Do $f(R)$ theories matter?

We consider a modified action functional with a nonminimum coupling between the scalar curvature and the matter Lagrangian, and study its consequences on stellar equilibrium. Particular attention is paid to the validity of the Newtonian regime, and on the boundary and exterior matching conditions, as well as on the redefinition of the metric components. Comparison with solar observables is achieved through numerical analysis, and constraints on the nonminimum coupling are discussed.

Figure 1

Profiles for the unperturbed solution ${\theta }_0$ (top) and absolute perturbation $\Delta =\delta {\theta }_0$ (bottom), for $2.8\le n\le 3.2$.

Figure 2

Profile of the relative perturbation $\delta$ for $2.8\le n\le 3.2$.

Figure 3

Fraction of gravitational to total mass as a function of $A_c$, for $2.8\le n\le 3.2$.

Figure 4

Relative deviation of the central temperature $T_c/T_{c0}-1$ as a function of $A_c$, for $2.8\le n\le 3.2$.

Figure 5

Relative deviation of the central temperature $T_c/T_{c0}-1$ as a function of $A_c$ and $n$.

Figure 6

Contour plot for the relative deviation of the central temperature $T_c/T_{c0}-1$ as a function of $A_c$ and $n$, with contour lines of step 0.1%.

Figure 7

Mass profiles, for $n=3$ and $A_c=-1$, 0, and 1.

Figure 8

Profiles of $C_{3,m}$, for $m=-1$, 0, 1, superimposed on the profile of ${\theta }_0$ and ${\theta }_0^{\prime }$, with $n=3$.