Synergistic constraints on extensions of teleparallel gravity from primordial nucleosynthesis and cosmic chronometers

Abstract This study presents a dual-constraint framework to test <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>f</mml:mi> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> gravity models, by combining observations from Big Bang Nucleosynthesis (BBN) and cosmic chronometers (CC). We investigate a new modified power-law model with dimensionless parameters, as well as an exponential and two logarithmic models. By incorporating recent data on the primordial helium-4 abundance—used to constrain the fractional variation in freeze-out temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="|" open="|"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> —alongside measurements of the Hubble parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>H</mml:mi> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi mathvariant="script">z</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> , we identify parameter sets consistent with both early and late cosmic evolution. Using chi-square minimization, our approach improves upon previous BBN-only studies by providing tighter constraints that connect early-universe physics with the universe’s later expansion. These results support <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>f</mml:mi> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> gravity as a promising alternative to General Relativity and establish a versatile methodology for future cosmological tests.