What Narlikar showed
The above might be in agreement with the article
Is Physics Slowly Changing?
, written by the inventor of the changing mass hypothesis himself: Halton Arp.
A useful reference may be: What's the point of the Hoyle–Narlikar theory of gravity?
Quote: What Narlikar showed is that the rigorous solution of the field equations (which in flat space are simply conservation of
energy/momentum) requires the elementary particles to gain mass as $m=t^2$. Where $t$ is to be interpreted as gravitational time,
of course, because General Relativity as developed by Albert Einstein is only about gravity; it has not a shred of atomic physics
in its theoretical framework.
Remember the decreasing particle mass sequence which is in one-to-one correspondence with the ten timestamps histogram, the only difference
being a quadratic decrease instead of a linear one:
| m |
|---| = 1.0 0.81 0.64 0.49 0.36 0.25 0.16 0.09 0.04 0.01
|m_0|
Consequently, if $\,T\,$ is gravitational time, according to Narlikar:
$$
\frac{m}{m_0} =\left(\frac{T-A}{T_0-A}\right)^2
$$
Similar reasonings as in Proof of Hyperbola then leads to the following result:
$$
\frac{\Delta t}{\Delta T} \to \frac{dt}{dT} = \left(\frac{T_0-A}{T-A}\right)^2
$$
Where $dt$ and $dT$ are the infinitesimal units of atomic time and gravitational time respectively; $T$ is gravitational time; $T_0$
is gravitational reference time, which is the "nowadays" timestamp and $A$ is the gravitational timestamp corresponding with the beginning,
at the time when mass is created out of nothing.
Let's integrate the equation:
$$
t = \int \left(\frac{T_0-A}{T-A}\right)^2 dT = -(T_0-A)\frac{T_0-A}{T-A} + C
$$
From $t=t_0=T_0=T$ we obtain the information necessary to determine the integration constant $\,C$ :
$$
T_0 = -(T_0-A) + C \quad \Longrightarrow \quad C = 2\,T_0-A
$$
The graph of the function $\,t(T)\,$ has an asymptote for $\,T\to A$ , which is to be expected and correct.
But for $\,T\to \infty\,$ we have:
$$
\lim_{T\to\infty} t(T) = T_0 + (T_0-A)\left[1 - \lim_{T\to\infty}\frac{T_0-A}{T-A}\right] = 2\,T_0-A = C
$$
Which means that atomic time has come to rest, when compared with gravitational time; atomic time does no longer proceed, in the far future.
There is an upper limit for atomic time. I think that's an absurd conclusion, thus debunking (part of) the Narlikar theory, but I'm not sure.
Another possibility, theoretically, is the following law for increase of elementary particle mass proportions:
$$
\frac{m}{m_0} = \sqrt{\frac{T-A}{T_0-A}}
$$
Similar reasonings as in Proof of Hyperbola then leads to the following result:
$$
\frac{\Delta t}{\Delta T} \to \frac{dt}{dT} = \sqrt{\frac{T_0-A}{T-A}}
$$
Let's integrate the equation:
$$
t = \int \sqrt{\frac{T_0-A}{T-A}} dT = 2\sqrt{(T-A)(T_0-A)} + C
$$
From $t=t_0=T_0=T$ we obtain all information necessary to determine the integration constant $\,C$ :
$$
T_0 = 2(T_0-A) + C \quad \Longrightarrow \quad C = 2A-T_0 \\ \Longrightarrow \quad t = 2\sqrt{(T-A)(T_0-A)} + 2A-T_0
$$
For the time stamp $T=A$ at the moment of Creation we find:
$$
t = C = 2A-T_0
$$
Meaning that the Big Bang (which is meant to be in atomic time $\,t$ ) would have occurred at $2\times (-8000) - 2018 = 16018 \mbox{ B.C.}$
I think that neither evolutionists nor creationists will be happy with this outcome.