Shaposhnikov and Hossenfelder, Higgs and MOND

[mitchell porter]

We had two papers yesterday making big claims in the realm of minimal BSM theory.

http://arxiv.org/abs/1803.08907
Conformal symmetry: towards the link between the Fermi and the Planck scales
Mikhail Shaposhnikov, Andrey Shkerin
(Submitted on 23 Mar 2018)
If the mass of the Higgs boson is put to zero, the classical Lagrangian of the Standard Model (SM) becomes conformally invariant (CI). Taking into account quantum non-perturbative QCD effects violating CI leads to electroweak symmetry breaking with the scale v∼Λ_QCD∼100 MeV which is three orders of magnitude less than it is observed experimentally. Depending on the mass of the top quark, the radiative corrections may lead to another minimum of the effective potential for the Higgs field with v≳M_P, where M_P is the Planck mass, at least 16 orders of magnitude more than it is observed. We explore yet another source of CI breaking associated with gravity. We suggest a non-perturbative mechanism that can reproduce the observed hierarchy between the Fermi and the Planck scales, by constructing an instanton configuration contributing to the vacuum expectation value of the Higgs field. The crucial role in this effect is played by the non-minimal coupling of the Higgs field to the Ricci scalar and by the approximate Weyl invariance of the theory for large values of the Higgs field.

http://arxiv.org/abs/1803.08683
The Redshift-Dependence of Radial Acceleration: Modified Gravity versus Particle Dark Matter
Sabine Hossenfelder, Tobias Mistele
(Submitted on 23 Mar 2018)
Modified Newtonian Dynamics has one free parameter and requires an interpolation function to recover the normal Newtonian limit. We here show that this interpolation function is unnecessary in a recently proposed covariant completion of Erik Verlinde's emergent gravity, and that Verlinde's approach moreover fixes the function's one free parameter. The so-derived correlation between the observed acceleration (inferred from rotation curves) and the gravitational acceleration due to merely the baryonic matter fits well with data. We then argue that the redshift-dependence of galactic rotation curves could offer a way to tell apart different versions of modified gravity from particle dark matter.

 

[ohwilleke]

Not impressed by Shaposhnikov's paper. It feels like it is grasping at straws and rehashing all of the faults associated with letting theory be driven by what is "natural".

Bee's paper, which derives a MOND-like modified gravity model with no non-GR parameters (it derives its counterpart to the MOND parameter from the cosmological constant of GR and still needs Newton's constant) and no arbitrary interpolation function, is impressive and a step towards a better theory, although it still isn't comprehensive and has a systemic difference just barely within margin of error from the best fit value for its derived parameter.

 

[strangerep]

Bee's paper, which derives a MOND-like modified gravity model with no non-GR parameters (it derives its counterpart to the MOND parameter from the cosmological constant of GR and still needs Newton's constant) and no arbitrary interpolation function, is impressive and a step towards a better theory, although it still isn't comprehensive and has a systemic difference just barely within margin of error from the best fit value for its derived parameter.

Sabine's "impostor field" $u^\mu$ is an assumption. IIUC, it is not "derived" in any sense, since she doesn't "sign up" to Verlinde's interpretation of it as the displacement field of an elastic medium. There also seems to be a fair bit of arbitrariness remaining in the choice of $u$ kinetic terms in the Lagrangian.

Caveat: I'm still trying to understand clearly how Sabine gets from "minimal coupling" to an "effective metric". I'm guessing it's something to do with the form of $T_{\mu\nu}$ for a perfect fluid, but I don't yet see the logic chain clearly.

 

[martinbn]

In the Hossenfelder-Mistele paper, for the covariant emergent gravity, they cite [11]. If I am not mistaken in it the theory they study is described by simply adding an extra term to the Lagrangian, namely the Lagrangian for the impostor field. My question is why is this modified gravity and not just gravity plus matter described by the impostor field?

 

[Urs Schreiber]

In the Hossenfelder-Mistele paper, for the covariant emergent gravity, they cite [11]. If I am not mistaken in it the theory they study is described by simply adding an extra term to the Lagrangian, namely the Lagrangian for the impostor field. My question is why is this modified gravity and not just gravity plus matter described by the impostor field?

Indeed. And the same comment applies already to the first proposal for making MOND relativistic, the "TeVeS"-theory of Bekenstein 04. This is actually plain Einstein-gravity coupled to peculiar vector and scalar "matter" fields. This is manifest on p. 9 of the article:

Such approaches to MOND are actually "dark matter"-theories themselves, just with a proposal for the dark matter sector that is way more ad hoc than the standard one that it is meant to replace.

 

[ohwilleke]

Such approaches to MOND are actually "dark matter"-theories themselves, just with a proposal for the dark matter sector that is way more ad hoc than the standard one that it is meant to replace.

Calling these "more ad hoc" understates the extent to which dark matter particle theories need not just the properties of a dark matter particle, but also an associated cosmological evolution theory that explains how inferred dark matter ended up in the places where it is seen. The latter "invisible" part of dark matter theories that explain why dark matter is distributed in such a systemic manner is often very ad hoc and problematic.

