"increase indefinitely" is correct and usable in written English.
It means to increase without limit. For example, "The demand for the product is expected to increase indefinitely."
"Of course, no one could expect them to increase indefinitely.
Most forecasting models that governments employ assume that driving will continue to increase indefinitely.
They cannot increase indefinitely and will be hard to unwind without sending the world economy into recession.
"It cannot increase indefinitely otherwise you will end up with no one wanting to work at the BBC".
Exploitation of the ecosystem is what generates economic growth, but the rate of the exploitation cannot increase indefinitely without overdriving the system & pushing it to the point of collapse.
In their most general form, these involve the notion that a step loading (a suddenly imposed stress that is subsequently maintained constant) causes an immediate strain followed by a time-dependent strain which, for different materials, either may have a finite limit at long time or may increase indefinitely with time.
It would therefore not be logical to assume that spore production increases indefinitely with increased lesion size.
However, it cannot be used for a steady-state current, which would require a magnetic flux increasing indefinitely over time.
The ergodic theorem says that under certain circumstances and as the number of measurements increases indefinitely, the time average equals the space average.
I can almost imagine a yoga instructor asking a class to meditate on what would happen if the number of sides kept increasing indefinitely.
The singular insight of Adam Smith, Ferris writes, was to recognize that wealth creation and the production of material comforts might be "increased indefinitely if individuals are free to invest and to innovate".
