We study heavy-quark potential in an inflationary braneworld scenario. The scenario we consider is an (Euclidean) inflating braneworld $AdS_4$ embedded in a static Euclidean $AdS_5$. Using gauge/gravity duality we obtain a confining phase depending o
n the ratio between the Hubble parameter $H$ in the braneworld and the brane tension $sigma$.
We investigate early time inflationary scenarios in an Universe filled with a dilute noncommutative bosonic gas at high temperature. A noncommutative bosonic gas is a gas composed of bosonic scalar field with noncommutative field space on a commutati
ve spacetime. Such noncommutative field theories was recently introduced as a generalization of quantum mechanics on a noncommutative spacetime. As key features of these theories are Lorentz invariance violation and CPT violation. In the present study we use a noncommutative bosonic field theory that besides the noncommutative parameter $theta$ shows up a further parameter $sigma$. This parameter $sigma$ controls the range of the noncommutativity and acts as a regulator for the theory. Both parameters play a key role in the modified dispersion relations of the noncommutative bosonic field, leading to possible striking consequences for phenomenology. In this work we obtain an equation of state $p=omega(sigma,theta;beta)rho$ for the noncommutative bosonic gas relating pressure $p$ and energy density $rho$, in the limit of high temperature. We analyse possible behaviours for this gas parameters $sigma$, $theta$ and $beta$, so that $-1leqomega<-1/3$, which is the region where the Universe enters an accelerated phase.
