We investigated the observational viability of an f(T) gravity model, defined by <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$f(T) = T e^{\beta T_0/T}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>T</mi> <msup> <mi>e</mi> <mrow> <mi>β</mi> <msub> <mi>T</mi> <mn>0</mn> </msub> <mo stretchy="false">/</mo> <mi>T</mi> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, as an alternative to the standard <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\Lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation>CDM cosmology. A key theoretical advantage of this model is that its free parameter <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> is fully determined by the present-day cosmological density parameters via the Lambert <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mathcal {W}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">W</mi> </math></EquationSource> </InlineEquation> function, thereby introducing no additional degrees of freedom relative to <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\Lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation>CDM. The model was constrained using baryon acoustic oscillation measurements from DESI DR2, combined with four Type Ia supernova compilations: PantheonPlus (PP), PantheonPlus+SH0ES (PPS), Union 3.0, and DESY5. Our analysis demonstrates that the f(T) model consistently produces elevated values of the Hubble constant <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$H_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> in comparison to <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\Lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation>CDM across all dataset combinations. Specifically, the DESI-DR2+PPS combination yields <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$H_0 = 73.39 \pm 0.50$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>H</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>73.39</mn> <mo>±</mo> <mn>0.50</mn> </mrow> </math></EquationSource> </InlineEquation> km/s/Mpc within the f(T) framework, diminishing the <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$H_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> tension, as inferred from late-time observations, from approximately <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$(2.77\sigma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>2.77</mn> <mi>σ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> in <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$\Lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation>CDM to about <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$(0.30\sigma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>0.30</mn> <mi>σ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Crucially, this alleviation is robust across all dataset combinations, including SH0ES-independent datasets: PP (<InlineEquation ID="IEq15"> <EquationSource Format="TEX">$0.79\sigma $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.79</mn> <mi>σ</mi> </mrow> </math></EquationSource> </InlineEquation>), Union3 (<InlineEquation ID="IEq16"> <EquationSource Format="TEX">$0.90\sigma $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.90</mn> <mi>σ</mi> </mrow> </math></EquationSource> </InlineEquation>), and DESY5 (<InlineEquation ID="IEq17"> <EquationSource Format="TEX">$0.69\sigma $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.69</mn> <mi>σ</mi> </mrow> </math></EquationSource> </InlineEquation>), confirming that the result is not driven by SH0ES calibration bias. The <InlineEquation ID="IEq18"> <EquationSource Format="TEX">$\chi ^2_{min}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>χ</mi> <mrow> <mi mathvariant="italic">min</mi> </mrow> <mn>2</mn> </msubsup> </math></EquationSource> </InlineEquation> values for both models were similar across all the datasets. These results demonstrate that the exponential infrared f(T) model fits the current observational data as well as <InlineEquation ID="IEq19"> <EquationSource Format="TEX">$\Lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation>CDM, while significantly alleviating the <InlineEquation ID="IEq20"> <EquationSource Format="TEX">$H_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> tension within the late-time observational framework.

Alleviating the Hubble Tension in Exponential f(T) Gravity with the Lambert $\mathcal {W}$ Function

期刊论文
发表日期：

2026年6月1日

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Saurabh Verma,
Archana Dixit,
Anirudh Pradhan,
M. S. Barak

摘要

We investigated the observational viability of an f(T) gravity model, defined by $f(T) = T e^{\beta T_0/T}$ $f (T) = T e^{β T_{0} / T}$ , as an alternative to the standard $\Lambda $ $Λ$ CDM cosmology. A key theoretical advantage of this model is that its free parameter $\beta $ $β$ is fully determined by the present-day cosmological density parameters via the Lambert $\mathcal {W}$ $W$ function, thereby introducing no additional degrees of freedom relative to $\Lambda $ $Λ$ CDM. The model was constrained using baryon acoustic oscillation measurements from DESI DR2, combined with four Type Ia supernova compilations: PantheonPlus (PP), PantheonPlus+SH0ES (PPS), Union 3.0, and DESY5. Our analysis demonstrates that the f(T) model consistently produces elevated values of the Hubble constant $H_0$ $H_{0}$ in comparison to $\Lambda $ $Λ$ CDM across all dataset combinations. Specifically, the DESI-DR2+PPS combination yields $H_0 = 73.39 \pm 0.50$ $H_{0} = 73.39 \pm 0.50$ km/s/Mpc within the f(T) framework, diminishing the $H_0$ $H_{0}$ tension, as inferred from late-time observations, from approximately $(2.77\sigma )$ $(2.77 σ)$ in $\Lambda $ $Λ$ CDM to about $(0.30\sigma )$ $(0.30 σ)$ . Crucially, this alleviation is robust across all dataset combinations, including SH0ES-independent datasets: PP ( $0.79\sigma $ $0.79 σ$ ), Union3 ( $0.90\sigma $ $0.90 σ$ ), and DESY5 ( $0.69\sigma $ $0.69 σ$ ), confirming that the result is not driven by SH0ES calibration bias. The $\chi ^2_{min}$ $χ_{\min}^{2}$ values for both models were similar across all the datasets. These results demonstrate that the exponential infrared f(T) model fits the current observational data as well as $\Lambda $ $Λ$ CDM, while significantly alleviating the $H_0$ $H_{0}$ tension within the late-time observational framework.

Alleviating the Hubble Tension in Exponential f(T) Gravity with the Lambert \(\mathcal {W}\) Function

摘要