Before Dark Energy could be discovered, several preconditions needed to be in place. Tick all the factors below which were necessary for the discovery of dark energy.

Radio interferometers, Large telescopes such as Keck, Knowledge of the correlation between peak brightness and duration for Type 1a supernovae, Knowledge that Type 1a supernovae come from white dwarf explosions , - incorrect Large format detectors for wide field imagingRadio interferometersLarge telescopes such as KeckKnowledge of the correlation between peak brightness and duration for Type 1a supernovaeKnowledge that Type 1a supernovae come from white dwarf explosions

To determine the factors necessary for the discovery of dark energy, we need to evaluate the given options:

1. Radio interferometers: Radio interferometers are not directly related to the discovery of dark energy. They are instruments used to study radio waves emitted by celestial objects. Therefore, this option is incorrect.

2. Large telescopes such as Keck: Large telescopes can be instrumental in observing celestial objects and phenomena, including those related to dark energy. They allow astronomers to collect more data and gather more accurate information. Thus, large telescopes like Keck can contribute to the discovery of dark energy. This option is correct.

3. Knowledge of the correlation between peak brightness and duration for Type 1a supernovae: Type 1a supernovae are used as standard candles in cosmology because they have a consistent peak brightness. Understanding the correlation between their brightness and duration is crucial for accurate measurements of distant objects. This knowledge is essential for determining the presence of dark energy, as it was through the study of Type 1a supernovae that the acceleration of the expansion of the universe and the existence of dark energy were first observed. Thus, this option is correct.

4. Knowledge that Type 1a supernovae come from white dwarf explosions: This knowledge is important for understanding the nature of Type 1a supernovae but not directly related to discovering dark energy. Therefore, this option is incorrect.

5. Large format detectors for wide field imaging: Large format detectors are useful for capturing wider fields of view, but they are not specific to dark energy research. While they can aid astronomers in their observations, they are not a prerequisite for the discovery of dark energy. Thus, this option is incorrect.

In conclusion, the factors necessary for the discovery of dark energy are:

- Large telescopes such as Keck
- Knowledge of the correlation between peak brightness and duration for Type 1a supernovae