Why there is no Newtonian backreaction

Understand

In the conventional framework for cosmological dynamics the scale factor $a(t)$ is assumed to obey the `background' Friedmann equation for a perfectly homogeneous universe while particles move according to equations of motions driven by the gravity of the density fluctuations.

• It has recently been suggested that the emergence of structure modifies the evolution of $a(t)$ via Newtonian (or `kinematic') backreaction and that this may avoid the need for dark energy.
• Here we point out that the conventional system of equations is exact in Newtonian gravity and there is no approximation in the use of the homogeneous universe equation for $a(t)$.
• The recently proposed modification of Racz et al.\ (2017) does not reduce to Newtonian gravity in the limit of low velocities.