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The experimental studies of the type Ia supernovae and of the cosmic microwave background radiation have shown the recent accelerated expansion of the Universe. To explain this behavior, a hypothetical form of energy called the dark energy was introduced. On the other hand, the presence of a cosmological constant in the field equations causes an accelerated expansion of the Universe; thus, the latter is identified with the dark energy. Moreover, the energy of the vacuum state exhibits the same consequences of a cosmological constant; therefore, the experimental value of the vacuum energy must contribute to the experimental value of the cosmological constant, and both values must have the same order of magnitude. However, when the two values are compared, there exists a difference of more than 55 orders of magnitude. In order to establish concordance, it is necessary to do a fine-tuning in the experimental value of the cosmological constant. The impossibility to avoid this fine-tuning is called the old cosmological constant problem. Many solutions have been raised, such as the replacement of the cosmological constant by a scalar field; however, these solutions do not actually solve the problem. We will present an alternative solution, in which the cosmological constant is complemented by a new term originated from modifications of gravity. The modification is performed by introducing a function f(R, G), where R is the Ricci scalar and G is the Gauss-Bonnet invariant. The new term, which can be interpreted as a cosmic fluid with a particular form for its equation of state, evolves in time dynamically relaxing the enormous difference between the vacuum energy and the cosmological constant.
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