Showing papers by "Salvatore Capozziello published in 2018"

Cosmographic analysis with Chebyshev polynomials

Abstract: The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parametrize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Pade series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Pade approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the Joint Light-curve Analysis supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.

Effective gravitational coupling in modified teleparallel theories

Abstract: In the present study, we consider an extended form of teleparallel Lagrangian $f(T,\ensuremath{\phi},X)$, as function of a scalar field $\ensuremath{\phi}$, its kinetic term $X$ and the torsion scalar $T$. We use linear perturbations to obtain the equation of matter density perturbations on sub-Hubble scales. The gravitational coupling is modified in scalar modes with respect to the one of general relativity, albeit vector modes decay and do not show any significant effects. We thus extend these results by involving multiple scalar field models. Further, we study conformal transformations in teleparallel gravity and we obtain the coupling as the scalar field is nonminimally coupled to both torsion and boundary terms. Finally, we propose the specific model $f(T,\ensuremath{\phi},X)=T+{\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\phi}{\ensuremath{\partial}}^{\ensuremath{\mu}}\ensuremath{\phi}+\ensuremath{\xi}T{\ensuremath{\phi}}^{2}$. To check its goodness, we employ the observational Hubble data, constraining the coupling constant, $\ensuremath{\xi}$, through a Monte Carlo technique based on the Metropolis-Hastings algorithm. Hence, fixing $\ensuremath{\xi}$ to its best-fit value got from our numerical analysis, we calculate the growth rate of matter perturbations and we compare our outcomes with the latest measurements and the predictions of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model.

Noether Symmetries as a geometric criterion to select theories of gravity

Abstract: We review the Noether Symmetry Approach as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories....

The gravitation energy–momentum pseudotensor: The cases of F(R) and F(T) gravity

Abstract: We derive the gravitational energy–momentum pseudotensor τ λσ in metric f(R) gravity and in teleparallel f(T) gravity. In the first case, R is the Ricci curvature scalar for a torsionless Levi-Civi...

Observational constraints on Gauss–Bonnet cosmology

Abstract: We analyze a fully geometric approach to dark energy in the framework of F(R,𝒢) theories of gravity, where R is the Ricci curvature scalar and 𝒢 is the Gauss–Bonnet topological invariant. The latte...

Classification of the Horndeski cosmologies via Noether symmetries.

Abstract: Adopting Noether point symmetries, we classify and integrate dynamical systems coming from Horndeski cosmologies. The method is particularly effective both to select the form of Horndeski models and to derive exact cosmological solutions. Starting from the Lagrangians selected by the Noether symmetries, it is possible to derive several modified theories of gravity like f(R) gravity, Brans–Dicke gravity, string inspired gravity and so on. In any case, exact solutions are found out.

Clustering of galaxies with f(R) gravity

Abstract: Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newton's potential given by $f(R)$ gravity. We compute the corrected $N$-particle partition function analytically. The corrected partition function leads to more exact equations of states of the system. By assuming that system follows quasi-equilibrium, we derive the exact distribution function which exhibits the $f(R)$ correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of $f(R)$ gravity on the power law behavior of particle-particle correlation function also. In order to check feasibility of an $f(R)$ gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalog.

Gravitational waves in modified teleparallel theories of gravity.

Abstract: 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 $$\phi $$ . 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.

Dynamical analysis on $f(R,\mathcal{G})$ cosmology

Abstract: We use a dynamical system approach to study the cosmological viability of $f(R,\mathcal{G})$ gravity theories. The method consists of formulating the evolution equations as an autonomous system of ODEs, using suitable variables. The formalism is applied to a class of models in which $f(R,\mathcal{G})\propto R^{n}\mathcal{G}^{1-n}$ and its solutions and corresponding stability are analysed in detail. New accelerating solutions that can be attractors in the phase space are found. We also find that this class of models does not exhibit a matter-dominated epoch, a solution which is inconsistent with current cosmological observations.

The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity

Abstract: We derive the gravitational energy-momentum pseudotensor $ \tau^{\sigma}_ {\phantom {\sigma} \lambda} $ in metric $ f\left (R \right) $ gravity and in teleparallel $ f\left (T\right) $ gravity. In the first case, $R$ is the Ricci curvature scalar for a torsionless Levi-Civita connection; in the second case, $T$ is the curvature-free torsion scalar derived by tetrads and Weitzenbock connection. For both classes of theories the continuity equations are obtained in presence of matter. $ f \left (R \right) $ and $ f \left (T \right) $ are non-equivalent but differ for a quantity $ \omega \left (T, B \right) $ containing the torsion scalar $T$ and a boundary term $ B $. It is possible to obtain the field equations for $ \omega \left (T, B \right) $ and the related gravitational energy-momentum pseudotensor $ \tau^{\sigma}_{\phantom {\sigma}\lambda} \vert \omega $. Finally we show that, thanks to this further pseudotensor, it is possible to pass from $ f \left (R \right) $ to $ f \left ( T \right) $ and viceversa through a simple relation between gravitational pseudotensors.

