Constraining torsion in maximally symmetric (sub)spaces

Sur, Sourav; Bhatia, Arshdeep Singh

doi:10.1088/0264-9381/31/2/025020

Cited by 20 publications

(29 citation statements)

References 86 publications

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“…In the other scheme, in which torsion directly affects maximal symmetry, following strictly the principle of general covariance, some more independent torsion components with only time-dependence, viz. T 001 , T 002 and T 003 , are allowed in the FRW context [159]. Hence, for the irreducible torsion modes, one finds that both the schemes are in agreement yielding Q µνσ = 0 and A µ = δ µ 0 λ(t) where λ(t) is a pseudoscalar function of time.…”

Section: Mst Theory In the Standard Cosmological Setupmentioning

confidence: 84%

Weakly dynamic dark energy via metric-scalar couplings with torsion

Sur¹,

Bhatia

2017

J. Cosmol. Astropart. Phys.

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Abstract. We study the dynamical aspects of dark energy in the context of a non-minimally coupled scalar field with curvature and torsion. Whereas the scalar field acts as the source of the trace mode of torsion, a suitable constraint on the torsion pseudo-trace provides a mass term for the scalar field in the effective action. In the equivalent scalar-tensor framework, we find explicit cosmological solutions representing dark energy in both Einstein and Jordan frames. We demand the dynamical evolution of the dark energy to be weak enough, so that the present-day values of the cosmological parameters could be estimated keeping them within the confidence limits set for the standard ΛCDM model from recent observations. For such estimates, we examine the variations of the effective matter density and the dark energy equation of state parameters over different redshift ranges. In spite of being weakly dynamic, the dark energy component differs significantly from the cosmological constant, both in characteristics and features, for e.g. it interacts with the cosmological (dust) fluid in the Einstein frame, and crosses the phantom barrier in the Jordan frame. We also obtain the upper bounds on the torsion mode parameters and the lower bound on the effective BransDicke parameter. The latter turns out to be fairly large, and in agreement with the local gravity constraints, which therefore come in support of our analysis.

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Section: Mst Theory In the Standard Cosmological Setupmentioning

confidence: 84%

Weakly dynamic dark energy via metric-scalar couplings with torsion

Sur¹,

Bhatia

2017

J. Cosmol. Astropart. Phys.

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“…T α νµ − T α ν µ − T α µ ν is the contorsion tensor, and the well-known commutation relation [107,222] ∇ µ , ∇ ν φ = T α µν ∂ α φ , (6.11) it is easy to show that Eq. (6.9) reduces to a µ = a µ − κ 2 T α µν ∂ α φ ∂ ν φ X , (6.12)…”

Section: Appendix: Mimetic Fluid Acceleration In Space-times With Tormentioning

confidence: 99%

Cosmological dark sector from a mimetic–metric–torsion perspective

Chothe

Dutta

Sur

2019

Int. J. Mod. Phys. D

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We generalize the basic theory of mimetic gravity by extending its purview to the general metriccompatible geometries that admit torsion, in addition to curvature. This essentially implies reinstating the mimetic principle of isolating the conformal degree of freedom of gravity in presence of torsion, by parametrizing both the physical metric and torsion in terms of the scalar 'mimetic' field and the metric and torsion of a fiducial space. We assert the requisite torsion parametrization from an inspection of the fiducial space Cartan transformation which, together with the conformal transformation of the fiducial metric, preserve the physical metric and torsion. In formulating the scalar-tensor equivalent Lagrangian, we consider an explicit contact coupling of the mimetic field with torsion, so that the former can manifest itself geometrically as the source of a torsion mode, and most importantly, give rise to a viable 'dark universe' picture from a mimicry of an evolving dust-like cosmological fluid with a non-zero pressure. A further consideration of higher derivatives of the mimetic field in the Lagrangian leads to physical bounds on the mimetic-torsion coupling strength, which we determine explicitly. * transformation of g µν , but also implicates that φ is left non-dynamical by the condition for the invertibility of g µν , viz. −κ 2 g µν ∂ µ φ∂ ν φ = 1 . This condition could be implemented in the theory as a constraint, using a Lagrange multiplier λ in an equivalent mimetic action. A further equivalence of the latter with the singular Brans-Dicke (BD) action (in which the BD parameter w = − 3 2 ) eventually shows that mimetic gravity is indeed a ratification of GR being raised to the status of a scalar-tensor equivalent MG theory [21][22][23][24]29].Detailed studies have revealed many attractive features of the basic mimetic model of Chemseddine and Mukhanov (henceforth, the CM model [21]) and its various extensions, from the perspectives of both cosmology and astrophysics . In particular, the CM Lagrangian extended by a potential V (φ) leads to the scenarios of a cosmologically evolving fluid -the so-called 'mimetic fluid' -which characterizes dust, albeit with a nonvanishing pressure 1 [22]. As such, no propagating scalar perturbation mode is there to suppress the growth of structures at smaller (sub-galactic) scales [26,27]. Nor it is possible to define the quantum fluctuations to the (non-dynamical) field φ, so that the latter can provide the seeds of the observed large scale structure of the universe [22,23]. A reasonable supposition has therefore been to extend the CM theory further by incorporating higher derivative (HD) term(s) for φ, e.g. (✷φ) 2 , which lead(s) to a non-vanishing sound speed c s of the mimetic matter perturbations, keeping the background solution unaffected qualitatively 2 [22,23,29]. However, the HD terms in general make the theory susceptible to Ostrogradsky ghost or(and) gradient instabilities [26,27,[64][65][66][67], possible wayouts of which point to more complicated extensions...

