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    Search for the f(R,T)f(R,T) gravity functional form via gaussian processes

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    The f(R,T)f(R,T) gravity models, for which RR is the Ricci scalar and TT is the trace of the energy-momentum tensor, elevate the degrees of freedom of the renowned f(R)f(R) theories, by making the Einstein field equations of the theory to also depend on TT. 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 TT, the formalism can truly surpass some deficiencies of f(R)f(R) gravity. As the f(R,T)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)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=0z=0, we were able to constrain the Hubble constant value to H0=69.97±4.13H_0=69.97\pm4.13$\rm \ km \ s^{-1} \ Mpc^{-1}with with 5\%$ 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
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