Imprints of Barrow–Tsallis cosmology in primordial gravitational waves

Abstract

Both the Barrow and Tsallis δ entropies are oneparameter generalizations of the black-hole entropy, with the same microcanonical functional form. The ensuing deformation is quantified by a dimensionless parameter, which in the case of Barrow entropy represents the anomalous dimension caused by quantum fluctuations over the horizon surface, while in Tsallis’ case, it describes the deviation of the holographic scaling from extensivity. Here, we utilize the gravity-thermodynamics conjecture with the Barrow–Tsallis entropy to investigate the implications of the related modified Friedmann equations on the spectrum of primordial gravitational waves. We show that, with the experimental sensitivity of the next generation of gravitational wave detectors, such as the Big Bang Observer, it will be possible to discriminate deviations from the CDM model up to O(10−3). In this limit, Barrow–Tsallis entropy reduces to a logarithmic correction to holographic scaling, which is nearly universally predicted by both entanglement entropy calculations in the UV regime and by several candidate theories of quantum gravity. Hence, our considerations and results are expected to have general validity in the quantum gravity framework.

PJ was in part supported by the Ministry of education grant MŠMT RVO 14000. GGL acknowledges the Spanish “Ministerio de Universidades” for the awarded Maria Zambrano fellowship and funding received from the European Union - NextGenerationEU. He is also grateful for participation to the LISA Cosmology Working group. GL and LM thank MUR for support. GL thanks INFN for suppor