The rest masses of fundamental particles certainly are NOT constants !
I will do copy/past from pages 6-9 (of 20) of a recent document by Alfredo (Independent researcher)
the sufficient information to show how atomic properties can change, including mass, at a cosmological level.
Starting only from data and making no hypothesis he formally presents a dilation(scaling) model of the universe where the atoms are not invariant and physical laws hold, without contradiction with GR, and compares the model with FRW and $\Lambda$CDM models.
(the whole paper deserves your attention, it is very clear and it only uses basic physics, imo accessible to undergraduated students. He makes a full study on how we measure, units, local and field constants and laws, how can exist a variation and why we are not aware of such, and a lot more)
quoting Alfredo:
How the universe can be scaling
We have seen that if space expansion traces a scaling phenomenon,
we should expect to detect varying field constants; we have now to
find out why that is not observed. The first thing to do is to look
up to the dimension functions of field and some other constants:
$$
\begin{array}{ccl}
\left[G\right] & = & M^{-1}L^{3}T^{-2}\\
\left[\varepsilon\right] & = & M^{-1}Q^{2}L^{-3}T^{2}\\
\left[c\right] & = & LT^{-1}\\
\left[h\right] & = & ML^{2}T^{-1}\\
\left[\sigma\right] & = & M^{-3}L^{-8}T^{5}.
\end{array}
$$
The equations of field constants ($G,\varepsilon$ and c) display
a peculiar characteristic: the summation of exponents of the
dimension function of each field constant is zero! This is unexpected
and does not happen with the other constants. It means that if all
the four base units concerned change by the same factor,
$$
M=Q=L=T,
$$
then the measuring units of field constants hold invariant, $[G]=[\varepsilon]=[c]=1$.
To see the relevance of this, let us consider that the atomic units
of mass, charge, length and time change all at the same rate in relation
to the space units. In that case, because of the property shown above,
the atomic units of the field constants hold invariant in relation
to the space ones and, therefore, the field constants are invariant
in both systems (they are invariant in space units by definition of
these ones). The geometry of space would be scaling in atomic units
while the value of field constants would hold invariant--- which
is exactly what cosmic data seems to display.
The fact that the dimensions of field constants display null summation
of exponents can just be a coincidence, but it is also the kind of
indication we were looking for, a property embedded in physical laws.
This is the only way we can consider a previously unknown fundamental
property without conflicting with established physics.
We have now the fundamental understanding that can support a scaling
(dilation) model of the universe and we will now proceed to the formal
development of that model.
...
Hence, one of the systems of units is defined from matter properties,
designated here by atomic system and identified by A ("A" from "atomic")
and the other is the space system of units, identified by S ("S"
from "space"); the later is such that space properties (geometry
and field constants) remain invariant in it, which is required to
qualify the S system as internally defined in relation to space. Thus,
the conditions that define the S system are the following:
- The units of S are such that the S measures of field constants hold
invariant;
- The length unit of S is such that the wavelength of a propagating
radiation in vacuum is time invariant.
The base quantities are Mass (M), Charge (Q), Time (T),
Length (L) and Temperature ($\theta$), and the ratio between
A and S base units is denoted by $M_{AS},Q_{AS},T_{AS},L_{AS},\theta_{AS}$.
Note that the ratio between the A and S units of any quantity or constant
is therefore expressed by the respective dimension function;
...
Postulates
The model will be deducted not from hypotheses
but from relevant observational results, which are stated as postulates:
- In atomic units (A), all local and field constants are
time-independent.
- $L_{AS}\,$decreases with time.
The first postulate is not fully supported in experience, as we cannot
state it with the required error margin; however, we have also no
sound indication from observations that it might be otherwise. The
second postulate represents the observed phenomenon of space expansion
in atomic units, stated in this unusual way because it is presented
as a function of $L_{AS}\,$, i.e., of the ratio between atomic
and space length units and not the inverse, as usual.
...
S units, by definition, are such that (eq.1)
\begin{equation}
\frac{dG_{S}}{dt_{S}}=\frac{d\varepsilon_{S}}{dt_{S}}=\frac{dc_{S}}{dt_{S}}=0.
