Are there infinitely many solutions to $\phi(n) = \phi(n+1)$, where $\phi$ is the Euler totient function?

Erdős, Pomerance, and Sárközy [EPS87] proved that for all large $x$, the number of $n \leq x$ with $\phi(n) = \phi(n+1)$ is at most $$\frac{x}{\exp((\log x)^{1/3})}$$.

[EPS87] Erdős, Paul and Pomerance, Carl and Sárközy, András, _On locally repeated values of certain arithmetic functions_. {II}. Proc. Amer. Math. Soc. (1987), 1--7.