If Inflation never happened before the CMB, and the present expansion were projected backwards, how old would the Universe be since the Big Bang?

Question

The Cosmic Microwave Background Radiation is the oldest thing we can directly observe. To explain the near uniformity of temperature of the CMBR and the flatness of space, Cosmic Inflation was invented, which has its own problems, such as the failure to explain the initial conditions of the Big Bang and the fine-tuning of the Universal Constants. The Multiverse explanation is inherently unscientific. The failure to imagine an alternative explanation for the CMBR is more a failure of imagination than an excuse to assume that inflation alone can explain everything. Other than the existence of near uniformity of temperature of the CMBR and the flatness of space, there is no need to invent Cosmic Inflation, for which no evidence exists. Assuming then that the Expansion of the Universe did not differ greatly from the present observed exansion, if we go back in time to when the Universe was intensely small and hot, how old would the Universe be? If the Universe were much older than what is assumed with inflation, would that be more compatible with recent observations of the James Webb Telescope?

Answer 1

The estimated age of the universe, - as in the time since it was much smaller and hotter - does not assume inflation occurred. It uses the measured cosmological parameters of the $\Lambda$CDM model and the Friedmann-Lemaitre equations.

Both inflation and the standard hot big bang model have the universe at approximately the same scale factor and temperature at about $10^{-32}$ s after the big bang (in the standard hot big bang model). The "age of the universe" that is conventionally discussed is the time since this point. The cosmic microwave background, the first stars and galaxies formed $10^5-10^8$ years after this, which is all that matters for interpreting the JWST results etc. and the exact zero point of the time axis for the universe isn't relevant.

If some form of inflation occurred prior to $10^{-32}$ s then it becomes difficult to assign an age (at that level of precision), since we don't know what the universe was like prior to inflation, and some inflationary models do not have a beginning to the universe.