Screening anisotropy via energy-momentum squared gravity: $\Lambda$CDM
  model with hidden anisotropy
  We construct a generalization of the standard $\Lambda$CDM model, wherein we
simultaneously replace the spatially flat Robertson-Walker metric with its
simplest anisotropic generalization (LRS Bianchi I metric), and couple the cold
dark matter to the gravity in accordance with the energy-momentum squared
gravity (EMSG) of the form $f(T_{\mu\nu}T^{\mu\nu})\propto
T_{\mu\nu}T^{\mu\nu}$. These two modifications -- namely, two new stiff
fluid-like terms of different nature -- can mutually cancel out, i.e., the
shear scalar can be screened completely, and reproduce mathematically exactly
the same Friedmann equation of the standard $\Lambda$CDM model. This evades the
BBN limits on the anisotropy, and thereby provides an opportunity to manipulate
the cosmic microwave background quadrupole temperature fluctuation at the
desired amount. We further discuss the consequences of the model on the very
early times and far future of the Universe. This study presents also an example
of that the EMSG of the form $f(T_{\mu\nu}T^{\mu\nu})\propto
T_{\mu\nu}T^{\mu\nu}$, as well as similar type other constructions, is not
necessarily relevant only to very early Universe but may even be considered in
the context of a major problem of the current cosmology related to the
present-day Universe, the so-called $H_0$ problem.