 

[Urs Schreiber]

dark matter particle theories need not just the properties of a dark matter particle, but also an associated cosmological evolution theory that explains how inferred dark matter ended up in the places where it is seen.

That seems to be a matter of course. You might mean to imply that theory building with dark matter is harder than if one modified the laws of gravity by hand. Nobody promised that science will be easy. But as we just saw, modifying gravity by hand breaks all kinds of things whose fix ends up being again nothing but the introduction of unobserved extra fields.

On the positive side, it seems to me that dynamical cosmic structure formation with dark matter is pretty well understood. For instance there is

Vogelsberger et. al.
"Introducing the Illustris Project: Simulating the coevolution of dark and visible matter in the Universe"
Monthly Notices of the Royal Astronomical Society, Volume 444, Issue 2, 21 October 2014,
doi:10.1093/mnras/stu1536, arXiv:1405.2921

From the abstract:

"The simulation reproduces reasonably well the cosmic star formation rate density, the galaxy luminosity function, and baryon conversion efficiency at z=0. It also qualitatively captures the impact of galaxy environment on the red fractions of galaxies. The internal velocity structure of selected well-resolved disk galaxies obeys the stellar and baryonic Tully-Fisher relation together with flat circular velocity curves. In the well-resolved regime the simulation reproduces the observed mix of early-type and late-type galaxies."

 

[Urs Schreiber]

On the positive side, it seems to me that dynamical cosmic structure formation with dark matter is pretty well understood.

For what it's worth, a quick but informed review is in:

• Volker Springel,
  Simulations of Cosmic Structure Formation,
  USP Cosmology Conference Sao Paulo, February 2013
  pdf

 

[mitchell porter]

More Higgs, more MOND:

http://arxiv.org/abs/1804.06376
Gravity, Scale Invariance and the Hierarchy Problem
Mikhail Shaposhnikov, Andrey Shkerin
(Submitted on 17 Apr 2018)
Combining the quantum scale invariance with the absence of new degrees of freedom above the electroweak scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the Planck scales remains unexplained. We argue that this hierarchy can be generated by a non-perturbative effect relating the low energy and the Planck-scale physics. The effect is manifested in the existence of an instanton configuration contributing to the vacuum expectation value of the Higgs field. We analyze such configurations in several toy models and in a phenomenologically viable theory encompassing the Standard Model and General Relativity in a scale-invariant way. Dynamical gravity and a non-minimal coupling of it to the Higgs field play a crucial role in the mechanism.

http://arxiv.org/abs/1804.05840
MOND from a brane-world picture
Mordehai Milgrom
(Submitted on 16 Apr 2018)
I describe a heuristic model where MOND dynamics emerge in a universe viewed as a nearly spherical brane embedded in a higher-dimensional flat space. The brane, described by ξ(Ω), is of density σ (ξ and Ω are the radial and angular coordinates in the embedding space). The brane and matter -- confined to the brane and of density ρ(Ω)≪σ -- are coupled to a potential ε(ξ). I restrict myself to shallow perturbations, ξ(Ω)=ℓ₀+ζ(Ω), |ζ|≪ℓ₀. A balanced brane implies â₀≡ε′(ℓ₀)∼T/σℓ₀, T is the brane tension, yielding for the velocity of small brane perturbations c²∼T/σ∼ℓ₀a^₀. But, â₀ plays the role of the MOND acceleration constant in local gravitational dynamics; so â₀∼c²/ℓ₀. What we, in the brane, perceive as the gravitational potential is ϕ≡ε[ξ(Ω)]≈ϕ₀+â₀ζ. Aspects of MOND that may emerge naturally as geometrical properties are: a. The special role of acceleration in MOND, and why it is an acceleration, a₀, that marks the transition from the standard dynamics much above a₀ to scale-invariant dynamics much below a₀. b. The intriguing connection of a₀ with cosmology. c. The Newtonian limit corresponds to local departure |ζ|≪ℓ₀; i.e., ϕ−ϕ₀∼a₀ζ≪a₀ℓ₀∼c² - whereas relativity enters when |ζ|$\not\ll$ℓ₀. The model also opens new vistas for extension, e.g., it points to possible dependence of a₀ on ϕ, and to a₀ losing its status and meaning altogether in the relativistic regime. Nonlocal effects that appear in the model dynamically might help solve the `old' cosmological-constant problem. I discuss possible connections with the nearly-de-Sitter nature of our Universe. (Abridged.)

 

[ohwilleke]

More Higgs, more MOND:

Good catch. I saw the second, but being immersed in doing my taxes (which seems every bit as difficult as modern physics these days - oh to live the poor and simple life of a grad student again), missed the first. Both are quite interesting.

The case for a desert between the electroweak and Planck scales is getting stronger on almost a weakly basis as alternatives are continually disfavored by new experiments that support the SM.

The MOND paper is also speculative but plausible.