Disclaimer: I'm no RF expert.
RF can be funny stuff!
I will modestly claim that I know "quite a bit about it".
The lower the frequency the higher capacitance the ground plane needs to be, meaning it needs to be larger.
To get an idea of what works well, think in terms of wavelength.
To work efficiently the elements of an antenna system need to be one quarter of a wavelength long.
434 Mhz has a wavelength of approximately 70cm, so, the two legs of a dipole should be 17.5cm long, or for a monopole antenna, a 17.5cm rod vertically mounted on a 17.5cm diameter conductive ground plane.
These are ideal conditions.
For most practical applications, the antenna is a piece of wire just flopping around and the groundplane is the rest of the circuit, whatever it is. Not great in terms of getting the maximum range from the device, but adequate for most purposes.
At UHF I would've thought a PCB ground plane or even a battery would be fine.
Exactly!
Consider the "plipper" you use to lock/unlock your car, that probably operates around 434Mhz, mine do.
There is nothing 17.5cm long about that.
The antenna for the receiver in the car is just a short wire dangling out of the box with the electronics (at least in one of my cars, I dont know about the other one), and dont forget that this is inside a steel box, something which is half way to being a Faraday Cage.
Yet it works OK, I can lock/unlock the doors from 5 or 6 metres away, I dont need any more range. In fact a longer range could be a disadvantage.
Using the same RF modules with dipole antennas mounted in the clear could have a much greater range (several hundred metres if not a km).
You only need a real earth connection at low frequencies.
At much lower frequencies, such as longwave, mediumwave and shortwave frequencies the usual "earth" connection is a mat of buried wires radiating radially from the base of the antenna mast.
There may be a hundred or more radial wires up to one quarter wavelength long. A LOT of buried copper.
As the frequency gets lower it becomes most impractical to have a quarter wavelength vertical element for the radiating part of the antenna system, in which case there is often a lot of horizontal wire at the top of the vertical element to provide top loading capacitance.
JimB