Modified gravity/dynamical dark energy vs $$\Lambda $$CDM: is the game over?

Abstract Over the last decades, tests on the standard model of cosmology, the so-called $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model, have been widely analysed and compared with many different models for describing dark energy. Modified gravities have played an important role in this sense as an alternative to $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model. Previous observational data has been always favouring $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model in comparison to any other model. While statistically speaking, alternative models have shown their power, fitting in some cases the observational data slightly better than $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM, the significance and goodness of the fits were not significantly relevant to exclude the standard model of cosmology. In this paper, a generalisation of exponential F ( R ) gravity is considered and compared with $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model by using the latest observational data. Also some well-known model independent parameterisations for the equation of state (EoS) of dark energy are explored. These scenarios are confronted with the renewed observational data involving the Pantheon plus datasets of supernovae type Ia, the Hubble parameter estimations, data from the cosmic microwave background and baryon acoustic oscillations, where the latter includes the data provided by Dark Energy Spectroscopic Instrument Collaboration. Results of this analysis suggest that standard exponential F ( R ) models provide much better fits than $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model, which is excluded at 4 $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> </mml:math> . Moreover, the parameterisations of the equation of state suggest a non-constant EoS parameter for dark energy, where $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model is also excluded at 4 $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> </mml:math> .

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