We consider gravity mediated by non-metricity, with vanishing curvature and torsion. The gravitational action, including an arbitrary function of the non-metric scalar, is investigated in view of ...characterizing the dark energy effects. In particular, we present a method to reconstruct the f(Q) action without resorting to a priori assumptions on the cosmological model. To this purpose, we adopt a method based on rational Padé approximations, which provides a stable behaviour of the cosmographic series at high redshifts, alleviating the convergence issues proper of the standard approach. We thus describe how to reconstruct f(Q) through a numerical inversion procedure based on the current observational bounds on cosmographic parameters. Our analysis suggests that the best approximation for describing the accelerated expansion of the universe is represented by a scenario with f(Q)=α+βQn. Finally, possible deviations from the standard ΛCDM model are discussed.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
We consider the cosmology derived from
f
(
T
,
B
) gravity where
T
is the torsion scalar and
B
=
2
e
∂
μ
(
e
T
μ
)
a boundary term. In particular we discuss how it is possible to recover, under the ...same standard, the teleparallel
f
(
T
) gravity, the curvature
f
(
R
) gravity, and the teleparallel–curvature
f
(
R
,
T
) gravity, which are particular cases of
f
(
T
,
B
). We adopt the Noether Symmetry Approach to study the related dynamical systems and to find cosmological solutions.
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f(G) Noether cosmology Bajardi, Francesco; Capozziello, Salvatore
The European physical journal. C, Particles and fields,
08/2020, Volume:
80, Issue:
8
Journal Article
Peer reviewed
Open access
We develop the
n
-dimensional cosmology for
f
(
G
)
gravity, where
G
is the
Gauss–Bonnet
topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select
f
(
G
)
≃
G
k
...power-law models where
k
is a real number. In particular, the case
k
=
1
/
2
for
n
=
4
results equivalent to General Relativity showing that we do not need to impose the action
R
+
f
(
G
)
to reproduce the Einstein theory. As a further result, de Sitter solutions are recovered in the case where
f
(
G
)
is non-minimally coupled to a scalar field. This means that issues like inflation and dark energy can be addressed in this framework. Finally, we develop the Hamiltonian formalism for the related minisuperspace and discuss the quantum cosmology for this model.
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We derive the gravitational waves for
f
T
,
B
gravity which is an extension of teleparallel gravity and demonstrate that it is equivalent to
f
(
R
) gravity by linearized the field equations in the ...weak field limit approximation.
f
(
T
,
B
) gravity shows three polarizations: the two standard of general relativity, plus and cross, which are purely transverse with two-helicity, massless tensor polarization modes, and an additional massive scalar mode with zero-helicity. The last one is a mix of longitudinal and transverse breathing scalar polarization modes. The boundary term
B
excites the extra scalar polarization and the mass of scalar field breaks the symmetry of the TT gauge by adding a new degree of freedom, namely a single mixed scalar polarization.
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We consider Non-local Gravity in view to obtain stable and traversable wormhole solutions. In particular, the class of Non-local Integral Kernel Theories of Gravity, with the inverse d'Alembert ...operator in the gravitational action, is taken into account. We obtain constraints for the null energy condition and derive the field equations. Two special cases for the related Klein-Gordan equation are assumed: one where the function in the gravitational action has a linear form and another one with exponential form. In each case, we take into account two forms for scalar fields and derive the shape functions. Asymptotic flatness and flaring-out conditions are checked. Energy conditions and dynamics of the solutions are examined at the throat. The main result is that non-local gravity contributions allow stability and traversability of the wormhole without considering any exotic matter.
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The cosmographic approach is gaining considerable interest as a model-independent technique able to describe the late expansion of the universe. Indeed, given only the observational assumption of the ...cosmological principle, it allows to study the today observed accelerated evolution of the Hubble flow without assuming specific cosmological models. In general, cosmography is used to reconstruct the Hubble parameter as a function of the redshift, assuming an arbitrary fiducial value for the current matter density, Ωm, and analysing low redshift cosmological data. Here we propose a different strategy, linking together the parametric cosmographic behavior of the late universe expansion with the small scale universe. In this way, we do not need to assume any “a priori” values for the cosmological parameters, since these are constrained at early epochs using both the Cosmic Microwave Background Radiation (CMBR) and Baryonic Acoustic Oscillation (BAO) data. In other words, we want to develop a cosmographic approach without assuming any background model but considering a f(z)CDM model where the function f(z) is given by a suitable combination of polynomials capable of tracking the cosmic luminosity distance, replacing the cosmological constant Λ. In order to test this strategy, we describe the late expansion of the universe using the Pad'e polynomials. Specifically, we adopt a P(2,2) series, that is a promising rational series which guarantees a good convergence also at high redshift. This approach is discussed in the light of the recent H(z) values indicators, combined with Supernovae Pantheon sample, galaxy clustering and early universe data, as CMBR and BAO. We found an interesting dependence of the current matter density value with cosmographic parameters, proving the inaccuracy of setting the value of Ωm in cosmographic analyses. Furthermore, a non-negligible effect of the cosmographic parameters on the CMBR temperature anisotropy power spectrum is shown, and constraints by selected joint datasets are reported. Finally, we found that the cosmographic series, truncated at third order, shows a better χ2 best fit value then the vanilla ΛCDM model. This can be interpreted as the requirement that higher order corrections have to be considered to correctly describe low redshift data and remove the degeneration of the models.
Teleparallel theory of gravity and its modifications have been studied extensively in literature. However, gravitational waves has not been studied enough in the framework of teleparallelism. In the ...present study, we discuss gravitational waves in general theories of teleparallel gravity containing the torsion scalar
T
, the boundary term
B
and a scalar field
ϕ
. The goal is to classify possible new polarizations generalizing results presented in Bamba et al. (Phys Lett B 727:194–198,
arXiv:1309.2698
,
2013
). We show that, if the boundary term is minimally coupled to the torsion scalar and the scalar field, gravitational waves have the same polarization modes of General Relativity.
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We discuss equivalent representations of gravity in the framework of metric-affine geometries pointing out basic concepts from where these theories stem out. In particular, we take into account ...tetrads and spin connection to describe the so called
Geometric Trinity of Gravity
. Specifically, we consider General Relativity, constructed upon the metric tensor and based on the curvature
R
; Teleparallel Equivalent of General Relativity, formulated in terms of torsion
T
and relying on tetrads and spin connection; Symmetric Teleparallel Equivalent of General Relativity, built up on non-metricity
Q
, constructed from metric tensor and affine connection. General Relativity is formulated as a geometric theory of gravity based on metric, whereas teleparallel approaches configure as gauge theories, where gauge choices permit not only to simplify calculations, but also to give deep insight into the basic concepts of gravitational field. In particular, we point out how foundation principles of General Relativity (i.e. the Equivalence Principle and the General Covariance) can be seen from the teleparallel point of view. These theories are dynamically equivalent and this feature can be demonstrated under three different standards: (1) the variational method; (2) the field equations; (3) the solutions. Regarding the second point, we provide a procedure starting from the (generalised) second Bianchi identity and then deriving the field equations. Referring to the third point, we compare spherically symmetric solutions in vacuum recovering the Schwarzschild metric and the Birkhoff theorem in all the approaches. It is worth stressing that, in extending the approaches to
f
(
R
),
f
(
T
), and
f
(
Q
) gravities respectively, the dynamical equivalence is lost opening the discussion on the different number of degrees of freedom intervening in the various representations of gravitational theories.
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