\end{equation}
Since the field constants are time-invariant also in atomic units,
as stated by postulate 1, and since the two systems of units are identical
at $t=0$, then the values of these constants are the same in the
two systems at whatever time moment: (eq.2)
$$
\begin{array}{ccccc}
G_{A} & = & G_{S} & = & G\\
\varepsilon_{A}^{\vphantom{l}^{\vphantom{L}}} & = & \varepsilon_{S} & = & \varepsilon\\
c_{A}^{\vphantom{l}^{\vphantom{L}}} & = & c_{S} & = & c.
\end{array}
$$
The relation between the S and A values of each constant is the one
between the respective A units and S units, which is given by the
dimension function,
therefore (eq.3)
$$
\begin{array}{ccccl}
\dfrac{G_{S}}{G_{A}} & = & \left[G\right]_{AS} & = & {M_{AS}^{-1}}{L_{AS}^{3}}{T_{AS}^{-2}}=1\\
\dfrac{\varepsilon_{S}^{\vphantom{l}^{\vphantom{L}}}}{\varepsilon_{A}} & = & \left[\varepsilon\right]_{AS} & = & {M_{AS}^{-1}}{Q_{AS}^{2}}{L_{AS}^{-3}}{T_{AS}^{2}}=1\\
\dfrac{c_{S}^{\vphantom{l}^{\vphantom{L}}}}{c_{A}} & = & \left[c\right]_{AS} & = & L_{AS}{T_{AS}^{-1}}=1.
\end{array}
$$
This set of equations implies $M_{AS}=Q_{AS}=T_{AS}=L_{AS}$. By postulate
2, $L_{AS}$ is a time function, therefore the solution can be presented
as: (eq.4)
$$
\begin{equation}
M_{AS}(t)\,=Q_{AS}(t)\,=T_{AS}(t)\,=L_{AS}(t)\,.\,
\end{equation}
$$
Note that temperature is independent of this result.
The next step is to define this time function, which is the space
scale factor law. As all the above four base quantities follow this
function, it is convenient to identify it by a specific designation;
in this work this scaling law is identified by the symbol $\mathcal{\alpha}$: (eq.5)
$$
\begin{equation}
\alpha(t)\,=\, L_{AS}(t).
\end{equation}
$$
...
The scaling law
To make no hypothesis on the cause of the expansion is to consider
that expansion is due to a fundamental property; to consider otherwise
would imply a specific hypothesis on a particular phenomenon driving
the expansion. Therefore, for this model, the space expansion is due
to a fundamental property, tracing a self-similar phenomenon. Likewise,
as no hypothesis is made on how fundamental properties may vary with
position on space and time, it is assumed that they do not depend
on it. This implies that the scaling has a constant time rate in some
physically relevant system of units, i.e., that the scaling
law is exponential in such system of units. There are only two possibilities
in the framework established for this model: either space expansion
is exponential in A units ($L_{SA}(t_{A})=\alpha^{-1}(t_{A})$ is
exponential) or matter evanesces exponentially in S units ($L_{AS}(t_{S})=\alpha(t_{S})$
is exponential). The former case does not fit observations; only the
later case is possible.
The general expression for a scaling law exponential in S units is (eq.6)
$$
\begin{equation}
\alpha(t_{S})=k_{1}e^{k_{2}\cdot t_{s}}\,;
\end{equation}
$$
at the moment $t_{A}=t_{S}=0$ it is $\alpha(0)=L_{AS}(0)=1,$ so
$k_{1}=1$; note now that (eq.7)
$$
\begin{equation}
\frac{dt_{S}}{dt_{A}}=T_{AS}=\alpha\,
\end{equation}
$$
which shows that the variation of the measure of time is inversely
proportional to the time unit; and that (eq.8)
$$
\begin{equation}
r_{A}=r_{S}{L_{AS}^{-1}}=r_{S}\cdot\alpha^{-1},
\end{equation}
$$
where r is the distance to some point, or its length coordinate;
as the rate of space expansion at t=0 is, by definition, the
value of Hubble constant, represented by $H_{0}$, then (eq.9)
$$
\begin{equation}
H_{0}=\left(\frac{1}{r_{A}}\frac{dr_{A}}{dt_{A}}\right)_{0}=-k_{2},
\end{equation}
$$
therefore (eq.10)
$$
\begin{equation}
\alpha(t_{S})=e^{-H_{0}\cdot t_{S}}.
\end{equation}
$$
Hubble constant is the present space expansion rate for an atomic
observer and is the matter evanescence rate (negative) for a space
observer.
