Abstract
We construct modified cosmological scenarios through the application of the first law of thermodynamics on the universe horizon, but using the generalized, nonextensive Tsallis entropy instead of the usual Bekenstein–Hawking one. We result to modified cosmological equations that possess the usual ones as a particular limit, but which in the general case contain extra terms that appear for the first time, that constitute an effective dark energy sector quantified by the nonextensive parameter delta . When the matter sector is dust, we extract analytical expressions for the dark energy density and equation-of-state parameters, and we extend these solutions to the case where radiation is present too. We show that the universe exhibits the usual thermal history, with the sequence of matter and dark-energy eras, and according to the value of delta the dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or experience the phantom-divide crossing during the evolution. Even in the case where the explicit cosmological constant is absent, the scenario at hand can very efficiently mimic Lambda hbox {CDM} cosmology, and is in excellent agreement with Supernovae type Ia observational data.
Highlights
The usual approach of constructing modified gravitational theories is to start from the Einstein–Hilbert action and add correction terms
One can apply the first law of thermodynamics in the universe horizon, and extract the Friedmann equations
In this way we will obtain new modified Friedmann equations that possess the usual ones as a particular limit, namely when the Tsallis generalized entropy becomes the usual one, but which in the general case contain extra terms that appear for the first time
Summary
The usual approach of constructing modified gravitational theories is to start from the Einstein–Hilbert action and add correction terms. We will apply the first law of thermodynamics, but instead of the usual entropy relation we will use the nonextensive, Tsallis entropy [45,46,47], which is the consistent generalization of the Boltzmann– Gibbs additive entropy in non-additive systems, such as gravitational ones In this way we will obtain new modified Friedmann equations that possess the usual ones as a particular limit, namely when the Tsallis generalized entropy becomes the usual one, but which in the general case contain extra terms that appear for the first time.
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