[paul cotter (OP)]

I am curious to understand the need for inflation in the big bang theory. I have in the past heard a dissertation on the subject but it seemed rather vague to me and I can't remember any of it.

[Origin]

This should help:  https://wmap.gsfc.nasa.gov/universe/bb_cosmo_infl.html#:~:text=The%20Inflation%20Theory%20proposes%20a,relatively%20gradually%20throughout%20its%20history.

[Eternal Student]

Hi.

The short article provided by @Origin  is extremely good.   It sets out the three main problems and explains how inflation solves these:

1.  That space does seem to be almost flat.

2.  That distant parts of space seem to be at similar temperatures, suggesting they were in thermal contact at some time.  Ordinary big bang expansion would have kept them apart and kept driving them apart faster than light could have travelled from one region to the other.   No exchange of heat between them should have occurred.  Without inflation, the only possibility is to assume that it was coincidence that all these regions had the same temperature after the big bang.  (That isn't an impossible coincidence, if the Big bang was very symmetric you might get something like that - but it's an assumption that you just don't need to make if the regions were in thermal contact with each other).

3.    Lack of our ability to find magnetic monopoles.

We can probably add two extra problems / observations:
4.    That space is surprisingly homogeneous and isotropic -  it's much the same density everywhere and in every direction.   With inflation you don't need to assume it was always this way just after the big bang.   A massive expansion of a less homogeneous space produces a large region where everything is much more homogeneous.
5.    Conversely, it isn't completely smooth.   There are small irregularities in density and this is what ultimately gives rise to the clumping of matter  -  the formation of galaxies in some places and voids in other places.   

   How 4. and 5.   work together is quite interesting.   They aren't really opposites of each other.    Assume the situation described by 4. happens: 
(i) The lengths over which differences are observed increases - differences in densities observed over a length of say 1 light-second are now only noticeable over a distance of 100 light seconds.
(ii)  The actual size of the density differences is also reduced:  Since the volumes of space were stretched the actual densities are brought closer to 0, so the difference in densities is reduced.
    This sort of change keeps happening.  Meanwhile there will always be small quantum fluctuations happening - things that might produce a difference in density that are observable at lengths of a (tiny) fraction of a light-second.   However, these small changes that were due to quantum fluctuations get stretched and eventually become density differences that are noticeable over lengths of about 1 light-second.  This whole thing keeps going and repeating (it's not a discrete, first this, then that,  it's a much more continuous thing but seeing it as series of small discrete steps is just easier to visualize).    Overall,  the coarse and large scale differences in density keep getting stretched and smoothed away, while the quantum fluctuations keep getting magnified to produce small differences in density that are noticeable over lengths of about 1 light-second.    We end up with a situation where the small differences in density that we want are assured while larger or more coarse differences are equally assured to have been removed.  "We want" these small differences in the sense that these do work well in the models and simulations for galaxy evolution.

    That's about it.   That's the limit of my understanding about inflation.   Sources of information were:
a)  "The History of the Universe", especially Chapter 13,  David H Lyth,  Publisher: Springer,  2016.
b)   NASA website provided by Origin earlier.
b)   Wikipedia:  https://en.wikipedia.org/wiki/Inflation_(cosmology)

A final note worth mentioning is that Inflation remains an optional addition to the Big Bang Theory:
The basic inflationary paradigm is accepted by most physicists, ..... however, a substantial minority of scientists dissent from this position       [Quote from Wikipedia]

Best Wishes.

[paul cotter (OP)]

I understand, albeit vaguely, the general arguments with one exception: from an engineering perspective(which is what I am limited to) ∇.b=0 precludes the possibility of magnetic monopoles. All the available evidence indicates that the magnetic field always forms closed loops. I would love to hear some elaboration on this, in particular why the bbt requires these monopoles. 

[Eternal Student]

Hi.

from an engineering perspective(which is what I am limited to) ∇.b=0 precludes the possibility of magnetic monopoles.

   Yes, more or less.

   We haven't observed any magnetic poles,  that is written in mathematical notation as  ∇.B  = 0.
That's all that is,  just a way of writing that phrase in mathematical notation.   It's not a proof that magnetic monopoles don't exist.    If they were found, then that equation in the set of Maxwell's equations would need to be changed. However, it would only need changing for those situations where there is a magnetic monopole in the experiment or situation being modelled.    Where there isn't any magnetic monopole then the equation obviously still holds.
   The existing theory of classical electromagnetism can be considered as some "proof" or evidence that magnetic monopoles are very rare and certainly don't contribute to many situations.   Maxwell's equations including  ∇.B  = 0   have proved very accurate and reliable in predicting and modeling electromagnetic phenomena.   If  ∇.B  is significantly not 0 in some situations we should have noticed it by now because Maxwell's equations would have given us predictions that didn't match the observations.
     However, that's as much as we can say - if they exist, then they will be rare and not important for the situations we have studied or modelled so far.   ∇.B(x, t)  ≈ 0   at all positions x in space and times t   should remain a very useful approximation.

I would love to hear some elaboration on this, in particular why the bbt requires these monopoles.

