No, it is not possible for an asteroid to be as big as or bigger than Earth. Asteroids are rocky objects that orbit the Sun, and they range in size from small boulders to several hundred kilometers in diameter. However, their sizes are significantly smaller compared to Earth.
Earth has a mean diameter of about 12,742 kilometers (7,918 miles) and a mass about 5.97 x 10^24 kilograms. In contrast, the largest known asteroid, Ceres, has a diameter of approximately 940 kilometers (583 miles). Even the largest asteroids in our solar system, such as Vesta and Pallas, have diameters of a few hundred kilometers at most.
Objects larger than Earth, such as planets, are formed through a process called accretion, where gravity causes smaller objects to come together and merge over long periods of time. This process leads to the formation of massive bodies like planets. Asteroids, on the other hand, are remnants from the early stages of our solar system's formation and did not undergo the same accretion process as planets.
Therefore, based on our current understanding of planetary formation and the known size distribution of asteroids, it is highly unlikely for an asteroid to be as big as or larger than Earth.