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Register a new userLinear growth in power law $f(T)$ gravity
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Spyros Basilakos
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We provide for the first time the growth index of linear matter fluctuations of the power law $f(T) propto (-T)^{b}$ gravity model. We find that the asymptotic form of this particular $f(T)$ model is $gamma approx frac{6}{11-6b}$ which obviously extends that of the $Lambda$CDM model, $gamma_{Lambda}approx 6/11$. Finally, we generalize the growth index analysis of $f(T)$ gravity in the case where $gamma$ is allowed to vary with redshift.
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Gravity is attributed to the spacetime curvature in classical General Relativity (GR). But, other equivalent formulation or representations of GR, such as torsion or non-metricity have altered the perception. We consider the Weyl-type $f(Q, T)$ gravity, where $Q$ represents the non-metricity and $T$ is the trace of energy momentum temsor, in which the vector field $omega_{mu}$ determines the non-metricity $Q_{mu u alpha}$ of the spacetime. In this work, we employ the well-motivated $f(Q, T)= alpha Q+ frac{beta}{6k^{2}} T$, where $alpha$ and $beta$ are the model parameters. Furthermore, we assume that the universe is dominated by the pressure-free matter, i.e. the case of dust ($p=0$). We obtain the solution of field equations similar to a power-law in Hubble parameter $H(z)$. We investigate the cosmological implications of the model by constraining the model parameter $alpha$ and $beta$ using the recent 57 points Hubble data and 1048 points Pantheon supernovae data. To study various dark energy models, we use statefinder analysis to address the current cosmic acceleration. We also observe the $Om$ diagnostic describing various phases of the universe. Finally, it is seen that the solution which mimics the power-law fits well with the Pantheon data better than the Hubble data.
The article presents modeling of inflationary scenarios for the first time in the $f(R,T)$ theory of gravity. We assume the $f(R,T)$ functional from to be $R + eta T$, where $R$ denotes the Ricci scalar, $T$ the trace of the energy-momentum tensor and $eta$ the model parameter (constant). We first investigated an inflationary scenario where the inflation is driven purely due to geometric effects outside of GR. We found the inflation observables to be independent of the number of e-foldings in this setup. The computed value of the spectral index is consistent with latest Planck 2018 dataset while the scalar to tensor ratio is a bit higher. We then proceeded to analyze the behavior of an inflation driven by $f(R,T)$ gravity coupled with a real scalar field. By taking the slow-roll approximation, we generated interesting scenarios where a Klein Gordon potential leads to observationally consistent inflation observables. Our results makes it clear-cut that in addition to the Ricci scalar and scalar fields, the trace of energy momentum tensor also play a major role in driving inflationary scenarios.
The evolution of the configurational entropy of the universe relies on the growth rate of density fluctuations and on the Hubble parameter. In this work, I present the evolution of configurational entropy for the power-law $f(T)$ gravity model of the form $f(T) = zeta (-T)^ b$, where, $zeta = (6 H_{0}^{2})^{(1-s)}frac{Omega_{P_{0}}}{2 s -1}$ and $b$ a free parameter. From the analysis, I report that the configurational entropy in $f(T)$ gravity is negative and decreases with increasing scale factor and therefore consistent with an accelerating universe. The decrease in configurational entropy is the highest when $b$ vanishes since the effect of dark energy is maximum when $b=0$. Additionally, I find that as the parameter $b$ increases, the growth rate, growing mode, and the matter density parameter evolve slowly whereas the Hubble parameter evolves rapidly. The rapid evolution of the Hubble parameter in conjunction with the growth rate for the $b=0$ may provide an explanation for the large dissipation of configurational entropy.
We study inflation in the framework of $f(T)$-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in $f(T)$-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law form for the $f(T)$ function in the action and examine the inflationary models with the power-law and intermediate scale factors. We see that in contrast with the standard inflationary scenario based on the Einstein gravity, in the considered $f(T)$-gravity scenario, the power-law and intermediate inflationary models can be compatible with the observational results of Planck 2015 at 68% CL. In our $f(T)$-gravity setting, the potentials responsible for both the power-law and intermediate inflationary models have the power-law form $V(phi ) propto {phi ^m}$ but the power $m$ is different for them. Therefore, we can refine some of power-law inflationary potentials in the framework of $f(T)$-gravity while they are disfavored by the observational data in the standard inflationary scenario. Interestingly enough, the self-interacting quartic potential $V(phi ) propto {phi ^4}$ which has special reheating properties, can be consistent with the Planck 2015 data in our $f(T)$-gravity scenario while it is ruled out in the standard inflationary scenario.
[Abridged] In its standard formulation, the $f(T)$ field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. A locally Lorentz covariant $f(T)$ gravity theory has been devised recently, and this local causality problem has been overcome. The nonlocal question, however, is left open. If gravitation is to be described by this covariant $f(T)$ gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Godel-type solutions, which necessarily leads to violation of causality on nonlocal scale. Here, to look into the potentialities and difficulties of the covariant $f(T)$ theories, we examine whether they admit Godel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Godel-type solution, which contains special solutions in which the essential parameter of Godel-type geometries, $m^2$, defines any class of homogeneous Godel-type geometries. We extended to the context of covariant $f(T)$ gravity a theorem, which ensures that any perfect-fluid homogeneous Godel-type solution defines the same set of Godel tetrads $h_A^{~mu}$ up to a Lorentz transformation. We also shown that the single massless scalar field generates Godel-type solution with no closed timelike curves. Even though the covariant $f(T)$ gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Godel-type solutions makes apparent that the covariant formulation of $f(T)$ gravity does not preclude non-local violation of causality in the form of closed timelike curves.
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