A left-chiral Goedel-like teleparallel universe with gravitational anomalies and dynamo action with torsional sources

Recently, Volovik has shown that it is possible to obtain gravitational anomalies from electromagnetism from emergent torsion. This allows him to obtain that axial anomalies are written in terms of gravitational anomalies in superfluids. In this paper, we show that the same effect happens in cosmology for a special class of de Sitter modified metric in teleparallel geometry $$T_{4}$$ , where the electric and magnetic fields may be expressed in terms of torsion. Gravitational and Nieh-Yan forms are calculated, and dynamo equation with a torsional source is obtained from the teleparallel condition. Chiral magnetic effect is used to simplify the computations. This same teleparallel technique was used previously to obtain torsional anomalies in black holes (Garcia de Andrade in CGG 38, 2021), where Riemann–Cartan spacetime case was also addressed. One of the main new physical features of this paper is that here we encoded a dynamo de Sitter factor which multiplies a B magnetic one-differential form in the de Sitter metric. In the cases of gravitational and axial anomalies, there are shown to be expanded in a polynomial with respect to Hubble constant up to fourth order. The torsional dynamo source is strongly suppressed beyond inflation as shown by Paul and SenGupta (EPJC, 2019) in the case of Friedmann cosmology with torsion without magnetic fields. Our choice of the de Sitter metric reduces to the metric of an inflating plane with time. It is shown that torsional tensor components of dynamo sources are shown to give rise to the Nieh-Yan torsional anomaly.