  We explore synergies between the Nancy Grace Roman Space Telescope and CMB
lensing data to constrain dark energy and modified gravity scenarios. A
simulated likelihood analysis of the galaxy clustering and weak lensing data
from the Roman Space Telescope High Latitude Survey combined with CMB lensing
data from the Simons Observatory is undertaken, marginalizing over important
astrophysical effects and calibration uncertainties. Included in the modeling
are the effects of baryons on small-scale clustering, scale-dependent growth
suppression by neutrinos, as well as uncertainties in the galaxy clustering
biases, in the intrinsic alignment contributions to the lensing signal, in the
redshift distributions, and in the galaxy shape calibration. The addition of
CMB lensing roughly doubles the dark energy figure-of-merit from Roman
photometric survey data alone, varying from a factor of 1.7 to 2.4 improvement
depending on the particular Roman survey configuration. Alternatively, the
inclusion of CMB lensing information can compensate for uncertainties in the
Roman galaxy shape calibration if it falls below the design goals. Furthermore,
we report the first forecast of Roman constraints on a model-independent
structure growth, parameterized by $\sigma_8 (z)$, and on the Hu-Sawicki f(R)
gravity as well as an improved forecast of the phenomenological
$(\Sigma_0,\mu_0)$ model. We find that CMB lensing plays a crucial role in
constraining $\sigma_8(z)$ at z>2, with percent-level constraints forecasted
out to z=4. CMB lensing information does not improve constraints on the f(R)
models substantially. It does, however, increase the $(\Sigma_0,\mu_0)$
figure-of-merit by a factor of about 1.5.
