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BBN to Late-Time Acceleration in $f(T,\mathcal{L}_m)$ Gravity

Sai Swagat Mishra, Suchita Patel, P. K. Sahoo

Abstract

We present, to our knowledge, the first systematic study of early-late cosmic evolution and acceleration in the framework of $f(T,\mathcal{L}_m)$ gravity, an extension of teleparallel theories coupling torsion with the matter Lagrangian. By incorporating the Big-Bang Nucleosynthesis (BBN) bound on the freeze-out temperature, we obtain a tight constraint on the inverse-torsion parameter, ensuring consistency with early-time physics. Employing Markov Chain Monte Carlo analyses with progressively richer observational datasets, CC, Union3, and SN22 supernovae, we constrain a well-motivated model and reconstruct key cosmological functions. The reconstructed Hubble and distance modulus functions show excellent agreement with the observations, confirming the observational viability of the model. The model successfully reproduces the observed late-time expansion history, yielding a transition from deceleration to acceleration through the deceleration parameter. The effective equation of state is found to remain negative throughout, with present values $w_0 > -1$, indicating a quintessence-like behavior rather than a cosmological constant or phantom regime. These results highlight the ability of $f(T,\mathcal{L}_m)$ gravity to mimic the concordance scenario while allowing controlled deviations in the expansion history.

BBN to Late-Time Acceleration in $f(T,\mathcal{L}_m)$ Gravity

Abstract

We present, to our knowledge, the first systematic study of early-late cosmic evolution and acceleration in the framework of gravity, an extension of teleparallel theories coupling torsion with the matter Lagrangian. By incorporating the Big-Bang Nucleosynthesis (BBN) bound on the freeze-out temperature, we obtain a tight constraint on the inverse-torsion parameter, ensuring consistency with early-time physics. Employing Markov Chain Monte Carlo analyses with progressively richer observational datasets, CC, Union3, and SN22 supernovae, we constrain a well-motivated model and reconstruct key cosmological functions. The reconstructed Hubble and distance modulus functions show excellent agreement with the observations, confirming the observational viability of the model. The model successfully reproduces the observed late-time expansion history, yielding a transition from deceleration to acceleration through the deceleration parameter. The effective equation of state is found to remain negative throughout, with present values , indicating a quintessence-like behavior rather than a cosmological constant or phantom regime. These results highlight the ability of gravity to mimic the concordance scenario while allowing controlled deviations in the expansion history.
Paper Structure (10 sections, 56 equations, 5 figures, 3 tables)

This paper contains 10 sections, 56 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background Equations of $f(T,\mathcal{L}_m)$ gravity
  3. BBN constraints on $f(T,\mathcal{L}_m)$ gravity
  4. The Model
  5. Observational Datasets
  6. Union3
  7. Cosmic Chronometers
  8. Pantheon+SH0ES (SN22)
  9. Results
  10. Concluding Remarks

Figures (5)

  • Figure 1: BBN bound on $\alpha$. The curve shows $\Delta\mathcal{T}_f/\mathcal{T}_f$, with dashed lines marking the limit $|\Delta\mathcal{T}_f/\mathcal{T}_f| < 4.7\times10^{-4}$. The shaded region indicates the allowed values of $\alpha$.
  • Figure 2: The 2D contours upto $2\sigma$ for the parameter space $\{H_0,\alpha\}$.
  • Figure 3: The left panel presents Hubble parameter evolution against the 34 CC data, and the right panel presents the 1701 SN22 data.
  • Figure 4: Distance modulus profile against redshift and Union3 datapoints.
  • Figure 5: Evolution of the Universe through deceleration parameter (left panel) and EoS parameter (right panel.)