Cosmic acceleration in non-flat f(T) cosmology

Abstract: We study f(T) cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial f(T) model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular f(T) models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3- $$\sigma $$ confidence level, emphasizing the fact that $$\Omega _{k0}$$ turns out to be non-compatible with zero at least at 1 $$\sigma $$ . Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the $$\Lambda $$ CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the f(T) models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat f(T) cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial f(T) approach provides an effective de-Sitter phase, whereas the second f(T) framework shows analogous results compared with the $$\Lambda $$ CDM predictions.

Kinematic model-independent reconstruction of Palatini $f(R)$ cosmology

Abstract: A kinematic treatment to trace out the form of $f(R)$ cosmology, within the Palatini formalism, is discussed by only postulating the universe homogeneity and isotropy. To figure this out we build model-independent approximations of the luminosity distance through rational expansions. These approximants extend the Taylor convergence radii computed for usual cosmographic series. We thus consider both Pade and the rational Chebyshev polynomials. They can be used to accurately describe the universe late-time expansion history, providing further information on the thermal properties of all effective cosmic fluids entering the energy momentum tensor of Palatini's gravity. To perform our numerical analysis, we relate the Palatini's Ricci scalar with the Hubble parameter $H$ and thus we write down a single differential equation in terms of the redshift $z$. Therefore, to bound $f(R)$, we make use of the most recent outcomes over the cosmographic parameters obtained from combined data surveys. In particular our clue is to select two scenarios, i.e. $(2,2)$ Pade and $(2,1)$ Chebyshev approximations, since they well approximate the luminosity distance at the lowest possible order. We find that best analytical matches to the numerical solutions lead to $f(R)=a+bR^n$ with free parameters given by the set $(a, b, n)=(-1.627, 0.866, 1.074)$ for $(2,2)$ Pade approximation, whereas $f(R)=\alpha+\beta R^m$ with $(\alpha, \beta, m)=(-1.332, 0.749, 1.124)$ for $(2,1)$ rational Chebyshev approximation. Finally, our results are compared with the $\Lambda$CDM predictions and with previous studies in the literature. Slight departures from General Relativity are also discussed.

Observational constraints on Gauss-Bonnet cosmology

Abstract: We analyze a fully geometric approach to dark energy in the framework of $F(R,{\cal G})$ theories of gravity, where $R$ is the Ricci curvature scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant. The latter invariant naturally exhausts, together with $R$, the whole curvature content related to curvature invariants coming from the Riemann tensor. In particular, we study a class of $F(R, {\cal G})$ models with power law solutions and find that, depending on the value of the geometrical parameter, a shift in the anisotropy peaks position of the temperature power spectrum is produced, as well as an increasing in the matter power spectrum amplitude. This fact could be extremely relevant to fix the form of the $F(R, {\cal G})$ model. We also perform a MCMC analysis using both Cosmic Microwave Background data by the Planck (2015) release and the Joint Light-Curve Analysis of the SNLS-SDSS collaborative effort, combined with the current local measurements of the Hubble value, $H_0$, and galaxy data from the Sloan Digital Sky Survey (BOSS CMASS DR11). We show that such a model can describe the CMB data with slightly high $H_0$ values, and the prediction on the amplitude matter spectrum value is proved to be in accordance with the observed matter distribution of the universe. At the same time, the value constrained for the geometric parameter implies a density evolution of such a components that is growing with time.

Cosmological perfect-fluids in f(R) gravity.

Abstract: We show that an n-dimensional generalized Robertson-Walker (GRW) space-time with divergence-free conformal curvature tensor exhibits a perfect fluid stress-energy tensor for any f(R) gravity model. Furthermore we prove that a conformally flat GRW space-time is still a perfect fluid in both f(R) and quadratic gravity where other curvature invariants are considered.

Cosmic acceleration in non-flat $f(T)$ cosmology

Abstract: We study $f(T)$ cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial $f(T)$ model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular $f(T)$ models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-$\sigma$ confidence level, emphasizing the fact that $\Omega_{k0}$ turns out to be non-compatible with zero at least at 1$\sigma$. Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the $\Lambda$CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the $f(T)$ models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat $f(T)$ cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial $f(T)$ approach provides an effective de-Sitter phase, whereas the second $f(T)$ framework shows analogous results compared with the $\Lambda$CDM predictions.

