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The $f(R,T)$ gravity models, for which $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor, elevate the degrees of freedom of the renowned $f(R)$ theories, by making the Einstein field equations of the theory to also depend on $T$. While such a dependence can be motivated by quantum effects, the existence of imperfect or extra fluids, or even a cosmological ``constant'' which effectively depends on $T$, the formalism can truly surpass some deficiencies of $f(R)$ gravity. As the $f(R,T)$ function is arbitrary, several parametric models have been proposed {\it ad hoc} in the literature and posteriorly confronted with observational data. In the present article, we use gaussian process to construct an $f(R,T)=R+f(T)$ model. To apply the gaussian process we use a series of measurements of the Hubble parameter. We then analytically obtain the functional form of the function. By construction, this form, which is novel in the literature, is well-adjusted to cosmological data. In addition, by extrapolating our reconstruction to redshift $z=0$, we were able to constrain the Hubble constant value to $H_0=69.97\pm4.13$$\rm \ km \ s^{-1} \ Mpc^{-1}$ with $5\%$ precision. Lastly, we encourage the application of the functional form herewith obtained to other current problems of observational cosmology and astrophysics, such as the rotation curves of galaxies.

Astronomical data have shown that the galaxy rotation curves are mostly flat in the far distance of the galactic cores, which reveals the insufficiency of our knowledges about how gravity works in these regimes. In this paper we introduce a resolution of this issue from the $f(R,T)$ modified gravity formalism perspective. By investigating two classes of models with separable (minimal coupling model) and inseparable (non-minimal coupling model) parts of the Ricci scalar $R$ and trace of the energy-momentum tensor $T$, we find that only in the latter models it is possible to attain flat galaxy rotation curves., 9 pages, 4 figures

We have analyzed in this work the updated sample of neutron star masses derived from the study of a variety of 96 binary systems containing at least one neutron star using Bayesian methods. After updating the multimodality of the distributions found in previous works, we determined the maximum mass implied by the sample using a robust truncation technique, with the result $m_{max} \sim 2.5-2.6 \, M_{\odot}$. We have checked that this mass is actually consistent by generating synthetic data and employing a Posterior Predictive Check. A comparison with seven published $m_{max}$ values inferred from the remnant of the NS-NS merger GW170817 was performed and the tension between the latter and the obtained $m_{max}$ value quantified. Finally, we performed a Local Outlier Factor test and verified that the result for $m_{max}$ encompasses the highest individual mass determinations with the possible exception of PSR J1748-2021B. The conclusion is that the whole distribution already points toward a high value of $m_{max}$, while several lower values derived from the NS-NS merger event are disfavored and incompatible with the higher binary system masses. A large $m_{max}$ naturally accommodates the lower mass component of the event GW190814 as a neutron star., 3 figures. Sumitted for publication

The detection of an unexpected $\sim 2.5 M_{\odot}$ component in the gravitational wave event GW190814 has puzzled the community of High-Energy astrophysicists, since in the absence of further information it is not clear whether this is the heaviest "neutron star" ever detected or either the lightest black hole known, of a kind absent in the local neighbourhood. We show in this work a few possibilities for a model of the former, in the framework of three different quark matter models with and without anisotropy in the interior pressure. As representatives of classes of "exotic" solutions, we show that even though the stellar sequences may reach this ballpark, it is difficult to fulfill simultaneously the constraint of the radius as measured by the NICER team for the pulsar PSR J0030+0451. Thus, and assuming both measurements stand, compact neutron stars can not be all made of self-bound quark matter, even within anisotropic solutions which boost the maximum mass well above the $\sim 2.5 M_{\odot}$ figure. We also point out that a very massive compact star will limit the absolute maximum matter density in the present Universe to be less than 6 times the nuclear saturation value., To appear in IJMPD, references added

For the accurate understanding of compact objects such as neutron stars and strange stars, the Tolmann-Openheimer-Volkof (TOV) equation has proved to be of great use. Hence, in this work, we obtain the TOV equation for the energy-momentum-conserved $f(R,T)$ theory of gravity to study strange quark stars. The $f(R,T)$ theory is important, especially in cosmology, because it solves certain incompleteness of the standard model. In general, there is no intrinsic conservation of the energy-momentum tensor in the $f(R,T)$ gravity. Since this conservation is important in the astrophysical context, we impose the condition $\nabla T_{\mu\nu}=0$, so that we obtain a function $f(R,T)$ that implies conservation. This choice of a function $f(R,T)$ that conserves the momentum-energy tensor gives rise to a strong link between gravity and the microphysics of the compact object. We obtain the TOV by taking into account a linear equation of state to describe the matter inside strange stars, such as $p=\omega\rho$ and the MIT bag model $p=\omega(\rho-4B)$. With these assumptions it was possible to derive macroscopic properties of these objects., Comment: preprint version with 14 pages and 3 figures. arXiv admin note: text overlap with arXiv:1803.07719

