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Register a new userConstraints on Cubic and $f(P)$ Gravity from the Cosmic Chronometers : Use of Machine Learning Algorithms
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In this work we perform an observational data analysis on Einsteinian cubic gravity and $f(P)$ gravity with the objective of constraining the parameter space of the theories. We use the 30 point $z-H(z)$ cosmic chronometer data as the observational tool for our analysis along with the BAO and the CMB peak parameters. The $chi^2$ statistic is used for the fitting analysis and it is minimized to obtain the best fit values for the free model parameters. We have used the Markov chain Monte Carlo algorithm to obtain bounds for the free parameters. To achieve this we used the publicly available textit{CosmoMC} code to put parameter bounds and subsequently generate contour plots for them with different confidence intervals. Besides finding the Hubble parameter $H$ in terms of the redshift $z$ theoretically from our gravity models, we have exercised correlation coefficients and two textit{machine learning} models, namely the linear regression (LR) and artificial neural network (ANN), for the estimation of $H(z)$. For this purpose, we have developed a textit{Python} package for finding the parameter space, performing the subsequent statistical analysis and prediction analysis using machine learning. We compared both of our theoretical and estimated values of $H(z)$ with the observations. It is seen that our theoretical and estimated models from machine learning performed significantly well when compared with the observations.
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An approach to estimate the spatial curvature $Omega_k$ from data independently of dynamical models is suggested, through kinematic parameterizations of the comoving distance ($D_{C}(z)$) with third degree polynomial, of the Hubble parameter ($H(z)$) with a second degree polynomial and of the deceleration parameter ($q(z)$) with first order polynomial. All these parameterizations were done as function of redshift $z$. We used SNe Ia dataset from Pantheon compilation with 1048 distance moduli estimated in the range $0.01<z<2.3$ with systematic and statistical errors and a compilation of 31 $H(z)$ data estimated from cosmic chronometers. The spatial curvature found for $D_C(z)$ parametrization was $Omega_{k}=-0.03^{+0.24+0.56}_{-0.30-0.53}$. The parametrization for deceleration parameter $q(z)$ resulted in $Omega_{k}=-0.08^{+0.21+0.54}_{-0.27-0.45}$. The $H(z)$ parametrization has shown incompatibilities between $H(z)$ and SNe Ia data constraints, so these analyses were not combined. The $D_C(z)$ and $q(z)$ parametrizations are compatible with the spatially flat Universe as predicted by many inflation models and data from CMB. This type of analysis is very appealing as it avoids any bias because it does not depend on assumptions about the matter content of the Universe for estimating $Omega_k$.
We study observational constraints on the cosmographic functions up to the fourth derivative of the scale factor with respect to cosmic time, i.e., the so-called snap function, using the non-parametric method of Gaussian Processes. As observational data we use the Hubble parameter data. Also we use mock data sets to estimate the future forecast and study the performance of this type of data to constrain cosmographic functions. The combination between a non-parametric method and the Hubble parameter data is investigated as a strategy to reconstruct cosmographic functions. In addition, our results are quite general because they are not restricted to a specific type of functional dependency of the Hubble parameter. We investigate some advantages of using cosmographic functions instead of cosmographic series, since the former are general definitions free of approximations. In general, our results do not deviate significantly from $Lambda CDM$. We determine a transition redshift $z_{tr}=0.637^{+0.165}_{-0.175}$ and $H_{0}=69.45 pm 4.34$. Also assuming priors for the Hubble constant we obtain $z_{tr}=0.670^{+0.210}_{-0.120}$ with $H_{0}=67.44$ (Planck) and $z_{tr}=0.710^{+0.159}_{-0.111}$ with $H_{0}=74.03$(SH0ES). Our main results are summarized in table 2.
The Universe is mostly composed of large and relatively empty domains known as cosmic voids, whereas its matter content is predominantly distributed along their boundaries. The remaining material inside them, either dark or luminous matter, is attracted to these boundaries and causes voids to expand faster and to grow emptier over time. Using the distribution of galaxies centered on voids identified in the Sloan Digital Sky Survey and adopting minimal assumptions on the statistical motion of these galaxies, we constrain the average matter content $Omega_mathrm{m}=0.281pm0.031$ in the Universe today, as well as the linear growth rate of structure $f/b=0.417pm0.089$ at median redshift $bar{z}=0.57$, where $b$ is the galaxy bias ($68%$ C.L.). These values originate from a percent-level measurement of the anisotropic distortion in the void-galaxy cross-correlation function, $varepsilon = 1.003pm0.012$, and are robust to consistency tests with bootstraps of the data and simulated mock catalogs within an additional systematic uncertainty of half that size. They surpass (and are complementary to) existing constraints by unlocking cosmological information on smaller scales through an accurate model of nonlinear clustering and dynamics in void environments. As such, our analysis furnishes a powerful probe of deviations from Einsteins general relativity in the low-density regime which has largely remained untested so far. We find no evidence for such deviations in the data at hand.
Using a new sub-sample of observed strong gravitational lens systems, for the first time, we present the equation for the angular diameter distance in the $y$-redshift scenario for cosmography and use it to test the cosmographic parameters. In addition, we also use the observational Hubble data from cosmic chronometers and a Joint analysis of both data is performed. Among the most important conclusions are that this new analysis for cosmography using Strong Lensing Systems is equally competitive to constrain the cosmographic parameters as others presented in literature. Additionally, we present the reconstruction of the effective equation of state inferred from our samples, showing that at $z=0$ those reconstructions from Strong Lensing Systems and Joint analysis are in concordance with the standard model of cosmology.
A modification of the action of the general relativity produces a different pattern for the growth of the cosmic structures below a certain length-scale leaving an imprint on the cosmic microwave background (CMB) anisotropies. We re-examine the upper limits on the length-scale parameter B0 of f (R) models using the recent data from the Planck satellite experiment. We also investigate the combined constraints obtained when including the Hubble Space Telescope H0 measurement and the baryon acoustic oscillations measurements from the SDSS, WiggleZ and BOSS surveys.
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