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They begin with a variant of general relativity that Einstein himself invented called unimodular gravity.

Unimodular gravity reproduces most of the predictions of general relativity.

Unimodular gravity doesn't require energy to be conserved, so theorists have to impose that constraint arbitrarily.

Now, however, Josset, Perez, and Sudarsky show that in unimodular gravity, if they just go with it and allow the violation of the conservation of energy and momentum, it actually sets the value of the cosmological constant.

Unimodular gravity possesses a more limited version of that mathematical symmetry.