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We present constraints on extensions of the minimal cosmological modelsdominated by dark matter and dark energy, $\Lambda$CDM and $w$CDM, by using acombined analysis of galaxy clustering and weak gravitational lensing from thefirst-year data of the Dark Energy Survey (DES Y1) in combination with externaldata. We consider four extensions of the minimal dark energy-dominatedscenarios: 1) nonzero curvature $\Omega_k$, 2) number of relativistic species$N_{\rm eff}$ different from the standard value of 3.046, 3) time-varyingequation-of-state of dark energy described by the parameters $w_0$ and $w_a$(alternatively quoted by the values at the pivot redshift, $w_p$, and $w_a$),and 4) modified gravity described by the parameters $\mu_0$ and $\Sigma_0$ thatmodify the metric potentials. We also consider external information from PlanckCMB measurements; BAO measurements from SDSS, 6dF, and BOSS; RSD measurementsfrom BOSS; and SNIa information from the Pantheon compilation. Constraints oncurvature and the number of relativistic species are dominated by the externaldata; when these are combined with DES Y1, we find$\Omega_k=0.0020^{+0.0037}_{-0.0032}$ at the 68% confidence level, and $N_{\rmeff}<3.28\, (3.55)$ at 68% (95%) confidence. For the time-varyingequation-of-state, we find the pivot value $(w_p, w_a)=(-0.91^{+0.19}_{-0.23},-0.57^{+0.93}_{-1.11})$ at pivot redshift $z_p=0.27$ from DES alone, and $(w_p,w_a)=(-1.01^{+0.04}_{-0.04}, -0.28^{+0.37}_{-0.48})$ at $z_p=0.20$ from DES Y1combined with external data; in either case we find no evidence for thetemporal variation of the equation of state. For modified gravity, we find thepresent-day value of the relevant parameters to be $\Sigma_0=0.43^{+0.28}_{-0.29}$ from DES Y1 alone, and $(\Sigma_0,\mu_0)=(0.06^{+0.08}_{-0.07}, -0.11^{+0.42}_{-0.46})$ from DES Y1 combined withexternal data, consistent with predictions from GR.

Dark Energy Survey Year 1 Results: Constraints on Extended Cosmological Models from Galaxy Clustering and Weak Lensing