BAO miscalibration cannot rescue late-time solutions to the Hubble tension

Baryon acoustic oscillation (BAO) measurements play a key role in ruling out postrecombination solutions to the Hubble tension. However, because the data compression leading to these measurements assumes a fiducial <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Λ</a:mi> <a:mi>CDM</a:mi> </a:math> cosmology, their reliability in testing late-time modifications to <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi mathvariant="normal">Λ</d:mi> <d:mi>CDM</d:mi> </d:math> has at times been called into question. We play devil’s advocate and posit that fiducial cosmology assumptions do indeed affect BAO measurements in such a way that low-redshift acoustic angular scales (proportional to the Hubble constant <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>H</g:mi> <g:mn>0</g:mn> </g:msub> </g:math> ) are biased low and test whether such a rescaling can rescue postrecombination solutions. The answer is no. First, strong constraints on the shape of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>z</i:mi> <i:mo>≲</i:mo> <i:mn>2</i:mn> </i:math> expansion history from unanchored Type Ia Supernovae (SNeIa) prevent large deviations from <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi mathvariant="normal">Λ</k:mi> <k:mi>CDM</k:mi> </k:math> . In addition, unless <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi mathvariant="normal">Ω</n:mi> <n:mi>m</n:mi> </n:msub> </n:math> is significantly lower than 0.3, the rescaled BAO measurements would be in strong tension with geometrical information from the cosmic microwave background. We demonstrate this explicitly on several dark energy (DE) models ( <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>w</q:mi> <q:mi>CDM</q:mi> </q:math> , CPL DE, phenomenologically emergent DE, holographic DE, <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi mathvariant="normal">Λ</s:mi> <s:mi>s</s:mi> </s:msub> <s:mi>CDM</s:mi> </s:math> , and the negative cosmological constant model), finding that none can address the Hubble tension once unanchored SNeIa are included. We argue that the <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:msub> <v:mi mathvariant="normal">Λ</v:mi> <v:mi>s</v:mi> </v:msub> <v:mi>CDM</v:mi> </v:math> sign-switching cosmological constant model possesses interesting features which make it the least unpromising one among those tested. Our results demonstrate that possible fiducial cosmology-induced BAO biases cannot be invoked as loopholes to the Hubble tension “no-go theorem”, and highlight the extremely important but so far underappreciated role of unanchored SNeIa in ruling out postrecombination solutions.