Big Bang cosmology (AKA the Big Bang theory)
is a grand paradigm.
The
ΛCDM model (AKA concordance model)
from one perspective is a special case of
Big Bang cosmology: it is specialized to have
specific features.
From another perspective,
Big Bang cosmology is an ingredient in
the ΛCDM model.
Both perspectives are valid.
Now Big Bang cosmology is a very robust
theoryit
would be astonishing if it were just plain wronga lot of fundamental observations about the
observable universe would have
be interpreted in some other way if it were just plain wrong.
On the other hand,
the ΛCDM model
may need revision to the point of becoming a different
theory.
However, circa 2020,
it fits nearly all
observations of the
observable universe from
the whole on average down to the
large scale structure,
or more precisely, the
large scale structure's
statistical properties.
Because it fits so much is why the
ΛCDM model
is also called the
concordance model (though that name
is now disfavored) and sometimes
standard model of cosmology (SMC).
Now limitations are things a theory does
NOT explain (even if is right as far as it goes)
and tensions
are significant discrepancies short of
falsification and which can also be called
paradigm anomalies.
The Big Bang cosmology
has limitations, but NO tensions
at presentand as aforesaid,
it would be astonishing if it was just plain wrong.
The ΛCDM model has both
limitations and tensions.
 Limitations of Big Bang Cosmology and the ΛCDM Model:
Limitations of
Big Bang cosmology
and the ΛCDM model mostly phrased
as questions:
 Why
ΛCDM model parameters
have the values they have?
Those values are fitted from observations of the
observable universe
(see Wikipedia: ΛCDM: Parameters).
Example free parameters are,
the
Hubble constant = fiducial value 70 km/s/Mpc,
the
density parameter =
Ω = rho/rho_crit = fiducial value 1,
and the
baryontophoton ratio
η=6.16*10**(10) (Planck2018)
(see also
Wikipedia: Big Bang nucleosynthesis: Baryontophoton ratio η;
An Etymological Dictionary of Astronomy: baryontophoton ratio η).
 What happened before the
Big Bang?
In yours truly's
view, the Big Bang
is the era when the fundamental particles first existed and
Big Bang nucleosynthesis
occurred, and NOT the
big bang singularitywhich no one
believes in since quantum gravity
must supercede general relativity
at some point
as we run cosmic time back to
the Planck era.
 What the universe
is like at some point well beyond the
observable universe?
The observed homogeneity and isotropy of the
observable universe
(as an axiom called the
cosmological principle)
shows that the universe
beyond the observable universe
is probably much the same as the
observable universe for a long way,
but NOT far, far away.
We've only verified the
cosmological principle
(insofar as we have verified it) for the
observable universe.
 What will be the fate of the
observable universe?
Except by extreme and very speculative extrapolation,
the ΛCDM model
does NOT tell us.
Yes, the observable universe
is well described since the
Big Bang ∼ 13.8 Gyr ago
(see Wikipedia: Age of the universe = 13.797(23) Gyr (Planck 2018)).
But extrapolating
for hundreds of gigayears and further into the future of
cosmic time is, indeed, highly speculative.
See
Wikipedia:
Graphical timeline from Big Bang to Heat Death (but note that the lefthand vertical scale is tricky:
it is x=100*log[log(t_year)] and so t_year=10**[10**(x/100)])
and Wikipedia: Graphical timeline
of the Stelliferous Era.
 What dark matter is?
 What dark energy is?
Because
we do NOT understand what dark energy is
we do NOT understand
the acceleration of the universe
or how long it will last.
 Because of their limitations, Big Bang cosmology
and
the ΛCDM model
are actually superficialdespite the fact that they explain an awful lot about
the observable universe
and are huge triumphs.
By superficial, one means the whole universe
(the sum of all reality) may be very different on average.
Maybe the whole universe is the
multiverse: maybe in the version of
eternal inflation; maybe in
some other version.
Recall in the eternal inflation
version of the multiverse paradigm,
the observable universe
is embedded in a
pocket universe beyond
which whole universe
(i.e., the multiverse)
could be very different from the
observable universe
both in setup and even in some
physical laws.

