Synonyms for Escalation:

n.

acceleration, increase, growth. enlargement, buildup, amplification, multiplication, aggrandizement, hike, jump, upturn, boost, proliferation, swell, upsurge, augment, raise, upswing, augmentation. ascent (noun)
rise, lift, elevation, mounting, rising, uprising, scale, levitation, ascent, ascension.
elevation (noun)
raising, exaltation, upraising, heightening, uplifting.
increase (noun)
upturn, aggrandizement.
intensification (noun)
acceleration, increase, rise, growth.

Other synonyms:

aggrandizement. amplification, upturn, upswing, multiplication. augmentation, proliferation, buildup. enlargement. growth. growth
increase.
Other relevant words:
enlargement, augment, upswing, hike, amplification, acceleration, upsurge, augmentation, jump, buildup, aggrandizement, raise, growth, multiplication, boost, upturn, proliferation, swell, increase.