On leading order gravitational backreactions in de Sitter spacetime

TL;DR

This paper investigates the gravitational backreaction effects of quantum matter fluctuations in de Sitter space, emphasizing the necessity of de Sitter invariance to avoid linearization instabilities in Einstein's equations.

Contribution

It demonstrates that maintaining de Sitter invariance of quantum states is essential to prevent linearization instabilities in the gravitational backreaction analysis.

Findings

Linearization instabilities arise without invariance assumptions.

De Sitter invariance of quantum states avoids these instabilities.

Quantum anomalies do not prevent invariance enforcement.

Abstract

Backreactions are considered in a de Sitter spacetime whose cosmological constant is generated by the potential of scalar field. The leading order gravitational effect of nonlinear matter fluctuations is analyzed and it is found that the initial value problem for the perturbed Einstein equations possesses linearization instabilities. We show that these linearization instabilities can be avoided by assuming strict de Sitter invariance of the quantum states of the linearized fluctuations. We furthermore show that quantum anomalies do not block the invariance requirement. This invariance constraint applies to the entire spectrum of states, from the vacuum to the excited states (should they exist), and is in that sense much stronger than the usual Poincare invariance requirement of the Minkowski vacuum alone. Thus to leading order in their effect on the gravitational field, the quantum states of the matter and metric fluctuations must be de Sitter invariant.