Pressure, as commonly understood, is not easily related to General Relativity.
However, if we think of space-time as a coiled spring, it is easy to understand that if you compress that spring, you increase its energy, and the curvature of space-time around it.
An easy to understand excerpt from https://ned.ipac.caltech.edu/level5/Guth/Guth3.html
explains the relationship between pressure, energy density, space-time curvature ( gravity ) and expansion/inflation.
"THE PRESSURE OF THE FALSE VACUUM can be determined by a simple energy-conservation argument. Imagine a chamber filled with false vacuum, as shown in the diagram below.
For simplicity, assume that the chamber is small enough so that gravitational effects can be ignored. Since the energy density of the false vacuum is fixed at some value uf, the energy inside the chamber is U=ufV, where V is the volume. Now suppose the piston is quickly pulled outward, increasing the volume by dV. If any familiar substance were inside the chamber, the energy density would decrease. The false vacuum, however, cannot rapidly lower its energy density, so the energy density remains constant and the total energy increases. Since energy is conserved, the extra energy must be supplied by the agent that pulled on the piston. A force is required, therefore, to pull the piston outward, implying that the false vacuum creates a suction, or negative pressure p. Since the change in energy is dU = ufdV, which must equal the work done, dW = -pdV, the pressure of the false vacuum is given by
p = -uf.
The pressure is negative, and extremely large. General relativity predicts that the gravitational field which slows the expansion of the universe is proportional to uf + 3p, so the negative pressure of the false vacuum overcomes the positive energy density to produce a net repulsive gravitational field. "