  Assuming a spatially flat universe, we study the cosmological viability of an
infrared corrected teleparallel gravity model, which accounts for late
acceleration by weakening gravity at later times on cosmological distances. The
theory does not introduce any additional free parameters into the cosmological
model, as is commonly the case with modified gravity based cosmologies. This
feature renders the cosmological model statistically comparable, on equal
footing, with $\Lambda$CDM. In this context, using recent cosmological
observations -- Pantheon supernova Type Ia, Hubble constant $H_0$, Baryon
acoustic oscillation, redshift space distortions, Big Bang nucleosynthesis and
the cosmic microwave background constraint on the decoupling acoustic scale --
we show that, although the exponential infrared-corrected gravity and
$\Lambda$CDM are physically different, they are phenomenologically and
statistically equivalent. However, the former is more adept at fitting
accurately determined observational constraints while decreasing the $H_0$
tension without worsening the $S_8$ tension. This calls for full examination of
the empirical viability of the theory at the linear perturbation level, which
is the subject of paper II.
