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Model-independent reconstruction of $f(T)$ gravity from Gaussian Processes

Yi-Fu Cai, Martiros Khurshudyan, Emmanuel N. Saridakis

TL;DR

The paper tackles the problem of constraining the functional form of $f(T)$ gravity in a model-independent way using observational data. It employs Gaussian Processes to reconstruct the expansion history from $H(z)$ data, including cosmic chronometers and radial BAO, while incorporating the local value $H_0$ to address the $H_0$ tension. From the reconstructed $H(z)$ and $H'(z)$, it derives a model-free $f(T)$, finding a mean quadratic form $f(T) \approx -2\Lambda+\xi T^2$ with $\Lambda$ fixed by $H_0$ and $\Omega_{m0}$, and constrains $\xi$; it also tests three one-parameter $f(T)$ models and yields tighter bounds than standard analyses. The results demonstrate that model-independent reconstructions with Gaussian Processes can meaningfully probe modified gravity and may be extendable to other theories.

Abstract

We apply Gaussian processes and Hubble function data in $f(T)$ cosmology, to reconstruct for the first time the $f(T)$ form in a model-independent way. In particular, using $H(z)$ datasets coming from cosmic chronometers as well as from the radial BAO method, alongside the latest released local value $H_{0} = 73.52 \pm 1.62$ km/s/Mpc, we reconstruct $H(z)$ and its derivatives, resulting eventually in a reconstructed region for $f(T)$, without any assumption. Although the cosmological constant lies in the central part of the reconstructed region, the obtained mean curve follows a quadratic function. Inspired by this we propose a new $f(T)$ parametrization, i.e. $f(T) = -2Λ+ξT^2$, with $ξ$ the sole free parameter that quantifies the deviation from $Λ$CDM cosmology. Additionally, we confront three viable one-parameter $f(T)$ models of the literature, which respectively are the power-law, the square-root exponential, and the exponential one, with the reconstructed $f(T)$ region, and then we extract significantly improved constraints for their model parameters, comparing to the constraints that arise from usual observational analysis. Finally, we argue that since we are using the direct Hubble measurements and the local value for $H_0$ in our analysis, with the above reconstruction of $f(T)$, the $H_0$ tension can be efficiently alleviated.

Model-independent reconstruction of $f(T)$ gravity from Gaussian Processes

TL;DR

The paper tackles the problem of constraining the functional form of gravity in a model-independent way using observational data. It employs Gaussian Processes to reconstruct the expansion history from data, including cosmic chronometers and radial BAO, while incorporating the local value to address the tension. From the reconstructed and , it derives a model-free , finding a mean quadratic form with fixed by and , and constrains ; it also tests three one-parameter models and yields tighter bounds than standard analyses. The results demonstrate that model-independent reconstructions with Gaussian Processes can meaningfully probe modified gravity and may be extendable to other theories.

Abstract

We apply Gaussian processes and Hubble function data in cosmology, to reconstruct for the first time the form in a model-independent way. In particular, using datasets coming from cosmic chronometers as well as from the radial BAO method, alongside the latest released local value km/s/Mpc, we reconstruct and its derivatives, resulting eventually in a reconstructed region for , without any assumption. Although the cosmological constant lies in the central part of the reconstructed region, the obtained mean curve follows a quadratic function. Inspired by this we propose a new parametrization, i.e. , with the sole free parameter that quantifies the deviation from CDM cosmology. Additionally, we confront three viable one-parameter models of the literature, which respectively are the power-law, the square-root exponential, and the exponential one, with the reconstructed region, and then we extract significantly improved constraints for their model parameters, comparing to the constraints that arise from usual observational analysis. Finally, we argue that since we are using the direct Hubble measurements and the local value for in our analysis, with the above reconstruction of , the tension can be efficiently alleviated.

Paper Structure

This paper contains 7 sections, 21 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. $f(T)$ gravity and cosmology
  3. Gaussian Process using $H(z)$ data
  4. Gaussian Process
  5. $H(z)$ data
  6. Reconstructing $f(T)$ form from GP
  7. Conclusions

Figures (4)

  • Figure 1: GP reconstruction of $H(z)$ and $H^{\prime}(z)$ (primes denote derivative with respect to the redshift $z$), using the Hubble data arising from the differential evolution of cosmic chronometers ($30$-point sample) and from the radial BAO method ($10$-point sample) Zhang:2016tto, presented in Table \ref{['tab:Table0']}, alongside the latest released local value $H_{0} = 73.52 \pm 1.62$ km/s/Mpc Riess:2016jrr, using the squared exponential kernel (\ref{['eq:kernel1']}). In each graph the black curve marks the mean reconstructed curve, while the light blue region marks the 1$\sigma$ errors coming from the data errors, as well as from the GP errors. We use units of km/s/Mpc.
  • Figure 2: GP reconstruction of the $f(T)$ form in a model-independent way, using the reconstructed from Hubble data forms of $H(z)$ and $H^{\prime}(z)$ of Figure \ref{['fig:Fig0_2']} and the squared exponential kernel (\ref{['eq:kernel1']}), imposing $\Omega_{m0}=0.302$. The black curve marks the mean reconstructed curve, while the light blue region marks the 1$\sigma$ errors coming from the GP errors. Moreover, the dotted line marks the cosmological constant scenario $f(T)=-2\Lambda=-6H_0^2(1-\Omega_{m0})$. Both $T$ and $f(T)$ are measured in units of $H^2$, i.e. $(\text{km/s/Mpc})^2$, and we present them divided by $10^5$.
  • Figure 3: GP reconstruction of the $f(T)$ form in a model-independent way, using the reconstructed from Hubble data forms of $H(z)$ and $H^{\prime}(z)$ of Figure \ref{['fig:Fig0_2']} and the squared exponential kernel (\ref{['eq:kernel1']}), imposing $\Omega_{m0}=0.302$. Additionally, we have added the predictions of three viable $f(T)$ models of the literature, for their edge parameter choices in order to still lie inside the reconstructed region, namely $b=-0.0005$ and $b=0.0004$ (black-solid curves) for the power-law model (\ref{['powermod']}), $b=1/p=0$ and $b=1/p=0.15$ (red-dashed curves) for the square-root exponential model (\ref{['Lindermod']}), and $b=1/p=0$ and $b=1/p=0.13$ (green-dotted curves) for the exponential model (\ref{['f3cdmmodel']}). Both $T$ and $f(T)$ are measured in units of $H^2$, i.e. $(\text{km/s/Mpc})^2$, and we present them divided by $10^5$.
  • Figure 4: The reconstructed forms of the dark energy density parameter $\Omega_{DE}$ from (\ref{['rhoDDE']}) (upper graph), as well as of the dark energy EoS parameter $w_{DE}$ from (\ref{['wefftotf']}) (lower graph), as they arise using the obtained reconstructions of $H(z)$, $H'(z)$ and $f(T)$. In each graph the black curve marks the mean reconstructed curve, while the light blue region marks the 1$\sigma$ errors coming from the data errors, as well as from the GP errors.