Modified gravity from the quantum part of the metric

Abstract

It is shown that if a metric in quantum gravity can be decomposed as a sum of classical and quantum parts, then Einstein quantum gravity looks approximately like modified gravity with a nonminimal interaction between gravity and matter.

Propagation of gravitational waves in the nonperturbative spinor vacuum

“…This is the main problem encountered in Heisenberg's nonperturbative quantization technique, discussed also in Ref. [5].…”

“…For the nonperturbative quantization, we have to write the following equations (for details, see Ref. [5]):…”

“…For them we can write down an infinite set of equations (for details, see Ref. [5]). Such an infinite system of equations can be solved approximately by cutting it off to obtain a finite set of equations.…”

“…In our opinion, this can be considered as some approximate way to cutoff the infinite system of differential equations for all Green functions of the nonperturbative quantum spinor field used in our calculations (for a more detailed discussion of this question, see Ref. [5]). (ii) The right-hand side of the Einstein equations contains first derivatives of the tetrad with respect to the coordinates that is a consequence of the presence of the spin connection.…”

Modeling a nonperturbative spinor vacuum interacting with a strong gravitational wave

“…This will permit us to reduce the infinite system of differential equations for all Green functions of the nonperturbative quantum spinor field to the finite set of equations (for more details, see Refs. [1,2]). …”