Why does dark energy make universe accelerate not slow down? If mass=energy, then why doesn't dark energy not make the expansion slow down rather than accelerate seeing as gravity pulls masses together?
 A: In General Relativity, what determines spacetime curvature is neither mass, nor simply energy, but rather the density and flow of energy and momentum. In the case where the contents of the universe (galaxies, cosmic microwave background, dark matter, dark energy) are modeled as a perfect fluid which is homogeneous and isotropic on the largest scales, this means that it depends on the energy density and the pressure of that "fluid".
The Friedmann equation for the acceleration of the scale factor $a(t)$ of the universe is
$$\frac{\ddot{a}}{a}=-\frac{4\pi G}{3}\left(\rho+\frac{3p}{c^2}\right)$$
where $G$ is the gravitational constant, $\rho(t)$ the is uniform-but-time-varying energy density of the contents of the universe, and $p(t)$ is the uniform-but-time-varying pressure of the contents of the universe. This equation can be derived from the Einstein field equations, in the case of a homogeneous and isotropic universe.
There are contributions to $\rho$ and $p$ from normal matter, radiation, dark matter, and dark energy.
Normal matter, radiation, and dark matter all have positive energy density and positive pressure, so their contributions tend make the acceleration be negative, meaning that they slow the expansion. 
But dark energy has positive energy density and large negative pressure. In fact, its equation of state is $p=-\rho c^2$, so $\rho+3p/c^2$ is $-2\rho$. Thus the contribution of dark energy is to make the acceleration be positive, meaning that it speeds up the expansion.
According to the current Lambda-CDM model of cosmology, the contributions from dark energy have dominated the contributions from normal matter, radiation, and dark matter for the last 5 billion years. Thus the expansion has been speeding up for 5 billion years.
You might wonder how it is possible for dark energy to have such a strange relationship between pressure and density. We know of two things that theoretically produce this equation of state.
The first is a slowly-varying scalar field with a nonzero energy of self-interaction, which is what many models of inflation assume produced an accelerating scale factor in the very early universe.
For a uniform scalar field $\phi(t)$ with self-interaction $V(\phi)$, one finds
$$\rho=\frac{1}{2}\dot{\phi}^2-V(\phi)$$
and
$$p=\frac{1}{2}\dot{\phi}^2+V(\phi)$$
in units where $c=1$; in the limit of slow variation, this means $p=-\rho$.
The second is the energy of quantum vacuum fluctuations. In the vacuum state, there is no tensor other than the metric tensor from which to construct the energy-momentum-stress tensor. If we assume that $T_{\mu\nu}$ is proportional to $g_{\mu\nu}$ then we find that $p=-\rho$ again.
