'vast sphere' is correct and usable in written English.
You can use it as a metaphor or figure of speech to represent a broad range of elements, such as an idea or concept. For example, "Her experience covers a vast sphere of business operations."
Of about 130 known exoplanets, astronomers think nearly all are vast spheres of gas like Jupiter.
From the early 1500s, northern Indian cities in particular were brought into a vast Muslim sphere of influence under the Mughal empire.
In his vast trilogy Spheres, published between 1998 and 2004, Sloterdijk wrote the metaphysical history of enclosed spaces including Buckminster Fuller's geodesic domes and space travel, though not Apple's iCloud (it hadn't yet appeared to Steve Jobs in a dream).
His geocentric cosmos began with an explosion of a type of light he called lux, which expanded into a vast, ever-thinning sphere of matter and light.
Technology alone is a revolution with vast consequences for every sphere – business, public services, lifestyle and Government.
Pop stars and their parent corporations are the true élites of the cultural sphere, reaping vast rewards from a winner-takes-all system.
At day 7, the vast majority of the spheres have only one type of fluorescence, indicating that they have a single cell origin.
Those knowledge and information prove to be extremely vast and complex in the sphere of urban recovery, especially when the active involvement of several different participants, such as private companies, the Public Administration, and the citizens, is taken into consideration.
They were vast, vaguely biomorphic cities with spheres and towers built on the ocean or asteroids.
The Dutch English connection in the person of William III, the continuing threat of Louis XIV, and a succession of shattering events in various spheres stimulated a vast production of cartoons from the 1680s on.
