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Register a new userA new test of $f(R)$ gravity with the cosmological standard rulers in radio quasars
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As an important candidate gravity theory alternative to dark energy, a class of $f(R)$ modified gravity, which introduces a perturbation of the Ricci scalar $R$ in the Einstein-Hilbert action, has been extensively applied to cosmology to explain the acceleration of the universe. In this paper, we focus on the recently-released VLBI observations of the compact structure in intermediate-luminosity quasars combined with the angular-diameter-distance measurements from galaxy clusters, which consists of 145 data points performing as individual cosmological standard rulers in the redshift range $0.023le zle 2.80$, to investigate observational constraints on two viable models in $f(R)$ theories within the Palatini formalism: $f_1(R)=R-frac{a}{R^b}$ and $f_2(R)=R-frac{aR}{R+ab}$. We also combine the individual standard ruler data with the observations of CMB and BAO, which provides stringent constraints. Furthermore, two model diagnostics, $Om(z)$ and statefinder, are also applied to distinguish the two $f(R)$ models and $Lambda$CDM model. Our results show that (1) The quasars sample performs very well to place constraints on the two $f(R)$ cosmologies, which indicates its potential to act as a powerful complementary probe to other cosmological standard rulers. (2) The $Lambda$CDM model, which corresponds to $b=0$ in the two $f(R)$ cosmologies is still included within $1sigma$ range. However, there still exists some possibility that $Lambda$CDM may not the best cosmological model preferred by the current high-redshift observations. (3) The information criteria indicate that the cosmological constant model is still the best one, while the $f_1(R)$ model gets the smallest observational support. (4) The $f_2(R)$ model, which evolves quite different from $f_1(R)$ model at early times, still significantly deviates from both $f_1(R)$ and $Lambda$CDM model at the present time.
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In this paper, we present a new compiled milliarcsecond compact radio data set of 120 intermediate-luminosity quasars in the redshift range $0.46< z <2.76$. These quasars show negligible dependence on redshifts and intrinsic luminosity, and thus represents, in the standard model of cosmology, a fixed comoving-length of standard ruler. We implement a new cosmology-independent technique to calibrate the linear size of of this standard ruler as $l_m= 11.03pm0.25$ pc, which is the typical radius at which AGN jets become opaque at the observed frequency $ usim 2$ GHz. In the framework of flat $Lambda$CDM model, we find a high value of the matter density parameter, $Omega_m=0.322^{+0.244}_{-0.141}$, and a low value of the Hubble constant, $H_0=67.6^{+7.8}_{-7.4}; rm{kms}^{-1}rm{Mpc}^{-1}$, which is in excellent agreement with the CMB anisotropy measurements by textit{Planck}. We obtain ${Omega_m}=0.309^{+0.215}_{-0.151}$, $w=-0.970^{+0.500}_{-1.730}$ at 68.3% CL for the constant $w$ of a dynamical dark-energy model, which demonstrates no significant deviation from the concordance $Lambda$CDM model. Consistent fitting results are also obtained for other cosmological models explaining the cosmic acceleration, like Ricci dark energy (RDE) or Dvali-Gabadadze-Porrati (DGP) brane-world scenario. While no significant change in $w$ with redshift is detected, there is still considerable room for evolution in $w$ and the transition redshift at which $w$ departing from -1 is located at $zsim 2.0$. Our results demonstrate that the method extensively investigated in our work on observational radio quasar data can be used to effectively derive cosmological information. Finally, we find the combination of high-redshift quasars and low-redshift clusters may provide an important source of angular diameter distances, considering the redshift coverage of these two astrophysical probes.
We study the $f(R,T)$ cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the Field Equations (FE) admit exact self-similar solutions through the matter collineation approach. We study two models: the case$ f(R,T)=f_{1}(R)+f_{2}(T)$ and the case $f(R,T)=f_{1}(R)+f_{2} (R)f_{3}(T)$. In each case, we state general theorems which determine completely the form of the unknown functions $f_{i}$ such that the field equations admit self-similar solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous self-similar metric$.$ In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.
We consider $f(R)$ gravity theories which unify $R^n$ inflation and dark energy models. First, from the final Planck data of the cosmic microwave background, we obtain a condition, $1.977 < n < 2.003$. Next, under this constraint, we investigate local-gravity tests for three models. We find that the $R^n$ term can dominate over the dark energy term even at the Earths curvature scale, contrary to intuition; however, the $R^n$ term does not relax or tighten the constraints on the three models.
Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newtons 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.
We perform a general test of the $Lambda{rm CDM}$ and $w {rm CDM}$ cosmological models by comparing constraints on the geometry of the expansion history to those on the growth of structure. Specifically, we split the total matter energy density, $Omega_M$, and (for $w {rm CDM}$) dark energy equation of state, $w$, into two parameters each: one that captures the geometry, and another that captures the growth. We constrain our split models using current cosmological data, including type Ia supernovae, baryon acoustic oscillations, redshift space distortions, gravitational lensing, and cosmic microwave background (CMB) anisotropies. We focus on two tasks: (i) constraining deviations from the standard model, captured by the parameters $DeltaOmega_M equiv Omega_M^{rm grow}-Omega_M^{rm geom}$ and $Delta w equiv w^{rm grow}-w^{rm geom}$, and (ii) investigating whether the $S_8$ tension between the CMB and weak lensing can be translated into a tension between geometry and growth, i.e. $DeltaOmega_M eq 0$, $Delta w eq 0$. In both the split $Lambda{rm CDM}$ and $w {rm CDM}$ cases, our results from combining all data are consistent with $DeltaOmega_M = 0$ and $Delta w = 0$. If we omit BAO/RSD data and constrain the split $w {rm CDM}$ cosmology, we find the data prefers $Delta w<0$ at $3.6sigma$ significance and $DeltaOmega_M>0$ at $4.2sigma$ evidence. We also find that for both CMB and weak lensing, $DeltaOmega_M$ and $S_8$ are correlated, with CMB showing a slightly stronger correlation. The general broadening of the contours in our extended model does alleviate the $S_8$ tension, but the allowed nonzero values of $DeltaOmega_M$ do not encompass the $S_8$ values that would point toward a mismatch between geometry and growth as the origin of the tension.
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