I have to use the Arial font and I do that as follows (Helvetica is close to Arial):
\renewcommand{\rmdefault}{phv} % Helvetica
\renewcommand{\sfdefault}{phv} % Helvetica
The other solution I have found is to use the commands:
\usepackage{helvet}
\renewcommand{\familydefault}{\sfdefault}
Both work and as far as I can see, both solutions look the same. I use the following packages for math fonts because it looks nice with Arial fonts:
\usepackage[amsthm,mathsfit]{libertinust1math}
I want to modify some font sizes as follows (it looks nice with 1, but it looks nicer with 1.2):
\makeatletter
\newcommand*{\LinuxLibertineT@scale}{1.2}
\makeatother
The issue I have is that the \mathcal fonts are apparently not scalable as far as I understand the problem. Is there any way to overcome the problem ? (I know nothing about fonts sorry)

12ptas one of the optional arguments of the\documentclassinstruction:\documentclass[12pt,...]{...}. – Mico Oct 07 '23 at 09:23\renewcommand{\rmdefault}{phv} % Arialhas absurd comment, should be\renewcommand{\rmdefault}{phv} % Helvetica. And the answers you pointed include the correct notices about Helvetica. – wipet Oct 08 '23 at 04:05phvis no more Helvetica than it is Arial. Which font you get is extent system-dependent, but most people will get e.g. URW NimbusSanL (uhv) and not Adobe Helvetica (phv). It's true the metrics may differ from those of Arial (but not Helvetica). – cfr Oct 08 '23 at 05:19