Constraining the entropy corrected (m, n)-type pilgrim dark energy in fractal cosmology

Abstract This study explores the impact of introducing particle and future event horizon as infrared (IR) cutoff on ( m , n )-type entropy corrected versions of pilgrim dark energy. We investigate ( m , n )-type power-law entropy corrected pilgrim dark energy in a flat fractal platform by considering a non-interacting scenario with cold dark matter. Then, our focus shifts to ( m , n )-type logarithmic entropy corrected pilgrim dark energy. We derive the evolution of some relevant cosmological parameters and cosmological planes. Finally, we constrain the model parameters using $$H(z)+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:math> BAO combined observational data from the DA and BAO methods. For statistical analysis, we apply the $$\chi ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -minimization technique (equivalent to the maximum likelihood method) to estimate the best-fit value of the model parameters. We incorporate public Cosmo Hammer (EMCEE) Python package code to perform the MCMC method. Finally, we display the plot of cosmological parameters and cosmological plane and analyze the triangular contour plot by using the optimal values of the model parameters.