A class of wormhole solutions permitted in a theory with Gauss-Bonnet terms in the gravitational action in higher dimensions have been studied. The case of de-Sitter type instantons, with a compact inner space, are of particular interest here. Some of the configurations, when continued analytically to the Lorentzian metric lead to the standard inflationary universe. Some multiple-sphere configurations of the type studied by Myers have also been noted. The Euclidean action for the solutions has been calculated and the relevance of the solutions in the quantum creation of the universe has been considered.

The effect of particle production on the evolution of the spatially flat Friedmann-Lemaitre-Robertson-Walker cosmological model during the early stages of the universe is analysed in the framework of higher derivative theory. The universe has been considered as an open thermodynamic system where particle production gives rise to a supplementary negative creation pressure in addition to the thermodynamic pressure. The dynamical behaviour of both exponential as well as power law solutions have been discussed.

In this work, we study a cosmological model based on the cosmological principle which exhibits a transition from deceleration to acceleration. We consider baryonic matter dark energy (DE), and ‘curvature’ energy. Both baryonic matter and DE have variable equations of state. It is assumed that DE interacts with and transforms energy to baryonic matter. A Friedmann–Robertson–Walker (FRW) Universe filled with two fluids has been discussed. The model is shown to satisfy current observational constraints. This Universe is at present in a phantom phase after passing through a quintessence phase in the past. Various cosmological parameters regarding the accelerating Universe have been presented. The evolution of DE, Hubble, deceleration parameters, etc. have been described with the aid of figures. Our theoretical results have been compared with the SNe Ia related Union 2.1 compilation 581 data and we have observed that our derived model is in good agreement with the current observational constraints. We have also explored the physical properties of the model.