By combining general relativity and CPT symmetry, the theory of CPT gravity predicts gravitational repulsion between matter and CPT-transformed matter, i.e. antimatter inhabiting an inverted space-time. Such repulsive gravity turned out to be an excellent candidate for explaining the accelerated expansion of the Universe, without the need for dark energy. The recent results of the ALPHA-g experiment, which show gravitational attraction between antihydrogen atoms and the Earth, seem to undermine this success in the cosmological field. Analyzing the above theory, we find two solutions that can be consistent with the experimental results, while preserving the large-scale gravitational repulsion. The first highlights how repulsive gravity can be the result of the interaction with an inverted space-time, but occupied by matter and not antimatter, and therefore the antimatter present in our space-time has no reason to exhibit gravitational repulsion. The second retains the original CPT transformation, resulting in repulsive gravity between matter and antimatter, but with the caveat that antimatter immersed in our space-time cannot exhibit the PT transformation which is the cause of the repulsion. Finally, it is shown that, in a Newtonian approximation of the geodesic equation, time reversal is not a necessary operation for repulsive gravity, therefore opening the possibility of an expanding cosmos with a single time direction.

In this research, the other reasonable explanations for the cosmic microwave background radiation is revealed. Due to the microwave resolution, it very roughly shows the image of galaxies in the universe. Moreover, the intensity measurement on each pixel of the image is the sum of the incident microwaves from different directions, so the microwave image cannot represent the microwave sources clearly far away from the Earth. Hence, we propose a simulation after removing several strongest microwave sources, the remaining microwave radiation sources can establish a very uniform intensity distribution over a range of several ten light years. On the other hand, Sloan Digital Sky Survey reveals 200 million galaxies in the universe and, in fact, only to eliminate the contributions of all galaxies from the microwave image is impossible. The way to further obtain the fine-scale structure by only removing the few strongest microwave sources as the foreground effect will keep the other contributions from all the rest galaxies and stars. Therefore, the Cosmic Microwave Background cannot be uniquely explained the radiation which was left after the initial formation of the universe. Moreover, it is the mainly residual radiation from the un-calculated galaxies and inaccurate estimation of the microwave source strength.