Inflation without Inflaton: A Model for Dark Energy
  The interaction between two initially causally disconnected regions of the
universe is studied using analogies of non-commutative quantum mechanics and
deformation of Poisson manifolds. These causally disconnect regions are
governed by two independent Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW)
metrics with scale factors $a$ and $b$ and cosmological constants $\Lambda_a$
and $\Lambda_b$, respectively. The causality is turned on by positing a
non-trivial Poisson bracket $[ {\cal P}_{\alpha}, {\cal P}_{\beta} ]
=\epsilon_{\alpha \beta}\frac{\kappa}{G}$, where $G$ is Newton's gravitational
constant and $\kappa $ is a dimensionless parameter. The posited deformed
Poisson bracket has an interpretation in terms of 3-cocycles, anomalies and
Poissonian manifolds. The modified FLRW equations acquire an energy-momentum
tensor from which we explicitly obtain the equation of state parameter. The
modified FLRW equations are solved numerically and the solutions are
inflationary or oscillating depending on the values of $\kappa$. In this model
the accelerating and decelerating regime may be periodic. The analysis of the
equation of state clearly shows the presence of dark energy. By completeness,
the perturbative solution for $\kappa \ll1 $ is also studied.
