Effects of Dark Energy anisotropic stress on the matter power spectrum
  We study the effects of dark energy (DE) anisotropic stress on features of
the matter power spectrum (PS). We employ the Parametrized Post-Friedmannian
(PPF) formalism to emulate an effective DE, and model its anisotropic stress
properties through a two-parameter equation that governs its overall amplitude
($g_0$) and transition scale ($c_g$). For the background cosmology, we consider
different equations of state to model DE including a constant $w_0$ parameter,
and models that provide thawing (CPL) and freezing (nCPL) behaviors. We first
constrain these parameters by using the Pantheon, BAO, $H_0$ and CMB Planck
data. Then, we analyze the role played by these parameters in the linear PS. In
order for the anisotropic stress not to provoke deviations larger than $10\%$
and $5\%$ with respect to the $\Lambda$CDM PS at $k \sim 0.01 \,h/\text{Mpc}$,
the parameters have to be in the range $-0.30< g_0 < 0.32$, $0 \leq c_g^2 <
0.01$ and $-0.15 < g_0 < 0.16$, $0 \leq c_g^2 < 0.01$, respectively.
Additionally, we compute the leading nonlinear corrections to the PS using
standard perturbation theory in real and redshift space, showing that the
differences with respect to the $\Lambda$CDM are enhanced, especially for the
quadrupole and hexadecapole RSD multipoles.