Tensions of the ΛCDM Model Circa 2020s:
 The
Hubble tension is discussed in the figure below
(local link /
general link: hubble_tension.html).
 After searching with increasing effort
since circa 1980,
we have NOT discovered the
dark matter particle
despite plausible suggestions from
quantum field theory
about what it is.
There current points circa 2020:
 One
dark matter detection
experiment
DAMA/LIBRA has reported a detection
since 2003, but
this detection has NOT been confirmed, just recently by
a group doing the same experiment
(see COSINE100 2018).
It is NOT yet clear what explains the
DAMA/LIBRA result,
but it seems unlikely at the moment that it is
a real detection of
a dark matter particle.
 An analysis of a balloon experiment
ANITA
reports the detection of an unstable
dark matter particle
which may be related to the
(stable) dark matter particle
(Fox et al. 2018;
Nautilus: Interview with Derek Fox, 2018oct11).
This Large Hadron Collider (LHC)
may be on the verge of detecting the
related (stable) dark matter particle.
 Dark matter may NOT
be an exotic particle, but
may be primordial black holes.
This theory has been disfavored, but
there are arguments in its favor
(see Seven Hints for Primordial Blackhole Dark Matter,
Sebastien Clesse, Juan GarciaBellido, 2017).
 Maybe the dark matter particle
does NOT exist.
The alternative is MOND (MOdified Newtonian Dynamics)
which dispenses with the dark matter particle
and works well for galaxies, but
NOT well galaxy clusters
(see review
Massimi 2018)
and takes the
cold dark matter (CDM) out of
the ΛCDM model.
MOND requires both
Newtonian gravity
and
general relativity
to be modified for very low accelerations.
Such modifications could radically change much of our
cosmological theory.
 The positive curvature problem:
The ΛCDM model
assumes a
flat universe
and a very close to
flat universe
is strong generic prediction of
inflation cosmology
which also gives a strong generic prediction of the density fluctuations that
seed the
large scale structure of universe
so far successfully in
computer simulations.
However, in recent years some analyses
(e.g., Qi et al. 2018;
Dinda et al. 2023) suggest that the
observable universe has
significant
positive curvature (k > 0, Ω_k < 0).
If the
positive curvature
extends without limit, it means that
the universe is a closed universe: i.e.,
a finite, but unbounded, 3dimensional surface of
a 4dimensional hyperspherejust
like Albert Einstein (18791955)
suggested back in 1917 with the
Einstein universewhich,
however, was static, and so is NOT correct.
The analyses suggesting
positive curvature
are, however, in disagreement with other analyses that still show no significant
positive curvature.
At the moment,
positive curvature
seems disfavored.
But if it is true, it vastly upsets
the ΛCDM model
since the inflation paradigm
(which requires extreme, but NOT, exact flatness)
is usually regarded as an ingredient in
the ΛCDM model.
Note the inflation paradigm provides
natural seeds for the growth of the
large scale structure
(computer simulations of which
are a triumph of
the ΛCDM model)
and solves
the horizon problem
and the flatness problem
(which is what you have when there is NO
positive curvature
problem) which are otherwise unexplained
initial conditions
of Big Bang cosmology
and the ΛCDM model.
 Other tensions
(see, e.g.,
"Cosmological tensions in the birthplace of
the heliocentric model", Eleonora Di Valentino, Emmanuel Saridakis, & Adam Riess, 2022).
 The above tensions
may all evaporatebut the
Hubble tension
seems like it is here to staybut the fact that their are several all at once is very
exciting and suggests that we might be on the verge of a
paradigm shift (AKA Kuhnian scientific revolution):
the ΛCDM model may need
major revision or replacement.
It has to be admitted that the
ΛCDM model has become a bit boringit's
a bit like a blank wall that stops you from seeing further.
We want a new
standard model of cosmology (SMC).
Local file: local link: big_bang_cosmology_limitations.html.
File: Cosmology file:
big_bang_cosmology_limitations.html.