6740 10.1140/epjc/s10052-019-6740-5 242 64 Modified cosmology from extended entropy with varying exponent Regular Article - Theoretical Physics 1 10 2019 3 4 2018 12 3 2019 3 3 2019 3 16 The Author(s) 2019 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Funded by SCOAP3 Shin’ichi Nojiri nojiri@gravity.phys.nagoya-u.ac.jp Sergei D. Odintsov odintsov@ieec.uab.es Emmanuel N. Saridakis Emmanuel_Saridakis@baylor.edu 0000 0001 0943 978X grid.27476.30 Department of Physics Nagoya University Nagoya 464-8602 Japan 0000 0001 0943 978X grid.27476.30 Kobayashi-Maskawa Institute for the Origin of Particles and the Universe Nagoya University Nagoya 464-8602 Japan grid.7080.f Institut de Ciencies de lEspai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans s/n 08193 Cerdanyola del Valles Barcelona Spain 0000 0000 9601 989X grid.425902.8 Institució Catalana de Recerca i Estudis Avançats (ICREA) Passeig Lluís Companys, 23 08010 Barcelona Spain 0000 0001 2185 9808 grid.4241.3 Department of Physics National Technical University of Athens Zografou Campus GR 157 73 Athens Greece 0000000121679639 grid.59053.3a Department of Astronomy, School of Physical Sciences University of Science and Technology of China Hefei 230026 China 0000 0001 0790 1301 grid.112471.0 Tomsk State Pedagogical University 634061 Tomsk Russia 0000 0000 9460 4294 grid.440738.c Int. Lab. of Theor. Cosmology, TUSUR 634050 Tomsk Russia Abstract We present a modified cosmological scenario that arises from the application of non-extensive thermodynamics with varying exponent. We extract the modified Friedmann equations, which contain new terms quantified by the non-extensive exponent, possessing standard ΛCDM cosmology as a subcase. Concerning the universe evolution at late times we obtain an effective dark energy sector, and we show that we can acquire the usual thermal history, with the successive sequence of matter and dark-energy epochs, with the effective dark-energy equation-of-state parameter being in the quintessence or in the phantom regime. The interesting feature of the scenario is that the above behaviors can be obtained even if the explicit cosmological constant is set to zero, namely they arise purely from the extra terms. Additionally, we confront the model with Supernovae type Ia and Hubble parameter observational data, and we show that the agreement is very good. Concerning the early-time universe we obtain inflationary de Sitter solutions, which are driven by an effective cosmological constant that includes the new terms of non-extensive thermodynamics. This effective screening can provide a description of both inflation and late-time acceleration with the same parameter choices, which is a significant advantage.