We present results from our recent calculation of the QCD equation of state to $\mathcal{O}(\mu_B^6)$ in the baryon chemical potential $\mu_B$ using the method of Taylor expansions. Our calculations were carried out using the Highly Improved Staggered Quark action (HISQ). The strange quark mass was fixed to its physical value while the light quark mass was fixed at two values viz. $m_l/m_s=1/20$ and $1/27$, which in the continuum limit correspond to pion masses of about 160 MeV and 140 MeV respectively. The calculations were carried out at multiple lattice spacings $N_\tau = 6 - 16$.

Using our sixth-order results for Taylor expansion coefficients to estimate the truncation errors of the fourth-order expansion, we show that truncation errors are small for baryon chemical potentials less then twice the temperature ($\mu_B \leq 2T$). Apart from the basic thermodynamic quantities, we will also describe how to construct lines of constant physics as well as provide estimates for the location of a possible critical point.

Nonzero Temperature and Density