Some driving questions:

- How do the constraints on γ propagate into constraints on specific modified gravity models? Which (classes of) models can be discarded by strong lensing (SL)?
- Can we write the lens equation in a simple form in non-homogeneous universes (e.g. spherically symmetric, LTB models)?
- To what extent, can SL in multiple lines-of-sight constrain inhomogeneous models?
- Are there models with different high-z behavior for which the SL tests would be more stringent?
- What are the constraints on specific classes of MOG models from the combination of SL with other data (e.g. gravity waves, extra-solar planets, other cosmological probes)

**Suggested reading lists**

General MOG refs and cosmological tests:

- Jain, Bhuvnesh; Khoury, Justin, 2010,
*Cosmological tests of gravity*, Annals of Physics, 325, 1479 (ADS link) - Jain, Bhuvnesh, et al., 2013,
*Novel Probes of Gravity and Dark Energy*, arXiv:1309.5389 - DE and Modified Gravity: Austin Joyce, Lucas Lombriser, Fabian Schmidt, 2016,
*Dark Energy vs. Modified Gravity*, arXiv:1601.06133 - Status of ΛCDM: Philip Bull, et al., 2015,
*Beyond ΛCDM: Problems, solutions, and the road ahead*, arXiv:1512.05356

Examples of SL constraining cosmology and MOG:

Potentially relevant papers for extending the lens equation to inhomogeneous cosmologies:

- G. Fanizza, M. Gasperini, G. Marozzi and G. Veneziano,
*An exact Jacobi map in the geodesic light-cone gauge*, JCAP 1311, 019 (2013) [doi:10.1088/1475-7516/2013/11/019, arXiv:1308.4935] - G. Fanizza and F. Nugier,
*Lensing in the geodesic light-cone coordinates and its (exact) illustration to an off-center observer in Lemaître-Tolman-Bondi models*, JCAP 1502, 002 (2015) [doi:10.1088/1475-7516/2015/02/002, arXiv:1408.1604]

Below are two inspiring plots that motivate this group in light of the observational constraints on modified gravity. BTW, the recent Gravitational Wave results strengthen the importance of using cosmology to constrain the gravity theory, as they are complementary to those derived from GW ("This improves on Solar System and binary pulsar bounds [98,99] by factors of a few and a thousand, respectively, but does not improve on the model-dependent bounds derived from the dynamics of Galaxy clusters [100] and weak lensing observations [101]" [PRL 116, 061102 (2016)]).

Tests of gravity at diferent length scales. Red lines shows observations that probe
the sum of metric potentials via weak and strong gravitational lensing or the ISW effect. Blue
lines show dynamical measurements that rely on the motions of stars or galaxies or other
non-relativistic tracers. [Fig. 8 from Jain, Bhuvnesh; Khoury, Justin, 2010, *Cosmological tests of gravity*, Annals of Physics, 325, 1479 (ADS link)]

Astrophysical [64, 38, 39] and cosmological [89, 90, 91] limits on chameleon theories. The spatial
scale on the x-axis gives the range of length scales probed by particular experiments. The parameter on the
y-axis is the background field value, or the range of the interaction (y-axis label on the right side) for an
*f(R)* model of the accelerating universe. The rectangular regions give the exclusion zone from a particular
experiment. All but the solar system results have been obtained in the last 5 years, illustrating the impressive
interplay between theory and experiment in the field. The two rectangles with dots are meant to indicate
preliminary results from ongoing work.
[Fig. 2 from Jain, Bhuvnesh, et al., 2013, *Novel Probes of Gravity and Dark Energy*, arXiv:1309.5389 (adapted from Lombriser et al. 2012, Phys.Rev.,
D85:102001)]

Notes on modifications of GR:

- Horndeski: Horndeski, IJTP 1974; Kobayashi et al. 2011
- Beyond Horndeski: PRLm 2015, %$\gamma_{\rm PPN} = \frac{1+\alpha_H}{c_T}$%, %$G_N = \frac{c_T^4}{8M^2 (1+\alpha_H)^2}$%
- Vainshtein
- Chamaleon, D. Mota, PLB, 2004; Khoury, PRL

Invited members: Felipe Tovar, Habib Dúmet, Miguel Quartin, Santiago Bergliaffa, Marcelo Vargas, Vanessa Pacheco (?); Remotos (?): Vinicius Bragança, Marcos Lima, Hermano Velten, Cristofher Zuñiga

-- MartinMakler - 2016-02-03

I | Attachment | Action | Size | Date | Who | Comment |
---|---|---|---|---|---|---|

png | GravityScales.png | manage | 60.4 K | 2016-03-01 - 01:41 | MartinMakler | Fig. 8 from Jain, Bhuvnesh; Khoury, Justin, 2010, Cosmological tests of gravity |

png | mg_limits.png | manage | 97.2 K | 2016-03-01 - 01:52 | MartinMakler | Fig. 2 from Jain, Bhuvnesh, et al., 2013 (adapted from Lombriser et al. 2012) |

Topic revision: r8 - 2017-02-26 - MartinMakler

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