Mimetic Weyl geometric gravity

TL;DR

This paper introduces a mimetic extension of Weyl geometric gravity, deriving cosmological equations and demonstrating that it can effectively replicate the observational data and predictions of the standard Lambda-CDM model.

Contribution

The work develops a novel mimetic Weyl geometric gravity model that maintains conformal invariance and matches observational cosmological data, offering an alternative to standard gravity theories.

Findings

The model reproduces the Lambda-CDM predictions.

Numerical solutions fit observational Hubble data.

The theory remains conformally invariant with a mimetic scalar field.

Abstract

We consider a mimetic type extension of the Weyl geometric gravity theory, by assuming that the metric of the space-time manifold can be parameterized in terms of a scalar field, called the mimetic field. The action of the model is obtained by starting from a conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and an effective matter term, respectively. after linearizing the action in the Weyl scalar by introducing an auxiliary scalar field, we include the mimetic field, constructed from the same auxiliary scalar field used to linearize the action, via a Lagrange multiplier. The conformal invariance of the action is maintained by imposing the trace condition on the effective matter energy-momentum tensor, built up from the ordinary matter Lagrangian, and some specific functions of the Weyl vector, and the scalar field, respectively, thus making the matter sector of the action conformally invariant. We investigate the cosmological implications of the Mimetic Weyl geometric gravity by considering the dynamics of an isotropic and homogeneous FRW Universe. The generalized Friedmann equations of the model are derived, and their solutions are obtained numerically for a dust filled Universe. Moreover, we perform a detailed comparison of the predictions of the considered model with a set of observational data for the Hubble function, and with the results of the $\Lambda$CDM standard paradigm. Our results indicate that the present model give a good description of the observational data, and they reproduce almost exactly the predictions of the $\Lambda$CDM scenario. Hence, Mimetic Weyl geometric gravity can be considered a viable alternative to the standard approaches to cosmology, and to the gravitational phenomena.