  I review and discuss the possible implications for inflation resulting from
considering new physics in light of the Hubble tension. My study is motivated
by a simple argument that the constraints on inflationary parameters, most
typically the spectral index $n_s$, depend to some extent on the cosmological
framework. To avoid broadening the uncertainties resulting from marginalizing
over additional parameters (typical in many alternative models), I first adopt
the same alternative viewpoint of previous studies and analyze what happens if
a physical theory can fix extra parameters to non-standard values. Focusing on
the dark energy equation of state $w$ and the effective number of relativistic
species $N_{\rm{eff}}$, I confirm that physical theories able to fix $w \approx
-1.2$ or $N_{\rm{eff}} \approx 3.9$ produce values of $H_0$ from CMB and BAO in
line with the local distance ladder estimate. While in the former case I do not
find any relevant implications for inflation, in the latter scenarios, I
observe a shift towards $n_s \approx 1$. From a model-selection perspective,
both cases are strongly disfavored compared to $\Lambda$CDM. However, models
with $N_{\rm{eff}} \approx 3.3 - 3.4$ could bring the $H_0$ tension down to
$\sim 3\sigma$ while being moderately disfavored. Yet, this is enough to change
the constraints on inflation so that the most accredited models (e.g.,
Starobinsky inflation) would no longer be favored by data. I then focus on
Early Dark Energy (EDE), arguing that an EDE fraction $f_{\rm{EDE}}\sim 0.04 -
0.06$ (only able to mildly reduce the $H_0$-tension down to $\sim 3\sigma$)
could already require a similar change in perspective on inflation. In fact,
performing a full joint analysis of EDE and Starobinsky inflation, I find that
the two models can hardly coexist for $f_{\rm{EDE}}\gtrsim 0.06$.