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“…Moreover, in order to preserve the FRW metric structure in a standard cosmological setup, one requires the tensor mode Q µνσ of torsion to vanish altogether, and the vector modes T µ and A µ to have only their temporal components existent. 30,59 Also since the torsion field is generally taken to be massless, 24,32 one expects the scalar field source φ, of its trace mode T µ to be massless as well. However, the pseudotrace mode of torsion, A µ , may effectively lead to a scalar field potential…”

Section: The General Mst Formalism In the Cosmological Setupmentioning

confidence: 99%

“…We may equally well look into the cosmologies emerging from the rather conventional extensions of General Relativity (GR), such as that formulated in the four-dimensional Riemann-Cartan (U 4 ) space-time with torsion -an antisymmetric tensor field that generalizes the LeviCivita connections in GR. [24][25][26][27][28][29][30] Torsion is often considered as a geometric entity that provides a classical background for quantized spinning matter, and is therefore an inherent part of a fundamental (quantum gravitational) theory, such as string theory. 28,31,32 A completely antisymmetric torsion can have its source in the closed string massless Kalb-Ramond mode, 33,34 with interesting implications in cosmology and astrophysics.…”

Section: Introductionmentioning

confidence: 99%

“…28,50,51 Now, in the standard cosmological framework, the torsion degrees of freedom get restricted by the FRW metric structure. 30 Also since φ acts as the source of the trace mode of torsion (via the corresponding equation of motion), we effectively have a scalar-tensor equivalent MST setup. The pseudo-trace mode of torsion can give rise to a mass term for φ, via suitable augmentation of the effective action with say, some higher order torsion terms.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical system analysis of dark energy models in scalar coupled Metric-Torsion theories

Bhatia

Sur

2017

Int. J. Mod. Phys. D

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We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting cosmic acceleration driven by the dark energy. The latter is so defined that it effectively has no direct interaction with the cosmological fluid, although in an equivalent scalar-tensor cosmological setup the scalar field interacts with the fluid (which we consider to be the pressureless dust). Determining the conditions for the existence of the stable critical points we check their physical viability in both Einstein and Jordan frames. We also verify that in either of these frames, the evolution of the universe at the corresponding stable points matches with that given by the respective exact solutions we have found in an earlier work (arXiv:1611.00654 [gr-qc]). We not only examine the regions of physical relevance in the phase space when the coupling parameter is varied, but also demonstrate the evolution profiles of the cosmological parameters of interest along fiducial trajectories in the effectively non-interacting scenarios, in both Einstein and Jordan frames.

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Constraining torsion in maximally symmetric (sub)spaces

Cited by 20 publications

References 86 publications

Weakly dynamic dark energy via metric-scalar couplings with torsion

Weakly dynamic dark energy via metric-scalar couplings with torsion

Cosmological dark sector from a mimetic–metric–torsion perspective

Dynamical system analysis of dark energy models in scalar coupled Metric-Torsion theories

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