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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.
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 ($H(z)$)
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 d
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 attrac
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 additi
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