Neutron stars in extended scalar-Gauss-Bonnet gravity: the richness of the solution spectrum

Neutron stars are natural laboratories for testing gravity in the strong field regime. That is why the full spectrum of neutron star solutions in different modified theories should be thoroughly studied. Among the most natural modifications of general relativity are the theories in which additional scalar degrees of freedom are present. That is why scalar-tensor theories like Brans--Dike and Damour--Esposito--Farese theories, as well as their extensions such as scalar-Gauss-Bonnet gravity, attracted attention throughout the years. In the present work, we combine those theory families and explore extensively the neutron star solution space in their realm. We identify qualitative new behavior of the solutions, including the existence of new types of phase transitions and new branches of solutions present only for high neutron star masses. Due to the peculiarities of the solutions, they can not be easily mimicked by a simple change of the equation of state.