Testing influence of Hubble tension on the early Universe

Abstract The Hubble tension has profoundly shaped modern cosmological research. This study explores its impact on the early-universe physics in the modified emergent dark energy (MEDE) and $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model using Planck PR4, BK18, DESI2024/2025, and supernova samples (Pan+, Union3). First, Hubble constant negligibly affects the tensor-to-scalar ratio ( $$r &lt; 0.031$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0.031</mml:mn> </mml:mrow> </mml:math> at 95%C.L.). Inclusion of DESI2025 achieves a 46% uncertainty reduction in key parameters. For CMB power spectra, DESI systematically amplifies TT/BB spectral discrepancies. Second, electron ionization fractions $$X_e(z)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>e</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> display pronounced deviations from the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model at $$z=9.17$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:mn>9.17</mml:mn> </mml:mrow> </mml:math> , suggesting a connection between Hubble tension and reionization history. This finding resonates with JWST measurements on high-redshift galaxy evolution. Future observations, such as 21-cm surveys, are highly anticipated to resolve these tensions by probing early-universe evolution and dark energy interactions.