The most recent theory that upholds the big bang theory, but suggests a sudden expansion after the bang, is called the
oscillating universe theory
inflation theory
steady state theory
big bang theory

Inflation theory.

Explanation:

Inflation theory examines the first moments of the universe after the big bang. It states that the universe was formed in a volatile energy state, that forced an accelerated expansion of the universe in its initial moments.

This means that the universe is much bigger than it was thought, and it allows predictions about the uniform distribution of energy and the flat geometry of spacetime, ideas the big bang theory hadn´t cover.