Constraining quintessence models with integrated Sachs-Wolfe thermal Sunyaev-Zel’dovich cross-correlations: A comparative analysis of thawing, tracker, and scaling-freezing dynamics

We present constraints on quintessence dark energy models using the observational detection of the integrated Sachs-Wolfe (ISW)–thermal Sunyaev-Zeldovich (tSZ) cross-correlation dataset. Our analysis compares three classes of quintessence dynamics: thawing, tracker, and scaling-freezing with the standard <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi mathvariant="normal">Λ</a:mi> </a:mrow> </a:math> cold dark matter ( <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> ) cosmology. Through a comprehensive likelihood analysis, we derive best-fit values and 68% confidence intervals for key cosmological parameters, finding <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:msub> <g:mrow> <g:mi mathvariant="normal">Ω</g:mi> </g:mrow> <g:mrow> <g:mi mathvariant="normal">m</g:mi> </g:mrow> </g:msub> <g:mo>=</g:mo> <g:mn>0.32</g:mn> <g:msubsup> <g:mrow> <g:mn>2</g:mn> </g:mrow> <g:mrow> <g:mo>−</g:mo> <g:mn>0.030</g:mn> </g:mrow> <g:mrow> <g:mo>+</g:mo> <g:mn>0.027</g:mn> </g:mrow> </g:msubsup> </g:mrow> </g:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>σ</k:mi> <k:mn>8</k:mn> </k:msub> <k:mo>=</k:mo> <k:mn>0.73</k:mn> <k:msubsup> <k:mn>5</k:mn> <k:mrow> <k:mo>−</k:mo> <k:mn>0.035</k:mn> </k:mrow> <k:mrow> <k:mo>+</k:mo> <k:mn>0.045</k:mn> </k:mrow> </k:msubsup> </k:math> for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi mathvariant="normal">Λ</m:mi> <m:mi>CDM</m:mi> </m:math> , with deviations in alternative models consistent within <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mn>1</p:mn> <p:mi>σ</p:mi> </p:math> . For the thawing model, we consider an exponential potential with slope <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>λ</r:mi> <r:mo>=</r:mo> <r:mn>0.73</r:mn> <r:msubsup> <r:mn>6</r:mn> <r:mrow> <r:mo>−</r:mo> <r:mn>0.227</r:mn> </r:mrow> <r:mrow> <r:mo>+</r:mo> <r:mn>0.270</r:mn> </r:mrow> </r:msubsup> </r:math> , while for the tracker and scaling-freezing models, we use inverse axionlike and double exponential potentials, respectively. Observationally, the tracker model yields <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mrow> <t:mi>n</t:mi> <t:mo>=</t:mo> <t:mn>5.65</t:mn> <t:msubsup> <t:mrow> <t:mn>1</t:mn> </t:mrow> <t:mrow> <t:mo>−</t:mo> <t:mn>1.604</t:mn> </t:mrow> <t:mrow> <t:mo>+</t:mo> <t:mn>1.625</t:mn> </t:mrow> </t:msubsup> </t:mrow> </t:math> and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi>f</v:mi> <v:mo>=</v:mo> <v:mn>0.25</v:mn> <v:msubsup> <v:mn>8</v:mn> <v:mrow> <v:mo>−</v:mo> <v:mn>0.096</v:mn> </v:mrow> <v:mrow> <v:mo>+</v:mo> <v:mn>0.149</v:mn> </v:mrow> </v:msubsup> </v:math> , and the scaling-freezing model gives <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi>λ</x:mi> <x:mn>1</x:mn> </x:msub> <x:mo>=</x:mo> <x:mn>0.40</x:mn> <x:msubsup> <x:mn>5</x:mn> <x:mrow> <x:mo>−</x:mo> <x:mn>0.322</x:mn> </x:mrow> <x:mrow> <x:mo>+</x:mo> <x:mn>0.293</x:mn> </x:mrow> </x:msubsup> </x:math> and <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msub> <z:mi>λ</z:mi> <z:mn>2</z:mn> </z:msub> <z:mo>=</z:mo> <z:mn>23.22</z:mn> <z:msubsup> <z:mn>6</z:mn> <z:mrow> <z:mo>−</z:mo> <z:mn>7.258</z:mn> </z:mrow> <z:mrow> <z:mo>+</z:mo> <z:mn>7.975</z:mn> </z:mrow> </z:msubsup> </z:math> . The dimensionless tSZ amplitude ( <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msup> <bb:mover accent="true"> <bb:mi>W</bb:mi> <bb:mo stretchy="false">˜</bb:mo> </bb:mover> <bb:mrow> <bb:mi>SZ</bb:mi> </bb:mrow> </bb:msup> </bb:math> ) and cosmic infrared background (CIB) parameters are tightly constrained across all models, providing additional insights into astrophysical foregrounds. Our results demonstrate the effectiveness of ISW-tSZ cross-correlations as a probe of dark energy dynamics, with the thawing quintessence model yielding the lowest <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msubsup> <fb:mi>χ</fb:mi> <fb:mi>min</fb:mi> <fb:mn>2</fb:mn> </fb:msubsup> </fb:math> among the tested scenarios, and highlight the need for future high-precision measurements to distinguish between quintessence models and <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mi mathvariant="normal">Λ</hb:mi> <hb:mi>CDM</hb:mi> </hb:math> .