstruction, but apart from that the physical origin of the model is not really clear...</li>
<li><a href="https://arxiv.org/abs/2307.10126"><tt>2307.10126</tt></a> So, what is a `Polish doughnut'? It is a thick accretion disk.</li>
<li><a href="https://arxiv.org/abs/2307.07743"><tt>2307.07743</tt></a> Personally the most interesting article this week, a letter. The authors are considering some simple toy models, for which there are UV and EFT versions. On the UV side, they consider the complex scalar with a mass and a quartic potential, with overall \(U(1)\) symmetry, and also the extension of this with a vector field to give Abelian Higgs. The EFT counterparts are then quite interesting, though the initial formulation is pretty textbook. For the scalar theory, the heavy radial dynamics are integrated out, and it turns out that the resulting Lagrangian for the azimuthal mode \((\partial\Theta)^2(1-(\partial\Theta)^2/M^2)\) is what the cosmologists have been calling \(K\)-esssence theory (I heard this term being thrown around since forever). In particular, the nomenclature requires the function \(K(X)\propto X-X^2/M^2\) to encode the kinetic structure. This doesn't look healthy, and it isn't: the Cauchy problem breaks down as \(K'\to 0\), which you can in principle reach on a physical phase trajectory. Up to a change of variables, the same effect can be seen when the radial mode is integrated out of the Abelian Higgs model, but the resulting EFT can be shown to be the nonlinear Proca model. To solve the Cauchy problem, there was previously proposed an approach of <i>fixing</i> the equations of motion. This seems an arbitrary approach, but the idea is to shift the field equations by introducing alternative variables which approximate the originals due to some suitable <i>driving</i> condition. The dynamical evolution can then be guided through the singular regions whilst remaining roughly faithful to the EFT. It seems there is a lot of work needed to make this robust. The letter itself makes some attempts at numerical implementation, showing that <i>fixing</i> is not satisfactory in many cases, and that the breakdown of the EFT dynamics seems to coincide with high-frequency modes in the corresponding UV model (I feel there is probably something interesting to say about that). This is all nice on its own, but for me the most interesting feature is that this letter is a goldmine of references for the dynamical failures of the nonlinear Proca model.</li>
<li><a href="https://arxiv.org/abs/2307.07668"><tt>2307.07668</tt></a> For fun, and only four pages or so! I learned that there is such a thing as <tt>hist-ph</tt>.</li>
</ol>Dr. Will E. V. BarkerarXiv Jan 4th-8th 20202021-01-09T00:00:00+00:002021-01-09T00:00:00+00:00http://wevbarker.com/2021/01/09/post-1<head>
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<h2><a href="https://arxiv.org/abs/2012.14984">2012.14984</a> xPPN: An implementation of the parametrized post-Newtonian formalism using xAct for Mathematica</h2>
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Many in the physics community are familiar with the <tt>xAct</tt> tensor manipulation suite for <tt>Mathematica</tt>, and those who aren't probably should be. In recent years, <tt>xAct</tt> has consolidated its place as the go-to computer algebra tool in gravitational theory, outperforming various predecessors with its powerful 'canonicalise' function, and attracting a flurry of applied package development. Some of these packages float and others sink: I'm curious to see how Manuel Hohmann's new <tt>xPPN</tt> package will fare.
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Most modifications to Einstein's theory can be cast in the parametrized post-Newtonian (PPN) formalism. PPN allows the theory to be compared, as a ten-parameter modification of the Newtonian theory, against the gold standard set by GR. The implementation of PPN is usually extremely complicated, and varies substantially from theory to theory. Thus xPPN, a general implementation of the PPN formalism, is potentially very exciting.
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At the heart of the implementation seems to be the definition of two bespoke manifolds for the \(3+1\) decomposition. Assuming that the covariant theory lives in some sense on \(M_4\), a spacelike foliation \(S_3\) and timelike threading \(T_1\) are introduced as separate <tt>xTensor</tt> manifolds, where \(M_4\cong T_1\times S_3\). This cuts right through the pre-existing notion of ADM decomposition in <tt>xAct</tt>, which I've wrestled with recently in the context of the <a href="https://arxiv.org/abs/2101.02645">Hamiltonian analysis</a>. In the end, I kept a single Minkowski manifold \(M_4\), and defined a set of projections accompanied by very many rules. This is not ideal, but the relevant parts of <tt>xAct</tt> (such as <tt>xCoba</tt>) have quite patchy documentation, which makes life less than easy! I won't go into the guts of the higher functions of the package, but suffice to say the post-Newtonian potentials are all defined, along with certain 'utility functions' which facilitate the human-assisted expansion. A nice walk-through is provided for a simple Brans-Dicke-like theory, but since I've not tried it out, I can't offer further comment.
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My main concern is the 'theory-scope' of the package. This is of course the hardest part to implement, since you can never tell quite in what terms the next theory will be cast. The Brans-Dicke theory obviously inherits much of the machinery of GR, but with an extra scalar \(\psi\) - I expect e.g. the variations on mimetic gravity could be similarly tackled. This scalar naturally has to be defined when using the package, and presumably one may extend to higher-spin fields also. Accordingly I've already recommended <tt>xPPN</tt> to a colleague who is <a href="https://arxiv.org/abs/2007.00082">working on the new relativistic completion of MOND</a>.
However, it is often interesting to build theories out of a gauge-covariant derivative. Accordingly, the <tt>xPPN</tt> package defines three connections: Levi-Civita, teleparallel and symmetric-teleparallel. I'm very happy about the last of these, which follows on from the <a href="https://arxiv.org/abs/1903.06830">non-metricity theories</a> of Jiménez, Heisenberg and Koivisto, and is something I'd like to work on at some point. However, in the short term I'm interested in a free connection, in the context of torsion theories. This is likely workable in the <tt>xPPN</tt> setup, but might take some <tt>xAct</tt>-jitsu. Again, I'd have to try.
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Overall, this paper introduces software rather than physics, and is structured accordingly. Nonetheless, I am happy to have come across <tt>xPPN</tt>, and am looking forward to trying it out in the near future.
</p>Dr. Will E. V. BarkerNew arXiv review blog coming soon!2020-12-22T00:00:00+00:002020-12-22T00:00:00+00:00http://wevbarker.com/2020/12/22/testpost<head>
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I'm setting up Blo\(g_{\mu\nu}\) to further hone my skills as a peer-review referee, and to draw well-deserved attention to new preprints that I find interesting. The idea is to write a short review of at least one preprint per week, likely drawn from the <tt>[gr-qc]</tt>, <tt>[astro-ph]</tt> or <tt>[hep-th]</tt> arXiv.
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This will likely start in the new year, as I still need to figure out comments on <tt>disqus</tt>, and how to handle arXiv trackbacks and <tt>RSS</tt> so that the authors are properly credited.
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The idea for Blo\(g_{\mu\nu}\) is unashamedly stolen from Dr. Sunny Vagnozzi's <a href="https://www.sunnyvagnozzi.com/blog">His Dark CMBlog</a>. Sunny's <a href="https://www.sunnyvagnozzi.com/">entire website</a> is absolutely fantastic, and you should explore it before reading any more of my posts.
</p>Dr. Will E. V. Barker