    It's not exactly the Big Bang Theory that demands monopoles.   The existence of magnetic monopoles is suggested by several more specific theories in physics.  For example, standard particle theories and superstring theory.   Of which the standard model of particle physics is probably the most important and most widely accepted, superstring theory is an optional addition. 
    So it's possible to imagine that the bare-bones of the ideas for the BBT could persist while some of the fine details for things like particle synthesis just after the Big bang are adapted.   Physicist's would like to find monopoles because that would support the overall conglomeration of ideas that make up our best theories of cosmology including things like particle synthesis.   These early moments of the Universe including processes like nucleosynthesis are all included under the umbrella term "the Big Bang Theory".

Best Wishes.

[Deecart]

An other point of view.

PS1 :: National Conference on CICAHEP, Dibrugarh (2015), 01, 94 – 99
Horizon, homogeneity and flatness problems – do their resolutions really
depend upon inflation?
Ashok K. Singal
Astronomy and Astrophysics Division, Physical Research Laboratory, Navrangpura, Ahmedabad-380 009, Gujarat, India
asingal@prl.res.in; COS3, Poster, CICAHEP15.169.1
In textbooks and review articles on modern cosmology [1, 2, 3, 4, 5, 6] one almost invariably comes across a
section devoted to the subject of observed homogeneity and near-flatness of the universe, where it is argued that
to explain these observations inflation is almost a must. In fact that was the prime motive of Guth [7] to propose
inflation in the first place. We show that the arguments offered therein are not proper. The horizon problem, which
leads to the causality arguments, arises only in the world models where homogeneity and isotropy (cosmological
principle) is presumed to begin with. We do not know whether the horizon problem would still arise in non-
homogeneous world models. Therefore as long as we are investigating consequences of the cosmological models
based on Robertson-Walker line element, there is no homogeneity issue.
We also show that the flatness problem, as it is posed, is not even falsifiable.


The usual argument used in literature
is that the present density of the universe is very close (within an order of magnitude) to the critical density value.
From this one infers that the universe must be flat since otherwise in past at 10−35 second (near the epoch of
inflation) there will be extremely low departures of density from the critical density value (i.e., differing from
unity by a fraction of order ∼ 10−53), requiring a sort of fine tuning. Actually we show that even if the present
value of the density parameter (in terms of the critical density value) were very different, still at 10−35 second it
would in any case differ from unity by a fraction of order ∼ 10−53. For instance, even if had an almost empty
universe, with say, ρo ∼ 10−56 gm/cc or so (with density parameter Ωo ∼ 10−28, having a mass equivalent to
that of Earth alone to fill the whole universe), we still get the same numbers for the density parameter at the epoch
of inflation. So such a fine-tuning does not discriminate between various world models and a use of fine tuning
argument amounts to a priori rejection of all models with k 6 = 0, because inflation or no inflation, the density
parameter in all Friedmann-Robertson-Walker (FRW) world models gets arbitrarily close to unity as we approach
the epoch of the big bang. That way, without even bothering to measure the actual density, we could use any
sufficiently early epoch and use “extreme fine-tuning” arguments to rule out all non-flat models. Thus without
casting any whatsoever aspersions on the inflationary theories, we point out that one cannot use these type of
arguments, viz. homogeneity and flatness, in support of inflation.

https://s3.cern.ch/inspire-prod-files-c/cf01320a84f09089fdb2318c01fc440b

[Eternal Student]

Hi.

    There's two things I could say about the post by @Deecart .

1.   They declared the information as an alternative view.  I absolutely agree that inflation is not accepted by all Physicists.

2.    They presented the reference, which I was able to go and follow up.   The website link seems safe enough - but I'm not a IT security expert, so make your own decisions.    The paper does also seem to be listed in the conventional arxiv print server site if you'd prefer to find it there  (that also seems to have a later version submitted 2022 which I haven't looked at).

    I think @Deecart is a fairly new member but for whatever it's worth,  I can't fault what was done there, that seemed like model practice.   Thank you very much @Deecart , I enjoyed looking over that paper.  I don't agree with all of it but that's a different issue.

- - - - - - - - - - -
   What seemed most relevant in the paper:

1.   They get around the horizon problem by suggesting that if space wasn't homogeneous (at early times) then the FRW metric doesn't apply at those early times.   That does seem like fair comment.   It falls short of demonstrating that there isn't still going to be a horizon problem - just that showing there is one by using the FRW metric was not and is not a sensible way to proceed.   They offer some evidence for a lack of homogeneity in the universe but mainly focus on identifying weakness in the existing arguments that support such homogeneity.
2.  They make some arguments about flatness - that seemed less rigorous to me.
3.  They state that inflation can produce isolated patches of universe that have never been in causal contact and consider that a problem.   In one sense you can see exactly what they are saying - it could cause a problem similar to the one it is trying to solve.   
    However, this is often not considered a "problem" but rather an interesting "feature" or possibility that is suggested by inflation - you can have multiple universes existing as patches of one shared space, they have never had or will ever have any casual influence on each other (assuming space continues to expand in the same sort of way).   Our local universe (or universe patch) has all the properties we observe (possibly thanks to inflation) and the other universe patches can exist and do their own thing.

Best Wishes.