The Chern‐Simons Current in Systems of DNA‐RNA Transcriptions

Abstract: A Chern-Simons current, coming from ghost and anti-ghost fields of supersymmetry theory, can be used to define a spectrum of gene expression in new time series data where a spinor field, as alternative representation of a gene, is adopted instead of using the standard alphabet sequence of bases $A, T, C, G, U$. After a general discussion on the use of supersymmetry in biological systems, we give examples of the use of supersymmetry for living organism, discuss the codon and anti-codon ghost fields and develop an algebraic construction for the trash DNA, the DNA area which does not seem active in biological systems. As a general result, all hidden states of codon can be computed by Chern-Simons 3 forms. Finally, we plot a time series of genetic variations of viral glycoprotein gene and host T-cell receptor gene by using a gene tensor correlation network related to the Chern-Simons current. An empirical analysis of genetic shift, in host cell receptor genes with separated cluster of gene and genetic drift in viral gene, is obtained by using a tensor correlation plot over time series data derived as the empirical mode decomposition of Chern-Simons current.

Classification of the Horndeski cosmologies via Noether Symmetries

Abstract: Adopting Noether point symmetries, we classify and integrate dynamical systems coming from Horndeski cosmologies. The method is particularly effective both to select the form of Horndeski models and to derive exact cosmological solutions. Starting from the Lagrangians selected by the Noether symmetries, it is possible to derive several modified theories of gravity like $f(R)$ gravity, Brans-Dicke gravity, string inspired gravity and so on. In any case, exact solutions are found out.

Gravitational Physics: From Quantum to Waves

Abstract: Gravitational interaction is widely considered one of the most challenging topics of physics. Despite of the undoubtful successes of General Relativity, the lack of a self-consistent theory, capable of encompassing gravitational aspects of quantum phenomena, local scales, galactic and extragalactic astrophysics up to cosmology, it is one of the most frustrating aspects of this long ranging interaction. Here, with no claim to completeness, we review some of these aspects considering the issues of foundation of General Relativity, quantum gravity, strong and weak field regimes, alternative theories of gravity, gravitational waves and multimessanger astronomy. The goal is to provide a quick summary and guideline for these open issues. Particular emphasis is given to the theory and the discovery gravitational waves that have been the experimentum crucis to confirm General Relativity and definitely opened the era of the so called gravitational astronomy.

Maximum turnaround radius in $f(R)$ gravity

Abstract: The accelerating behavior of cosmic fluid opposes to the gravitational attraction, at present epoch, whereas standard gravity is dominant at small scales. As a consequence, there exists a \emph{point} where the effects are counterbalanced, dubbed \emph{turnaround radius}, $r_{\text{ta}}$. By construction, it provides a bound on maximum structure sizes of the observed universe. Once an upper bound on $r_{\text{ta}}$ is provided, i.e. $R_{\text{TA,max}}$, one can check whether cosmological models guarantee structure formation. Here, we focus on $f(R)$ gravity, without imposing \emph{a priori} the form of $f(R)$. We thus provide an analytic expression for the turnaround radius in the framework of $f(R)$ models. To figure this out, we compute the turnaround radius in two distinct cases: 1) under the hypothesis of static and spherically symmetric space-time, and 2) by using the cosmological perturbation theory. We thus find a criterion to enable large scale structures to be stable in $f(R)$ models, circumscribing the class of $f(R)$ theories as suitable alternative to dark energy. In particular, we get that for constant curvature, the viability condition becomes $R_{\text{dS}}f'(R_{\text{dS}}) \leq 5.48 \Lambda \Rightarrow f'(R_{\text{dS}}) \leq 1.37$, with $\Lambda$ and $R_{\text{dS}}$ respectively the observed cosmological constant and the Ricci curvature. This prescription rules out models which do not pass the aforementioned $R_{\text{TA,max}}$ limit.

Charged Anti-de Sitter BTZ black holes in Maxwell-$f(T)$ gravity

Abstract: Inspired by the Banados, Teitelboim and Zanelli (BTZ) formalism, we discuss the Maxwell-f(T) gravity in (2 + 1) dimensions. The main task is to derive exact solutions for a special form of f(T) = T...

The Chern-Simons Current in Time Series of Knots and Links in Proteins

Abstract: A superspace model of knots and links for DNA time series data is proposed to take into account the feedback loop from docking to undocking state of protein-protein interactions. In particular, the direction of interactions between the 8 hidden states of DNA is considered. It is a $E_{8}\times E_{8}$ unified spin model where the genotype, from active and inactive side of DNA time data series, can be considered for any living organism. The mathematical model is borrowed from loop-quantum gravity and adapted to biology. It is used to derive equations for gene expression describing transitions from ground to excited states, and for the 8 coupling states between geneon and anti-geneon transposon and retrotransposon in trash DNA. Specifically, we adopt a modified Grothendieck cohomology and a modified Khovanov cohomology for biology. The result is a Chern-Simons current in $(8+3)$ extradimensions of a given unoriented super manifold with ghost fields of protein structures. The $8$ dimensions come from the 8 hidden states of spinor field of genetic code. The extradimensions come from the 3 types of principle fiber bundle in the secondary protein.

Qualitative behavior of cosmological models combining various matter fields

Abstract: The late time accelerated expansion of the universe can be realized using scalar fields with the given self-interacting potentials. Here, we consider a straightforward approach where a three cosmic...