Thermal description of braneworld effective theories

Abstract

Low-energy effective theories provide the natural description of four-dimensional physics in higher-dimensional geometries, where the imprint of the bulk appears as parameters of the lower dimensional theory. Motivated by the recent progress in the first-order thermodynamic formulation of modified gravity theories, we investigate the thermodynamics of effective theories in braneworld scenarios and thereby the attractor mechanism towards general relativity in such theories. We consider the two-brane Randall-Sundrum model where the low-energy theory on either brane is of scalar-tensor nature with the extra-dimensional radion playing the role of the scalar. We study the thermodynamic implications of a non-vanishing gravitational contribution to the radion potential, and further explore the dynamics in the presence of a bulk stabilizing field.

Figures (3)

• Figure 1: A schematic representation of the critical curves in three specific theories - electrovacuum Brans-Dicke (blue) [see Ref.faraoni1], TeV brane Brans-Dicke (red) and Planck brane Brans-Dicke (green). For each of the theories, solutions starting above the critical curve deviate forever from GR, those starting below converge to GR. The critical curves cannot be crossed. On left - without a stabilizing field. On right - with a stabilizing field - dynamics about the stabilized radion.
• Figure 2: $(V'-\frac{2V}{\Phi_\pm})$ vs $\Phi_\pm$ on Planck brane (in green) and on TeV brane (in brown) with parameter values $v_h/v_v=1.5$, $\alpha=10$ and $\epsilon = m^2/4k^2 = 0.01$ for a positive mass squared bulk scalar field. Bottom figures zoom in at large $\Phi_\pm$ values.
• Figure 3: $(V'-\frac{2V}{\Phi_\pm})$ vs $\Phi_\pm$ on Planck brane (in green) and on TeV brane (in brown) with parameter values $v_h/v_v=1.5$, $\alpha=10$ and $\epsilon = m^2/4k^2 = -0.01$ for a negative mass squared bulk scalar field. Bottom figures zoom in at large $\Phi_\pm$ values.