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Bouncing cosmologies in modified gravity with spacetime torsion

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Alam, Sonej, Sen, Somasri, Sengupta, Soumitra·2025·The European Physical Journal C
DOI 10.1140/epjc/s10052-025-15123-8

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Abstract

We explore the possibility of realizing a non-singular bounce in the early universe within the framework of modified gravity with spacetime torsion. In Einstein Cartan theory, torsion is embedded in the spacetime by adding an antisymmetric part in affine connection. We consider generalized version of the framework as $$f(\bar{R})$$ f ( R ¯ ) , $$\bar{R}$$ R ¯ being the scalar of the modified curvature tensor. $$f(\bar{R})$$ f ( R ¯ ) gravity is recast in Einstein frame as non-minimally coupled scalar tensor theory where the scalar field gets coupled with a rank 2 antisymmetric torsion field through derivative couplings. We investigate whether the introduction of three additional torsion-dependent terms in Einstein frame help to realize a bounce. We first explore this cosmological system in the background of a homogeneous and isotropic FRW spacetime but inclusion of the torsion terms are insufficient to produce a bounce in this symmetric setting. Motivated by this limitation, we relax the symmetry and generalize the background to include inhomogeneity and anisotropy. In this setup, the dynamics is modified in such a way that a bouncing solution is possible without invoking phantom fields or energy condition violations. We have found the exact solutions of all the fields and reconstructed the modified gravity form. We have addressed the behaviour of the fields under perturbation and investigated the stability of the solutions. Constraints on the model parameters have also been derived based on cosmological observations.

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  • Torsion-induced bounces have been realized in Einstein-Cartan and related torsionful models, including spinor-based constructions in which a single Dirac field drives both ekpyrotic contraction and a torsion-supported bounce.

    “Torsion-induced bounces have also been realized in Einstein-Cartan and related torsionful models, including spinor-based constructions in which a single Dirac field drives both ekpyrotic contraction and a torsionsupported bounce [11-13, 22, 28, 29].”

    From Dynamical systems analysis of an Einstein–Cartan ekpyrotic nonsingular bounce cosmology (2026) · cites this paper as [29]

    The Abstract and Section 4.2 describe a nonsingular bounce in a generalized Einstein–Cartan model with torsion, supporting the general claim that torsionful models can realize bounces. They describe scalar and torsion fields, however, not a single Dirac field driving ekpyrotic contraction and a bounce; searches for the spinor and ekpyrotic terms did not substantiate that specific construction in this paper. (LLM, conf=0.87)

    Experimental — accuracy not yet measured

  • At the background level the bounce is a nonsingular ρ2-type bounce, similar in spirit to the effective Friedmann equation in loop quantum cosmology and to other torsion-based bouncing models.

    “At the background level this is a nonsingular ρ 2 -type bounce, similar in spirit to the effective Friedmann equation in loop quantum cosmology [35] and to other torsion-based bouncing models [22,29].”

    From Dynamical systems analysis of an Einstein–Cartan ekpyrotic nonsingular bounce cosmology (2026) · cites this paper as [29]

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Cited by

Sorted by citations

Authors
Alam, S., Sen, S., & Sengupta, S.
Affiliations
  • Jamia Millia Islamia (IN)
  • Indian Association for the Cultivation of Science (IN)
Corresponding author
Sen, Somasri
ORCID
Venue
The European Physical Journal C
Publisher
Springer Science and Business Media LLC
Published
2025-12-13
Volume
85
Issue
12
ISSN
  • 1434-6044 (ISSN-L)
  • 1434-6052
DOI
10.1140/epjc/s10052-025-15123-8
OpenAlex
W4417298163
Cited by
0
References
2
FWCI
0.00
Type
journal article
Language
en
Open access
Licence
Locations
  • The European Physical Journal C (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Funders
Council for Scientific and Industrial Research, INDIA (CSIR-JRF scheme (file no. 09/0466(12904)/2021))
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
Keywords
bounce cosmology, non-singular bounce, modified gravity, spacetime torsion, Einstein-Cartan theory, f(T) gravity, f(R) gravity, torsion field, FRW cosmology, exact solutions, perturbation analysis, solution stability, energy conditions, cosmological constraints

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