Search for the f(R, T) gravity functional form via gaussian processes
J. A. S. Fortunato, P. H. R. S. Moraes, J. G. de Lima Júnior, E. Brito
Abstract
Abstract The f ( R , T ) gravity models, for which R is the Ricci scalar and T is the trace of the energy–momentum tensor, elevate the degrees of freedom of the renowned f ( R ) theories, by making the Einstein field equations of the theory to also depend on T . 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 T , the formalism can truly surpass some deficiencies of f ( R ) gravity. As the f ( R , T ) function is arbitrary, several parametric models have been proposed ad hoc in the literature and posteriorly confronted with observational data. In the present article, we use gaussian process to construct an $$f(R,T)=R+f(T)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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 $$z=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , we were able to constrain the Hubble constant value to $$H_0=69.97\pm 4.13\ \hbox {km}\ \hbox {s}^{-1} \ \hbox {Mpc}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>69.97</mml:mn> <mml:mo>±</mml:mo> <mml:mn>4.13</mml:mn> <mml:mspace/> <mml:mtext>km</mml:mtext> <mml:mspace/> <mml:msup> <mml:mtext>s</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:msup> <mml:mtext>Mpc</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> with $$5\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>5</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> 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.