New insights on the signature change via the Colombeau framework

Abstract

In this paper we propose a reinterpretation of the Mansouri–Nozari signature-change approach to the early Universe, in which the metric signature only occurs for t < 0 within the Euclidean regime, posing a challenge in providing coherent physical interpretations in advance. We ensure that the sign change occurs for t > 0 in the Euclidean regime. Our findings show that the energy-momentum tensor does not vanish on the signature-changing surface, even when we adopt conditions commonly used in the literature. Furthermore, we formulate a modified cosmology within the framework of signature-changing and discuss the modifications that our approach introduces to the cosmological equations. We establish a constraint relating the equation of state parameter and its singular part and we determine an effective equation of state as function of the redshift. Finally, we show that the law of conservation of matter in the modified ΛCDM model remains valid.