# Test of the FLRW Metric and Curvature with Strong Lens Time Delays

## Abstract

We present a new model-independent strategy for testing the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and constraining cosmic curvature, based on future time-delay measurements of strongly lensed quasar-elliptical galaxy systems from the Large Synoptic Survey Telescope and supernova observations from the Dark Energy Survey. The test only relies on geometric optics. It is independent of the energy contents of the universe and the validity of the Einstein equation on cosmological scales. The study comprises two levels: testing the FLRW metric through the distance sum rule (DSR) and determining/constraining cosmic curvature. We propose an effective and efficient (redshift) evolution model for performing the former test, which allows us to concretely specify the violation criterion for the FLRW DSR. If the FLRW metric is consistent with the observations, then on the second level the cosmic curvature parameter will be constrained to ∼0.057 or ∼0.041 (1 σ ), depending on the availability of high-redshift supernovae, which is much more stringent than current model-independent techniques. We also show that the bias in the time-delay method might be well controlled, leading to robust results. The proposed method is a new independent tool for both testing the fundamental assumptions of homogeneity and isotropy in cosmology and for determining cosmicmore »

- Authors:

- School of Science, Wuhan University of Technology, Wuhan 430070 (China)
- Department of Astronomy, Beijing Normal University, Beijing 100875 (China)
- Department of Physics and Mechanical and Electrical Engineering, Hubei University of Education, Wuhan 430205 (China)

- Publication Date:

- OSTI Identifier:
- 22663704

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 839; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BARYONS; COSMOLOGICAL MODELS; COSMOLOGY; DATA ANALYSIS; EINSTEIN FIELD EQUATIONS; ENERGY ACCOUNTING; ENERGY BALANCE; GALAXIES; GRAVITATIONAL LENSES; GRAY ENERGY; ISOTROPY; NONLUMINOUS MATTER; OSCILLATIONS; QUASARS; RED SHIFT; RELICT RADIATION; SUM RULES; SUPERNOVAE; TIME DELAY; UNIVERSE

### Citation Formats

```
Liao, Kai, Li, Zhengxiang, Wang, Guo-Jian, and Fan, Xi-Long, E-mail: liaokai@whut.edu.cn, E-mail: xilong.fan@glasgow.ac.uk.
```*Test of the FLRW Metric and Curvature with Strong Lens Time Delays*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA697E.

```
Liao, Kai, Li, Zhengxiang, Wang, Guo-Jian, & Fan, Xi-Long, E-mail: liaokai@whut.edu.cn, E-mail: xilong.fan@glasgow.ac.uk.
```*Test of the FLRW Metric and Curvature with Strong Lens Time Delays*. United States. doi:10.3847/1538-4357/AA697E.

```
Liao, Kai, Li, Zhengxiang, Wang, Guo-Jian, and Fan, Xi-Long, E-mail: liaokai@whut.edu.cn, E-mail: xilong.fan@glasgow.ac.uk. Thu .
"Test of the FLRW Metric and Curvature with Strong Lens Time Delays". United States.
doi:10.3847/1538-4357/AA697E.
```

```
@article{osti_22663704,
```

title = {Test of the FLRW Metric and Curvature with Strong Lens Time Delays},

author = {Liao, Kai and Li, Zhengxiang and Wang, Guo-Jian and Fan, Xi-Long, E-mail: liaokai@whut.edu.cn, E-mail: xilong.fan@glasgow.ac.uk},

abstractNote = {We present a new model-independent strategy for testing the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and constraining cosmic curvature, based on future time-delay measurements of strongly lensed quasar-elliptical galaxy systems from the Large Synoptic Survey Telescope and supernova observations from the Dark Energy Survey. The test only relies on geometric optics. It is independent of the energy contents of the universe and the validity of the Einstein equation on cosmological scales. The study comprises two levels: testing the FLRW metric through the distance sum rule (DSR) and determining/constraining cosmic curvature. We propose an effective and efficient (redshift) evolution model for performing the former test, which allows us to concretely specify the violation criterion for the FLRW DSR. If the FLRW metric is consistent with the observations, then on the second level the cosmic curvature parameter will be constrained to ∼0.057 or ∼0.041 (1 σ ), depending on the availability of high-redshift supernovae, which is much more stringent than current model-independent techniques. We also show that the bias in the time-delay method might be well controlled, leading to robust results. The proposed method is a new independent tool for both testing the fundamental assumptions of homogeneity and isotropy in cosmology and for determining cosmic curvature. It is complementary to cosmic microwave background plus baryon acoustic oscillation analyses, which normally assume a cosmological model with dark energy domination in the late-time universe.},

doi = {10.3847/1538-4357/AA697E},

journal = {Astrophysical Journal},

number = 2,

volume = 839,

place = {United States},

year = {Thu Apr 20 00:00:00 EDT 2017},

month = {Thu Apr 20 00:00:00 EDT 2017}

}