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We use Hamilton–Jacobi formalism to study the curvature and isocurvature perturbations during inflation. This formalism is suitable for going beyond slow roll regime. We solve the equation of fields’ perturbations for some two-field models, and calculate their spectra. We next use $$\delta N$$ formalism to calculate the curvature and isocurvature non-Gaussianity for a non-separable form of the Hubble expansion rate. Finally, using the sudden decay approximation, we obtain the link between the perturbations during inflation and after reheating for noninteracting fields.

Unimodular Gravity (UG) is a restricted version of General Relativity (GR) in which the determinant of the metric is a fixed function and the field equations are given by the trace-free part of the full Einstein equations. The background equations in UG and GR are identical. It was recently claimed that, the first order contribution in the temperature fluctuation of the Cosmic Microwave Background (CMB) in UG is different from GR. In this work, we calculate the first order perturbation equations in UG and show that the Sachs-Wolfe effect in UG, in terms of gauge invariant variables, is identical to GR. We also show that the second order perturbation equation of Mukhnanov-Sasaki variable in UG, is identical to GR. The only difference comes from the gauge choices due the constraint on the metric determinant. Hence, UG and GR are identical and indistinguishable in CMB data on large scales., Comment: 24 pages, no figures

We show, using a covariant and gauge– invariant approach to cosmological perturbation theory, that velocity and gravitational wave perturbations of the Friedmann– Lemaitre– Robertson– Walker (FLRW) model can lead to the generation and amplification of cosmic magnetic fields. It is argued that under certain conditions these fields can reach strengths capable of supporting the galactic dynamo mechanism.