We apply the Induced Matter Model to a five-dimensional metric. For the case with null cosmological constant, we obtain a solution able to describe the radiation-dominated era of the universe. The positive $\Lambda$ case yields a bounce cosmological model. In the negative five-dimensional cosmological constant case, the scale factor is obtained as $a(t)\sim\sqrt[]{\sinh t}$, which is able to describe not only the late-time cosmic acceleration but also the non-accelerated stages of the cosmic expansion in a continuous form. This solution together with the extra-dimensional scale factor solution yields the material content of the model to be remarkably related through an equation of state analogous to the renowned MIT bag model equation of state for quark matter $p=(\rho-4B)/3$. In our case, $\rho=\rho_m+B$, with $\rho_m$ being the energy density of relativistic and non-relativistic matter and $B=\ \Lambda\ /16\pi$ represents the bag energy constant, which plays the role of the dark energy in the four-dimensional universe, with $\Lambda$ being the cosmological constant of the AdS$_5$ space-time. Our model satisfactorily fits the observational data for the low redshift sample of the experimental measurement of the Hubble parameter, which resulted in $H_0=72.2^{+5.3}_{-5.5}$km s$^{-1}$ Mpc$^{-1}$., Comment: 14 pages, 11 figures

Braneworld models were firstly proposed as a great alternative for the hierarcy problem of particle physics, by allowing gravitons, differently from the other interacting bosons, to propagate through an extradimensional space named bulk. As time passed by the braneworld setup has also shown to be able to provide interesting results when applied to cosmology and stellar and gravitational wave astrophysics scenarios. In the present work we will construct Randall-Sundrum II braneworld wormholes whose interior space-time admits conformal motion. We show that for a wide range of positive values of the brane tension, it is possible to fill this wormholes with non-exotic matter, that is, matter obeying the energy conditions, departing from an important theoretical shortcoming of General Relativity wormholes., 10 Pages and 4 figures

In this paper we derive a novel cosmological model from the $f(R,T)$ theory of gravitation, for which $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor. We consider the functional form $f(R,T)=f(R)+f(T)$, with $f(R)$ being the Starobinksy model, named $R+\alpha R^{2}$, and $f(T)=2\gamma T$, with $\alpha$ and $\gamma$ being constants. We show that a hybrid expansion law form for the scale factor is a solution for the derived Friedmann-like equations. In this way, the model is able to predict both the decelerated and the accelerated regimes of expansion of the universe, with the transition redshift between these stages being in accordance with recent observations. We also apply the energy conditions to our material content solutions. Such an application makes us able to obtain the range of acceptability for the free parameters of the model, named $\alpha$ and $\gamma$., Comment: 8 pages, 8 figures

This article presents cosmological models that arise in a subclass of $f(R,T)=f(R)+f(T)$ gravity models, with different $f(R)$ functions and fixed $T$-dependence. That is, the gravitational lagrangian is considered as $f(R,T)=f(R)+\lambda T$, with constant $\lambda$. Here $R$ and $T$ represent the Ricci scalar and trace of the stress-energy tensor, respectively. The modified gravitational field equations are obtained through the metric formalism for the Friedmann-Lema\^itre-Robertson-Walker metric with signature $(+,-,-,-)$. We work with $f(R)=R+\alpha R^2-\frac{\mu^4}{R}$, $f(R)=R+k\ln(\gamma R)$ and $f(R)=R+me^{[-nR]}$, with $\alpha, \mu, k, \gamma, m$ and $n$ all free parameters, which lead to three different cosmological models for our Universe. For the choice of $\lambda=0$, this reduces to widely discussed $f(R)$ gravity models. This manuscript clearly describes the effects of adding the trace of the energy-momentum tensor in the $f(R)$ lagrangian. The exact solution of the modified field equations are obtained under the hybrid expansion law. Also we present the Om diagnostic analysis for the discussed models., Comment: 11 pages, 20 figures, Accepted version in EPJ C

