Arman777 said:
Just what I said, and described in my previous post. The model from which times like ##10^{-35}## second come from is not the actual inflationary model cosmologists are using. It's an idealized non-inflating FRW model. The correspondence between the two models, that is used to get the times cosmologists give, is done using temperature.
The actual inflationary model cosmologists are using doesn't even have an "initial singularity" in it at all. We don't know whether there was such a thing or not; in some inflationary models (the "eternal inflation" ones), the universe has no beginning, it extends infinitely far backward in time. Currently we don't have any way of testing which models are correct, so our current best-fit model makes no commitment on whether there was an initial singularity or not; it simply goes no further back than the beginning of inflation.
Arman777 said:
since the reheating happens the temperature of the universe would be the approximately same after and before the inflation.
I think you mean after and before the reheating? That is not the case: before reheating, there was a huge potential energy stored in the inflaton field, which had zero temperature (it was in a "false vacuum" state). After reheating, all of that energy is now in the Standard Model fields, which are therefore at very high temperature (because there is no "false vacuum" state for them, whatever energy they have is kinetic energy and must show up as temperature, at least under the conditions right after reheating, when all of the SM fields are massless).
Arman777 said:
don't you think we need time or time interval to understand where the inflation started and ended?
If we do, then cosmologists aren't telling us what the actual time or time interval was. See above.
Arman777 said:
If I just say it happened at ##10^{27} K## there will be confusion about, Is it the end of inflation ? or the beginning of the inflation?
The way to fix that is easy: just say which.