In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from 10^−36 seconds after the conjectured Big Bang singularity to some time between 10^−33 and 10^−32 seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate. . .Inflation theory was developed in the late 1970s and early 80s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. . . . It was developed further in the early 1980s.
From Wikipedia.It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see galaxy formation and evolution and structure formation). Many physicists also believe that inflation explains why the universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the universe is flat, and why no magnetic monopoles have been observed.The detailed particle physics mechanism responsible for inflation is unknown. The basic inflationary paradigm is accepted by most physicists, as a number of inflation model predictions have been confirmed by observation; however, a substantial minority of scientists dissent from this position.The hypothetical field thought to be responsible for inflation is called the inflaton.
I am skeptical of cosmological inflation theory for reasons similar to the reasons that Sabine Hossenfelder is skeptical of it. This group of theories is fundamentally a way to get from a particular set of initial conditions immediately after the Big Bang that is consistent with what we observe, to a different set of initial conditions that are just as arbitrary, a tiny fraction of a second earlier, with lots of intricate mathematical details that aren't easily distinguished from scores of alternative theories of the same genre.
The only reason to do this is that many scientists have presumptions, with no scientific basis, that don't match what we observe, about what the initial state of the universe must have looked like.
There also isn't a particularly credible calculation of what a non-inflationary baseline case to compare the predictions of a cosmological model to. Some scientists (educated layman's summary here) think that the baseline prediction of general relativity without inflation looks pretty much like what we see because ordinary gravitational evolution of the large scale structure of the universe should produces results like homogeneity that are often attributed to cosmological inflation.
I haven't invested much effort to really examining the issue with depth, however, because if we can get to initial conditions a fraction of a second after the Big Bang which would allegedly be produced by inflation and the earlier events are unknowable, this still seems like a very impressive accomplishment and knowing what happened in the very moment of creation isn't that important.