Comparing Equivalent Gravities: common features and differences

Capozziello, Salvatore; Falco, Vittorio De; Ferrara, Carmen

doi:10.48550/arxiv.2208.03011

Cited by 4 publications

(7 citation statements)

References 81 publications

(178 reference statements)

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“…Finally, as we said, if there is a one-to-one correspondence between f (R) and a map between real and effective EoS would be a proof which could be tested, in principle, by observations. Clearly, the approach can work also for other theories of gravity like teleparallel or symmetric teleparallel ones [17,62]. This will the topic of forthcoming studies.…”

Section: The Quadratic Effective Eosmentioning

confidence: 93%

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The effective equation of state in Palatini $$f({{\mathcal {R}}})$$ cosmology

et al. 2023

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We investigate how the cosmological equation of state can be used for scrutinizing extended theories of gravity, in particular, the Palatini $$f({{\mathcal {R}}})$$ f ( R ) gravity. Specifically, the approach consists, at first, in investigating the effective equation of state produced by a given model. Then, the inverse problem can also be considered in view of determining which models are compatible with a given effective equation of state. We consider and solve some cases and show that, for example, power-law models are (the only models) capable of transforming barotropic Equations of State into effective barotropic ones. Moreover, the form of equation of state is preserved (only) for $$f({{\mathcal {R}}})={{\mathcal {R}}}$$ f ( R ) = R , as expected. In this perspective, modified Equations of State are a feature capable of distinguishing extended gravity with respect to general relativity. We investigate also quadratic and non-homogeneous effective Equations of State showing, in particular, that they contain the Starobinsky model and other ones.

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Section: The Quadratic Effective Eosmentioning

confidence: 93%

“…In this debate, one can deal with approaches where the same basic foundations of GR are questioned [17], and then we deal with modified gravity, and models where GR is recovered as a particular case on in a particular limit. In this case, we deal with extended gravity [18].…”

Section: Introductionmentioning

confidence: 99%

The effective equation of state in Palatini $$f({{\mathcal {R}}})$$ cosmology

et al. 2023

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“…Generally, the affine connection Γ c ab is treated as an independent variable, which extends the geometric description of gravitation. The theory with a general affine connection is thus dubbed metric-affine gravity (MAG), which has been studied extensively [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. By coupling MAG to scalar field(s), one gets the so-called "metric-affine scalar-tensor theory" [56][57][58][59][60], which can be seen as an analogue of the scalar-tensor theory in Riemannian geometry.…”

Section: Introductionmentioning

confidence: 99%

Spatially covariant gravity with nonmetricity

Yu,

Chen,

Gao

2024

Eur. Phys. J. C

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Scalar fields play an important role in constructing modified gravity theories. In the case of a single scalar field with timelike gradient, the corresponding Lagrangian in the unitary gauge takes the form of spatially covariant gravity (SCG), which is proved useful in analyzing and extending the generally covariant theories. In this work, we apply the SCG method to the scalar-nonmetricity theory, of which the Lagrangian is built of the nonmetricity tensor and a scalar field. We derive the 3+1 decomposition of the geometric quantities and especially covariant derivatives of the scalar field up to the third order in the presence of a nonvanishing nonmetricity tensor. By fixing the unitary gauge, the resulting Lagrangian takes the form of a SCG with nonmetricity, in which all the ingredients are spatial tensors. We then exhaust the scalar monomials of SCG with nonmetricity up to $$d=3$$ d = 3 with d the total number of derivatives. Since the disformation tensor plays as an auxiliary variable, we take the Lagrangian with $$d=2$$ d = 2 as an example to show that after solving the disformation tensor, we can get an effective SCG theory for the metric variables but with modified coefficients. Our results provides a novel approach to extending the scalar-nonmetricity theory.

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“…In the recent past, a tremendous amount of works were carried out in the f (Q) theories [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Universe in $f(Q,T)$ gravity, a novel study

Loo¹,

Koussour²,

De³

2023

Preprint

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f (Q, T) theory of gravity is very recently proposed to incorporate within the action Lagrangian, the trace T of the energy-momentum tensor along with the non-metricity scalar Q. The cosmological application of this theory in a spatially flat isotropic and homogeneous Universe is well-studied. However, our Universe is not isotropic since the Planck era and therefore to study a complete evolution of the Universe we must investigate the f (Q, T) theory in a model with a small anisotropy. This motivated us to presume a locally rotationally symmetric (LRS) Bianchi-I spacetime and derive the motion equations. We analyse the model candidate f (Q, T) = αQ n+1 + βT, and to constrain the parameter n, we employ the statistical Markov chain Monte Carlo (MCMC) method with the Bayesian approach using two independent observational datasets, namely, the Hubble datasets, and Type Ia supernovae (SNe Ia) datasets.

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Comparing Equivalent Gravities: common features and differences

Cited by 4 publications

References 81 publications

The effective equation of state in Palatini $$f({{\mathcal {R}}})$$ cosmology

The effective equation of state in Palatini $$f({{\mathcal {R}}})$$ cosmology

Spatially covariant gravity with nonmetricity

Anisotropic Universe in $f(Q,T)$ gravity, a novel study

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