Global asymptotic dynamics of cosmological Einsteinian cubic gravity

We investigate the cosmological dynamics of an up to cubic curvature correction to general relativity (GR) known as cosmological Einsteinian cubic gravity, whose vacuum spectrum consists of the graviton exclusively. Its cosmology is well posed as an initial value problem. We are able to uncover the global asymptotic structure of the phase space of this theory. It is revealed that an inflationary, matter-dominated big bang is the global past attractor, which means that inflation is the starting point of any physically meaningful cosmic history. Given that higher-order curvature corrections to GR are assumed to influence the cosmological dynamics at early times—the high energy/large curvature limit—late-time inflation is possible only if one considers a nonvanishing cosmological constant term.

Figure 1

Phase portrait (left panel) of the dynamical system in Eq. (13) for radiation, ${\omega }_m=1/3$, and (right panel) of the dynamical system in Eq. (21), where $\mathrm{\Lambda }=0$. The physically meaningful region of the phase space $\mathrm{\Psi }$ [Eqs. (14) and (25)] lies below the boundary $\partial \mathrm{\Psi }$ (black solid curve). The gray region in the drawings does not represent physically meaningful cosmological evolution. The magenta region which is bounded by the curve [(left panel) Eq. (17), (right panel) Eq. (24)] is the subspace where the expansion is decelerated. The critical points of the dynamical systems appear to be enclosed by the small circles. The de Sitter attractor manifold ${\mathcal{M}}_{\mathrm{dS}}$ in Eq. (15), which exists only for the dynamical system in Eq. (13), is represented by the thick dash-dotted curve that coincides with the upper boundary $\partial \mathrm{\Psi }$ in the left panel.

Figure 2

Left panel: types of cosmic evolution. (1) Nonstandard (inflationary) Friedmann radiation-dominated evolution (dashed curve). (2) Nonstandard (inflationary) dust-dominated expansion (solid curve). (3) Standard (decelerated) radiation-dominated expansion (dash-dotted curve). (4) Standard dust-dominated evolution (dotted curve). Right panel: drawing of the Hubble rate $H$ vs the scale factor $a$—according to Eq. (29)—shown for the cases in which the cosmological constant $\mathrm{\Lambda }$ vanishes (solid curves) and when it is a nonvanishing quantity (dash-dotted curves). We consider expanding cosmology only so that in Eq. (29) we take the positive sign. The darker curves are for dust (${\rho }_d\propto a^{-3}$), while the remaining ones are for radiation (${\rho }_r\propto a^{-4}$). It is seen that for vanishing $\mathrm{\Lambda }=0$ the Hubble rate asymptotically vanishes, i.e., the end point of the expansion in this case is the static Universe.