In this article we study the hydrostatic equilibrium configuration of neutron stars (NSs) and strange stars (SSs), whose fluid pressure is computed from the equations of state $p=\omega\rho^{5/3}$ and $p=0.28(\rho-4{\cal B})$, respectively, with $\omega$ and ${\cal B}$ being constants and $\rho$ the energy density of the fluid. We also study white dwarfs (WDs) equilibrium configurations. We start by deriving the hydrostatic equilibrium equation for the $f(R,T)$ theory of gravity, with $R$ and $T$ standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Such an equation is a generalization of the one obtained from general relativity, and the latter can be retrieved for a certain limit of the theory. For the $f(R,T)=R+2\lambda T$ functional form, with $\lambda$ being a constant, we find that some physical properties of the stars, such as pressure, energy density, mass and radius, are affected when $\lambda$ is changed. We show that for some particular values of the constant $\lambda$, some observed objects that are not predicted by General Relativity theory of gravity can be attained. Moreover, since gravitational fields are smaller for WDs than for NSs or SSs, the scale parameter $\lambda$ used for WDs is small when compared to the values used for NSs and SSs., Comment: Invited talk presented at the XIV International Workshop on Hadron Physics, Florian\'opolis, Brazil, March 2018

We propose, as a novelty in the literature, the modelling of wormholes within the particular case of the $f(R,T)$ gravity, namely $f(R,T)=R+\alpha R^{2}+\lambda T$, with $R$ and $T$ being the Ricci scalar and trace of the energy-momentum tensor, respectively, while $\alpha$ and $\lambda$ are constants. Although such a functional form application can be found in the literature, those concern to compact astrophysical objects, such that no wormhole analysis has been done so far. The quadratic geometric and linear material corrections of this theory make the matter content of the wormhole to remarkably be able to obey the energy conditions., Comment: Published version

In this work we propose the modelling of static wormholes within the $f(R,T)$ extended theory of gravity perspective. We present some models of wormholes, which are constructed from different hypothesis for their matter content, i.e., different relations for their pressure components (radial and lateral) and different equations of state. The solutions obtained for the shape function of the wormholes obey the necessary metric conditions. They show a behaviour similar to those found in previous references about wormholes, which also happens to our solutions for the energy density of such objects. We also apply the energy conditions for the wormholes physical content., 15 figures

The recent article entitled "Cosmological inviability of $f(R,T)$ gravity" [Phys. Rev. D 95 (2017) 123536], by H. Velten and T.R.P. Caram\^es, claims that the reference "A transition from a decelerated to an accelerated phase of the universe expansion from the simplest non-trivial polynomial function of T in the f(R,T) formalism" by P.H.R.S. Moraes, G. Ribeiro and R.A.C. Correa [Astrophys. Space Sci. 361 (2016) 227] has "problematic points" concerning its mathematical approach and observable consequences. Velten and Caram\^es argue that the equation of the scale factor evolution in time in the $f(R,T)=R+\alpha T+\beta T^{2}$ cosmology was erroneously calculated. One crucial consequence of the supposed corrected version of such an equation, presented by the authors in [Phys. Rev. D 95 (2017) 123536], would be the absence of the transition from a decelerated to an accelerated phase of the expansion of the universe, an outcome originally predicted by Moraes, Ribeiro and Correa. We show that the above claim is incorrect and that there are no inconsistencies with the results by Moraes, Ribeiro and Correa in the referred work. In particular, we show that Velten and Caram\^es have incorrectly performed their calculations, invalidating all their mathematical and physical criticism regarding the article by Moraes, Ribeiro and Correa. In addition, we quote that the solutions obtained by Velten and Caram\^es are unfeasible in view of their mathematical misunderstanding., Comment: Pedro Moraes (moraes.phrs@gmail.com) We realyzed that the error pointed out in our article is merely a typo of Reference [Phys. Rev D ...] which does not propagate to the subsequent equations. Therefore, and once Velten and Caram\^es work is correct, we believe it is fair to withdraw this

In this paper we derive a cosmological model from the $f(R,T)$ theory of gravity, for which $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor. We consider $f(R,T)=f(R)+f(T)$, with $f(R)$ being the Starobinksy model $R+\alpha R^{2}$ and $f(T)=\gamma T$, with $\alpha$ and $\gamma$ constants. We find that from such a functional form, it is possible to describe the cosmological scenario of a radiation-dominated universe, which has shown to be a non-trivial feature within the $f(R,T)$ formalism.