Cosmic growth history and expansion history

The cosmic expansion history tests the dynamics of the global evolution of the universe and its energy density contents, while the cosmic growth history tests the evolution of the inhomogeneous part of the energy density. Precision comparison of the two histories can distinguish the nature of the physics responsible for the accelerating cosmic expansion: an additional smooth component—dark energy—or a modification of the gravitational field equations. With the aid of a new fitting formula for linear perturbation growth accurate to 0.05%–0.2%, we separate out the growth dependence on the expansion history and introduce a new growth index parameter $\gamma$ that quantifies the gravitational modification.

Figure 1

The growth history is shown for an extra dimensional braneworld model (long dashed, blue curve) and a quintessence model with $w_0=-0.78$, $w_a=0.32$ (short dashed, red), having nearly identical expansion histories. When proper account is taken of the effects of altered gravity on the braneworld growth history (solid, black curve) this allows distinction of these models. The expansion history can in turn rule out a quintessence model degenerate with the solid curve.

Figure 2

Expansion history and growth history constraints on the dark energy equation of state parameters can test the theoretical framework by looking for inconsistent results. The blue cross gives the best fit for the expansion history of a quintessence ($Q$) universe matching the braneworld ($BW$) scenario, but the red star gives the best fit for the growth history to a quintessence model, assuming general relativity. The black ellipse shows the constraints at 68% confidence level from next generation data composed of SNAP supernovae data and Planck CMB last scattering distance measurement.

Figure 3

While Fig. 2 showed that expansion history and growth history constraints on the dark energy equation of state parameters could test the theoretical framework by looking for inconsistent results, here we see quantitative measures of framework breaking by gravitational modification of the growth index $\gamma$. The red star gives the best fit for a quintessence ($Q$) model matching the expansion history of the braneworld ($BW$) scenario, but the blue cross gives the true result for the braneworld growth history. The black ellipse shows the constraints at 68% confidence level from next generation data composed of SNAP supernovae data and Planck CMB last scattering distance measurement, marginalized over the equation of state parameters $w_0$, $w_a$.