1.3 Screened Modified Gravity
1.3.5 Galaxy-Scale Tests
Chameleon gravity theories have been subject to a number of tests on a variety of scales, ranging from the laboratory to the cosmic microwave background. However, some of the strongest constraints to date have come from weak-field galaxy-scale probes (e.g., the con-straints of Desmond et al.,2018b, described below). At the same time, as I described in
§1.1.5, galaxy scales are actually among the least explored regions of parameter space for tests of gravity in general, but will increasingly be accessible with upcoming datasets (cf.
the ‘Novel Probes’ project of Baker et al.,2019). The coming years therefore hold a great deal of promise for the exploration of chameleon parameter space with galaxy-scale probes.
This section focuses on such galaxy-scale tests of chameleon theories. A more compre-hensive review of tests and constraints would venture beyond the scope of this thesis, but such works do exist in the literature. For example, the review article by Burrage & Sakstein (2018) compiles constraints on chameleon theories from all conceivable sources. More-over, the aforementioned work by Baker et al. (2019) and the review article by Sakstein (2018) both describe a number of astrophysical probes of modified gravity theories in great detail.
‘Galaxy-scale’ here means the scale of individual galaxies, or at most, the distances sepa-rating a galaxy from its satellites and near neighbours. This section therefore excludes tests based on galaxy clusters and tests based on intergalactic distance indicators, although both of these regimes provide rather powerful probes of modified gravity.
Interestingly, several of the observable signatures described below arise—directly or indirectly—as a result of the effective EP-violation described in §1.3.2. These signatures often utilise the fact that for χ0(or| ¯fR 0|) ® 10−6, main sequence stars will be self-screened.
As illustrated in the lower row of Figure1.14, these stars will not experience any external fifth force. However, if their host galaxies are unscreened then the diffuse dark matter and gas components will feel a fifth force, and interesting phenomenology can arise as a result.
For reasons of convenience, ¯fR 0is used in the descriptions below as a constraining pa-rameter. However, it should be noted that several of these tests (and chameleon tests in general) derive constraints in a two-dimensional β− χ0space, or equivalent.
Screening Maps
As discussed in §1.3.2, ‘environmental screening’ is a phenomenon whereby an object can be screened by its environment. A galaxy that would be unscreened in isolation could be partially or fully screened if instead it is situated in an overdense environment.
This is a significant hurdle to overcome for observational probes: if a galaxy shows no significant modified gravity signal, it is first necessary to understand whether it is screened by its environment before this can be translated into theory constraints.
In the chameleon context, it has been shown in simulations (e.g. Cabré et al., 2012) that as a first approximation, the degree of environmental screening of a given galaxy can be quantified by the gravitational potential due to external sources Φextwithin a Compton wavelength of the galaxy. The Compton wavelength λC relates to ¯fR 0via the approximate equation (Cabré et al.,2012)
λC ≈ 32
vt | ¯fR 0|
10−4 Mpc. (1.88)
For this very purpose of measuring the impact of environmental screening on tests of gravity, two groups—Cabré et al. (2012) and Desmond et al. (2018c)—have constructed
‘screening maps’: 3D maps of Φextthroughout the local Universe. Both maps convert ob-served galaxy catalogues into Φextmaps using sophisticated techniques to estimate ‘unseen’
mass residing in the haloes of the observed galaxies, in unseen haloes, and in the smooth intergalactic density field.
In Chapter3, we use the screening map of Desmond et al. (2018c) which uses updated techniques and catalogues compared to that of Cabré et al. (2012). Full details regarding the construction of the map can be found in the original paper.
Galaxy Offsets
Consider a galaxy situated within an external fifth force field. If the galaxy is unscreened but the stars within it are self-screened, then the gas disc will experience the fifth force while
Figure 1.16:Posterior of the fifth force coupling ∆G /GN(≡ 2β2in our notation), obtained by Desmond et al.
(2018b) from measurements of systematic offsets between gaseous and stellar components of galaxies. The Compton wavelength λC here is 1.8 Mpc. The red histogram is the posterior in a chameleon model in which galaxies are screened according to their Newtonian potential, and stars are self-screened against the fifth force. The authors find 6.6 σ evidence for a non-zero screened fifth force. The green histogram is a model in which the galaxy screening is turned off, but stars nonetheless do not feel the fifth force. Reproduced from Desmond et al. (2018b). © American Physical Society 2018. Reprinted with permission.
the stellar disc will not. Consequently, one would expect the stellar disc to be offset from the gas disc, and the direction of this offset to align with the direction of the external fifth force vector.
Desmond et al. (2018b,2019a) use a large sample of∼ 11,000 galaxies to search for this offset signature, calculating an upper bound on| ¯fR 0| of a few ×10−8. These are the strongest reported constraints on ¯fR 0to date. Away from f (R) gravity (i.e. allowing for a varying β), the study finds a statistically significant signal at 2β2≈ 10−2and λC ≈ 2 Mpc, as shown in Figure1.16. However, the authors add the cautionary note that the signal could well be a result of a number of other effects, including unaccounted-for galaxy formation physics.
The authors find that the signal vanishes when the offsets are artificially rotated in the sky, demonstrating that the signal does indeed arise from a significant correlation between the directions of the galaxy offsets and the calculated directions of the external fifth forces, whether these fifth forces are real or not. The signal also vanishes when all mass is in-cluded in the external fifth force calculation, rather than just unscreened mass. This model is shown by the green histogram in Figure1.16. This suggests that the tentative signal is somehow connected to the complex dynamics of screening.
Galaxy Warps
If a stellar disc is offset from the halo centre as described above, then the stellar disc would be expected to warp as a result of the potential gradient. Moreover, this warping should be
maximised when the rotation axis of the disc aligns with the external fifth force field.
Desmond et al. (2018a) search for this signature in data from∼ 4000 galaxies of the NASA Sloan Atlas. Tantalisingly, this study also finds support for a screened modified gravity with 2β2≈ 10−2and λC ≈ 2 Mpc, despite the independence of the dataset from that of the offset study described above.
Rotation Curves
Galaxy rotation curves offer a number of observable signatures:
1. If stars are self-screened in an unscreened galaxy, the gas rotation curve will show greater velocities than the stellar rotation curve. Vikram et al. (2018) searched for this signal in the rotation curves of 6 low surface-brightness galaxies, yielding an upper bound on| ¯fR 0| of 10−6.
2. If the rotation axis of a galactic disc is perpendicular the external fifth force field, the stellar-gas offset discussed above will result in asymmetries in the galaxy rota-tion curves. This effect was studied by Vikram et al. (2013), who found no significant deviations from standard gravity.
3. If a galaxy is partially screened, gas rotation curves will display an ‘upturn’ at the lo-cation of the screening radius. This effect is the subject of Chapters2and3.
Stellar Streams
Stellar streams arise from satellite galaxies and globular clusters being tidally disrupted by the central host galaxy. If the Milky Way is partially screened, then a DM-dominated satel-lite galaxy on an orbit outside the Milky Way screening radius will feel a fifth force. The screened stars within it, however, will not feel the fifth force but will be dragged along by the satellite’s halo. As the satellite is tidally disrupted by the Milky Way, the stars will be preferentially disrupted into the trailing stream, rather than the leading stream, leading to an asymmetry about the progenitor.
This effect was first predicted by Kesden & Kamionkowski (2006a,b) for an intrinsically EP-violating “dark matter force.” Chapter4studies this effect in the context of chameleon theories, where the EP-violation emerges as a result of screening.